Add Student's t-test aggregation support (#54469)

Adds t_test metric aggregation that can perform paired and unpaired two-sample
t-tests. In this PR support for filters in unpaired is still missing. It will
be added in a follow-up PR.

Relates to #53692

docs/build.gradle

@@ -539,6 +539,41 @@ for (int i = 0; i < 100; i++) {
             {"load_time": "$value"}"""
 }
 
+// Used by t_test aggregations
+buildRestTests.setups['node_upgrade'] = '''
+  - do:
+        indices.create:
+          index: node_upgrade
+          body:
+            settings:
+              number_of_shards: 1
+              number_of_replicas: 1
+            mappings:
+              properties:
+                name:
+                  type: keyword
+                startup_time_before:
+                  type: long
+                startup_time_after:
+                  type: long
+  - do:
+        bulk:
+          index: node_upgrade
+          refresh: true
+          body: |
+            {"index":{}}
+            {"name": "A", "startup_time_before": 102, "startup_time_after": 89}
+            {"index":{}}
+            {"name": "B", "startup_time_before": 99, "startup_time_after": 93}
+            {"index":{}}
+            {"name": "C", "startup_time_before": 111, "startup_time_after": 72}
+            {"index":{}}
+            {"name": "D", "startup_time_before": 97, "startup_time_after": 98}
+            {"index":{}}
+            {"name": "E", "startup_time_before": 101, "startup_time_after": 102}
+            {"index":{}}
+            {"name": "F", "startup_time_before": 99, "startup_time_after": 98}'''
+
 // Used by iprange agg
 buildRestTests.setups['iprange'] = '''
   - do:

docs/reference/aggregations/metrics.asciidoc

@@ -49,7 +49,7 @@ include::metrics/median-absolute-deviation-aggregation.asciidoc[]
 
 include::metrics/boxplot-aggregation.asciidoc[]
 
-
+include::metrics/t-test-aggregation.asciidoc[]
 
 
 

docs/reference/aggregations/metrics/t-test-aggregation.asciidoc

@@ -0,0 +1,114 @@
+[role="xpack"]
+[testenv="basic"]
+[[search-aggregations-metrics-ttest-aggregation]]
+=== TTest Aggregation
+
+A `t_test` metrics aggregation that performs a statistical hypothesis test in which the test statistic follows a Student's t-distribution
+under the null hypothesis on numeric values extracted from the aggregated documents or generated by provided scripts. In practice, this
+will tell you if the difference between two population means are statistically significant and did not occur by chance alone.
+
+==== Syntax
+
+A `t_test` aggregation looks like this in isolation:
+
+[source,js]
+--------------------------------------------------
+{
+    "t_test": {
+        "a": "value_before",
+        "b": "value_after",
+        "type": "paired"
+    }
+}
+--------------------------------------------------
+// NOTCONSOLE
+
+Assuming that we have a record of node start up times before and after upgrade, let's look at a t-test to see if upgrade affected
+the node start up time in a meaningful way.
+
+[source,console]
+--------------------------------------------------
+GET node_upgrade/_search
+{
+    "size": 0,
+    "aggs" : {
+        "startup_time_ttest" : {
+            "t_test" : {
+                "a" : {"field": "startup_time_before"}, <1>
+                "b" : {"field": "startup_time_after"}, <2>
+                "type": "paired" <3>
+            }
+        }
+    }
+}
+--------------------------------------------------
+// TEST[setup:node_upgrade]
+<1> The field `startup_time_before` must be a numeric field
+<2> The field `startup_time_after` must be a numeric field
+<3> Since we have data from the same nodes, we are using paired t-test.
+
+The response will return the p-value or probability value for the test. It is the probability of obtaining results at least as extreme as
+the result processed by the aggregation, assuming that the null hypothesis is correct (which means there is no difference between
+population means). Smaller p-value means the null hypothesis is more likely to be incorrect and population means are indeed different.
+
+[source,console-result]
+--------------------------------------------------
+{
+    ...
+
+   "aggregations": {
+      "startup_time_ttest": {
+         "value":  0.1914368843365979 <1>
+      }
+   }
+}
+--------------------------------------------------
+// TESTRESPONSE[s/\.\.\./"took": $body.took,"timed_out": false,"_shards": $body._shards,"hits": $body.hits,/]
+<1> The p-value.
+
+==== T-Test Types
+
+The `t_test` aggregation supports unpaired and paired two-sample t-tests. The type of the test can be specified using the `type` parameter:
+
+`"type": "paired"`:: performs paired t-test
+`"type": "homoscedastic"`:: performs two-sample equal variance test
+`"type": "heteroscedastic"`:: performs two-sample unequal variance test (this is default)
+
+==== Script
+
+The `t_test` metric supports scripting.  For example, if we need to adjust out load times for the before values, we could use
+a script to recalculate them on-the-fly:
+
+[source,console]
+--------------------------------------------------
+GET node_upgrade/_search
+{
+    "size": 0,
+    "aggs" : {
+        "startup_time_ttest" : {
+            "t_test" : {
+                "a": {
+                    "script" : {
+                        "lang": "painless",
+                        "source": "doc['startup_time_before'].value - params.adjustment", <1>
+                        "params" : {
+                            "adjustment" : 10   <2>
+                        }
+                    }
+                },
+                "b": {
+                    "field": "startup_time_after" <3>
+                },
+                "type": "paired"
+            }
+        }
+    }
+}
+--------------------------------------------------
+// TEST[setup:node_upgrade]
+
+<1> The `field` parameter is replaced with a `script` parameter, which uses the
+script to generate values which percentiles are calculated on
+<2> Scripting supports parameterized input just like any other script
+<3> We can mix scripts and fields
+

x-pack/plugin/analytics/build.gradle

@@ -18,6 +18,8 @@ dependencies {
 
   compileOnly project(path: xpackModule('core'), configuration: 'default')
   testCompile project(path: xpackModule('core'), configuration: 'testArtifacts')
+
+  compile 'org.apache.commons:commons-math3:3.2'
 }
 
 integTest.enabled = false

x-pack/plugin/analytics/licenses/commons-math3-3.2.jar.sha1

@@ -0,0 +1 @@
+ec2544ab27e110d2d431bdad7d538ed509b21e62

x-pack/plugin/analytics/licenses/commons-math3-LICENSE.txt

@@ -0,0 +1,475 @@
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+http://www.python.org. Full license is here:
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+  http://www.python.org/download/releases/2.4.2/license/
+
+Some code in core/src/java/org/apache/lucene/util/UnicodeUtil.java was
+derived from Python 3.1.2 sources available at
+http://www.python.org. Full license is here:
+
+  http://www.python.org/download/releases/3.1.2/license/
+
+Some code in core/src/java/org/apache/lucene/util/automaton was
+derived from Brics automaton sources available at
+www.brics.dk/automaton/. Here is the copyright from those sources:
+
+/*
+ * Copyright (c) 2001-2009 Anders Moeller
+ * All rights reserved.
+ * 
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ * 
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+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+ 
+The levenshtein automata tables in core/src/java/org/apache/lucene/util/automaton 
+were automatically generated with the moman/finenight FSA package.
+Here is the copyright for those sources:
+
+# Copyright (c) 2010, Jean-Philippe Barrette-LaPierre, <jpb@rrette.com>
+#
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+# copies of the Software, and to permit persons to whom the
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+# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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+
+Some code in core/src/java/org/apache/lucene/util/UnicodeUtil.java was
+derived from ICU (http://www.icu-project.org)
+The full license is available here: 
+  http://source.icu-project.org/repos/icu/icu/trunk/license.html
+
+/*
+ * Copyright (C) 1999-2010, International Business Machines
+ * Corporation and others.  All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy 
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights 
+ * to use, copy, modify, merge, publish, distribute, and/or sell copies of the 
+ * Software, and to permit persons to whom the Software is furnished to do so, 
+ * provided that the above copyright notice(s) and this permission notice appear 
+ * in all copies of the Software and that both the above copyright notice(s) and
+ * this permission notice appear in supporting documentation.
+ * 
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT OF THIRD PARTY RIGHTS. 
+ * IN NO EVENT SHALL THE COPYRIGHT HOLDER OR HOLDERS INCLUDED IN THIS NOTICE BE 
+ * LIABLE FOR ANY CLAIM, OR ANY SPECIAL INDIRECT OR CONSEQUENTIAL DAMAGES, OR 
+ * ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER 
+ * IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT 
+ * OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ *
+ * Except as contained in this notice, the name of a copyright holder shall not 
+ * be used in advertising or otherwise to promote the sale, use or other 
+ * dealings in this Software without prior written authorization of the 
+ * copyright holder.
+ */
+ 
+The following license applies to the Snowball stemmers:
+
+Copyright (c) 2001, Dr Martin Porter
+Copyright (c) 2002, Richard Boulton
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
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+    * this list of conditions and the following disclaimer.
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+    * documentation and/or other materials provided with the distribution.
+    * Neither the name of the copyright holders nor the names of its contributors
+    * may be used to endorse or promote products derived from this software
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+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
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+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+The following license applies to the KStemmer:
+
+Copyright © 2003,
+Center for Intelligent Information Retrieval,
+University of Massachusetts, Amherst.
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without modification,
+are permitted provided that the following conditions are met:
+
+1. Redistributions of source code must retain the above copyright notice, this
+list of conditions and the following disclaimer.
+
+2. Redistributions in binary form must reproduce the above copyright notice,
+this list of conditions and the following disclaimer in the documentation
+and/or other materials provided with the distribution.
+
+3. The names "Center for Intelligent Information Retrieval" and
+"University of Massachusetts" must not be used to endorse or promote products
+derived from this software without prior written permission. To obtain
+permission, contact info@ciir.cs.umass.edu.
+
+THIS SOFTWARE IS PROVIDED BY UNIVERSITY OF MASSACHUSETTS AND OTHER CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
+THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
+GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGE.
+
+The following license applies to the Morfologik project:
+
+Copyright (c) 2006 Dawid Weiss
+Copyright (c) 2007-2011 Dawid Weiss, Marcin Miłkowski
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without modification, 
+are permitted provided that the following conditions are met:
+
+    * Redistributions of source code must retain the above copyright notice, 
+    this list of conditions and the following disclaimer.
+    
+    * Redistributions in binary form must reproduce the above copyright notice, 
+    this list of conditions and the following disclaimer in the documentation 
+    and/or other materials provided with the distribution.
+    
+    * Neither the name of Morfologik nor the names of its contributors 
+    may be used to endorse or promote products derived from this software 
+    without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND 
+ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED 
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE 
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR 
+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES 
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON 
+ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+---
+
+The dictionary comes from Morfologik project. Morfologik uses data from 
+Polish ispell/myspell dictionary hosted at http://www.sjp.pl/slownik/en/ and 
+is licenced on the terms of (inter alia) LGPL and Creative Commons 
+ShareAlike. The part-of-speech tags were added in Morfologik project and
+are not found in the data from sjp.pl. The tagset is similar to IPI PAN
+tagset.
+
+---
+
+The following license applies to the Morfeusz project,
+used by org.apache.lucene.analysis.morfologik.
+
+BSD-licensed dictionary of Polish (SGJP)
+http://sgjp.pl/morfeusz/
+
+Copyright © 2011 Zygmunt Saloni, Włodzimierz Gruszczyński, 
+             Marcin Woliński, Robert Wołosz
+
+All rights reserved.
+
+Redistribution and  use in  source and binary  forms, with  or without
+modification, are permitted provided that the following conditions are
+met:
+
+1. Redistributions of source code must retain the above copyright
+   notice, this list of conditions and the following disclaimer.
+
+2. Redistributions in binary form must reproduce the above copyright
+   notice, this list of conditions and the following disclaimer in the
+   documentation and/or other materials provided with the
+   distribution.
+
+THIS SOFTWARE IS PROVIDED BY COPYRIGHT HOLDERS “AS IS” AND ANY EXPRESS
+OR  IMPLIED WARRANTIES,  INCLUDING, BUT  NOT LIMITED  TO,  THE IMPLIED
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED.  IN NO EVENT  SHALL COPYRIGHT  HOLDERS OR  CONTRIBUTORS BE
+LIABLE FOR  ANY DIRECT,  INDIRECT, INCIDENTAL, SPECIAL,  EXEMPLARY, OR
+CONSEQUENTIAL DAMAGES  (INCLUDING, BUT NOT LIMITED  TO, PROCUREMENT OF
+SUBSTITUTE  GOODS OR  SERVICES;  LOSS  OF USE,  DATA,  OR PROFITS;  OR
+BUSINESS INTERRUPTION) HOWEVER CAUSED  AND ON ANY THEORY OF LIABILITY,
+WHETHER IN  CONTRACT, STRICT LIABILITY, OR  TORT (INCLUDING NEGLIGENCE
+OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN
+IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

x-pack/plugin/analytics/licenses/commons-math3-NOTICE.txt

@@ -0,0 +1,9 @@
+Apache Commons Math
+Copyright 2001-2020 The Apache Software Foundation
+
+This product includes software developed at
+The Apache Software Foundation (http://www.apache.org/).
+
+This product includes software developed for Orekit by
+CS Systèmes d'Information (http://www.c-s.fr/)
+Copyright 2010-2012 CS Systèmes d'Information

x-pack/plugin/analytics/src/main/java/org/elasticsearch/xpack/analytics/AnalyticsPlugin.java

@@ -41,6 +41,11 @@ import org.elasticsearch.xpack.analytics.stringstats.StringStatsAggregationBuild
 import org.elasticsearch.xpack.analytics.topmetrics.InternalTopMetrics;
 import org.elasticsearch.xpack.analytics.topmetrics.TopMetricsAggregationBuilder;
 import org.elasticsearch.xpack.analytics.topmetrics.TopMetricsAggregatorFactory;
+import org.elasticsearch.xpack.analytics.ttest.InternalTTest;
+import org.elasticsearch.xpack.analytics.ttest.PairedTTestState;
+import org.elasticsearch.xpack.analytics.ttest.TTestAggregationBuilder;
+import org.elasticsearch.xpack.analytics.ttest.TTestState;
+import org.elasticsearch.xpack.analytics.ttest.UnpairedTTestState;
 import org.elasticsearch.xpack.core.XPackField;
 import org.elasticsearch.xpack.core.XPackPlugin;
 import org.elasticsearch.xpack.core.action.XPackInfoFeatureAction;
@@ -94,7 +99,12 @@ public class AnalyticsPlugin extends Plugin implements SearchPlugin, ActionPlugi
                 TopMetricsAggregationBuilder.NAME,
                 TopMetricsAggregationBuilder::new,
                 usage.track(AnalyticsUsage.Item.TOP_METRICS, checkLicense(TopMetricsAggregationBuilder.PARSER)))
-                .addResultReader(InternalTopMetrics::new)
+                .addResultReader(InternalTopMetrics::new),
+            new AggregationSpec(
+                TTestAggregationBuilder.NAME,
+                TTestAggregationBuilder::new,
+                usage.track(AnalyticsUsage.Item.T_TEST, checkLicense(TTestAggregationBuilder.PARSER)))
+                .addResultReader(InternalTTest::new)
         );
     }
 
@@ -130,6 +140,14 @@ public class AnalyticsPlugin extends Plugin implements SearchPlugin, ActionPlugi
         return singletonList(new AnalyticsUsage());
     }
 
+    @Override
+    public List<NamedWriteableRegistry.Entry> getNamedWriteables() {
+        return Arrays.asList(
+            new NamedWriteableRegistry.Entry(TTestState.class, PairedTTestState.NAME, PairedTTestState::new),
+            new NamedWriteableRegistry.Entry(TTestState.class, UnpairedTTestState.NAME, UnpairedTTestState::new)
+        );
+    }
+
     private static <T> ContextParser<String, T> checkLicense(ContextParser<String, T> realParser) {
         return (parser, name) -> {
             if (getLicenseState().isDataScienceAllowed() == false) {

x-pack/plugin/analytics/src/main/java/org/elasticsearch/xpack/analytics/AnalyticsUsage.java

@@ -25,7 +25,8 @@ public class AnalyticsUsage {
         BOXPLOT,
         CUMULATIVE_CARDINALITY,
         STRING_STATS,
-        TOP_METRICS;
+        TOP_METRICS,
+        T_TEST;
     }
 
     private final Map<Item, AtomicLong> trackers = new EnumMap<>(Item.class);
@@ -54,6 +55,7 @@ public class AnalyticsUsage {
                 trackers.get(Item.BOXPLOT).get(),
                 trackers.get(Item.CUMULATIVE_CARDINALITY).get(),
                 trackers.get(Item.STRING_STATS).get(),
-                trackers.get(Item.TOP_METRICS).get());
+                trackers.get(Item.TOP_METRICS).get(),
+                trackers.get(Item.T_TEST).get());
     }
 }

x-pack/plugin/analytics/src/main/java/org/elasticsearch/xpack/analytics/ttest/InternalTTest.java

@@ -0,0 +1,99 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+
+package org.elasticsearch.xpack.analytics.ttest;
+
+import org.elasticsearch.common.io.stream.StreamInput;
+import org.elasticsearch.common.io.stream.StreamOutput;
+import org.elasticsearch.common.xcontent.XContentBuilder;
+import org.elasticsearch.search.DocValueFormat;
+import org.elasticsearch.search.aggregations.InternalAggregation;
+import org.elasticsearch.search.aggregations.metrics.InternalNumericMetricsAggregation;
+
+import java.io.IOException;
+import java.util.List;
+import java.util.Map;
+import java.util.Objects;
+
+public class InternalTTest extends InternalNumericMetricsAggregation.SingleValue implements TTest {
+
+    protected final TTestState state;
+
+    InternalTTest(String name, TTestState state, DocValueFormat formatter, Map<String, Object> metadata) {
+        super(name, metadata);
+        this.state = state;
+        this.format = formatter;
+    }
+
+    /**
+     * Read from a stream.
+     */
+    public InternalTTest(StreamInput in) throws IOException {
+        super(in);
+        format = in.readNamedWriteable(DocValueFormat.class);
+        state = in.readNamedWriteable(TTestState.class);
+    }
+
+    @Override
+    protected void doWriteTo(StreamOutput out) throws IOException {
+        out.writeNamedWriteable(format);
+        out.writeNamedWriteable(state);
+    }
+
+    @Override
+    public String getWriteableName() {
+        return TTestAggregationBuilder.NAME;
+    }
+
+    // for testing only
+    DocValueFormat format() {
+        return format;
+    }
+
+    @Override
+    public InternalTTest reduce(List<InternalAggregation> aggregations, ReduceContext reduceContext) {
+        TTestState reduced = state.reduce(aggregations.stream().map(a -> ((InternalTTest) a).state));
+        return new InternalTTest(name, reduced, format, getMetadata());
+    }
+
+    @Override
+    public XContentBuilder doXContentBody(XContentBuilder builder, Params params) throws IOException {
+        double value = state.getValue();
+        boolean hasValue = Double.isNaN(value) == false;
+        builder.field(CommonFields.VALUE.getPreferredName(), hasValue ? value : null);
+        if (hasValue && format != DocValueFormat.RAW) {
+            builder.field(CommonFields.VALUE_AS_STRING.getPreferredName(), format.format(value).toString());
+        }
+        return builder;
+    }
+
+    @Override
+    public int hashCode() {
+        return Objects.hash(super.hashCode(), state);
+    }
+
+    @Override
+    public boolean equals(Object obj) {
+        if (this == obj) return true;
+        if (obj == null || getClass() != obj.getClass()) return false;
+        if (super.equals(obj) == false) return false;
+
+        InternalTTest that = (InternalTTest) obj;
+        return Objects.equals(state, that.state);
+    }
+
+    @Override
+    public double value() {
+        return state.getValue();
+    }
+
+    @Override
+    public double getValue() {
+        return state.getValue();
+    }
+
+}
+

x-pack/plugin/analytics/src/main/java/org/elasticsearch/xpack/analytics/ttest/PairedTTestAggregator.java

@@ -0,0 +1,91 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+
+package org.elasticsearch.xpack.analytics.ttest;
+
+import org.apache.lucene.index.LeafReaderContext;
+import org.elasticsearch.common.lease.Releasables;
+import org.elasticsearch.common.util.BigArrays;
+import org.elasticsearch.index.fielddata.SortedNumericDoubleValues;
+import org.elasticsearch.search.DocValueFormat;
+import org.elasticsearch.search.aggregations.AggregationExecutionException;
+import org.elasticsearch.search.aggregations.Aggregator;
+import org.elasticsearch.search.aggregations.LeafBucketCollector;
+import org.elasticsearch.search.aggregations.LeafBucketCollectorBase;
+import org.elasticsearch.search.aggregations.metrics.CompensatedSum;
+import org.elasticsearch.search.aggregations.pipeline.PipelineAggregator;
+import org.elasticsearch.search.aggregations.support.MultiValuesSource;
+import org.elasticsearch.search.internal.SearchContext;
+
+import java.io.IOException;
+import java.util.List;
+import java.util.Map;
+
+import static org.elasticsearch.xpack.analytics.ttest.TTestAggregationBuilder.A_FIELD;
+import static org.elasticsearch.xpack.analytics.ttest.TTestAggregationBuilder.B_FIELD;
+
+public class PairedTTestAggregator extends TTestAggregator<PairedTTestState> {
+    private TTestStatsBuilder statsBuilder;
+
+    PairedTTestAggregator(String name, MultiValuesSource.NumericMultiValuesSource valuesSources, int tails, DocValueFormat format,
+                          SearchContext context, Aggregator parent, List<PipelineAggregator> pipelineAggregators,
+                         Map<String, Object> metadata) throws IOException {
+        super(name, valuesSources, tails, format, context, parent, pipelineAggregators, metadata);
+        statsBuilder = new TTestStatsBuilder(context.bigArrays());
+    }
+
+    @Override
+    protected PairedTTestState getState(long bucket) {
+        return new PairedTTestState(statsBuilder.get(bucket), tails);
+    }
+
+    @Override
+    protected PairedTTestState getEmptyState() {
+        return new PairedTTestState(new TTestStats(0, 0, 0), tails);
+    }
+
+    @Override
+    protected long size() {
+        return statsBuilder.getSize();
+    }
+
+    @Override
+    public LeafBucketCollector getLeafCollector(LeafReaderContext ctx,
+                                                final LeafBucketCollector sub) throws IOException {
+        if (valuesSources == null) {
+            return LeafBucketCollector.NO_OP_COLLECTOR;
+        }
+        final BigArrays bigArrays = context.bigArrays();
+        final SortedNumericDoubleValues docAValues = valuesSources.getField(A_FIELD.getPreferredName(), ctx);
+        final SortedNumericDoubleValues docBValues = valuesSources.getField(B_FIELD.getPreferredName(), ctx);
+        final CompensatedSum compDiffSum = new CompensatedSum(0, 0);
+        final CompensatedSum compDiffSumOfSqr = new CompensatedSum(0, 0);
+
+        return new LeafBucketCollectorBase(sub, docAValues) {
+            @Override
+            public void collect(int doc, long bucket) throws IOException {
+                if (docAValues.advanceExact(doc) && docBValues.advanceExact(doc)) {
+                    if (docAValues.docValueCount() > 1 || docBValues.docValueCount() > 1) {
+                        throw new AggregationExecutionException("Encountered more than one value for a " +
+                            "single document. Use a script to combine multiple values per doc into a single value.");
+                    }
+                    statsBuilder.grow(bigArrays, bucket + 1);
+                    // There should always be one value if advanceExact lands us here, either
+                    // a real value or a `missing` value
+                    assert docAValues.docValueCount() == 1;
+                    assert docBValues.docValueCount() == 1;
+                    double diff = docAValues.nextValue() - docBValues.nextValue();
+                    statsBuilder.addValue(compDiffSum, compDiffSumOfSqr, bucket, diff);
+                }
+            }
+        };
+    }
+
+    @Override
+    public void doClose() {
+        Releasables.close(statsBuilder);
+    }
+}

x-pack/plugin/analytics/src/main/java/org/elasticsearch/xpack/analytics/ttest/PairedTTestState.java

@@ -0,0 +1,91 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+
+package org.elasticsearch.xpack.analytics.ttest;
+
+import org.apache.commons.math3.distribution.TDistribution;
+import org.elasticsearch.common.io.stream.StreamInput;
+import org.elasticsearch.common.io.stream.StreamOutput;
+
+import java.io.IOException;
+import java.util.Objects;
+import java.util.stream.Stream;
+
+public class PairedTTestState implements TTestState {
+
+    public static final String NAME = "P";
+
+    private final TTestStats stats;
+
+    private final int tails;
+
+    public PairedTTestState(TTestStats stats, int tails) {
+        this.stats = stats;
+        this.tails = tails;
+    }
+
+    public PairedTTestState(StreamInput in) throws IOException {
+        stats = new TTestStats(in);
+        tails = in.readVInt();
+    }
+
+    @Override
+    public void writeTo(StreamOutput out) throws IOException {
+        stats.writeTo(out);
+        out.writeVInt(tails);
+    }
+
+    @Override
+    public double getValue() {
+        if (stats.count < 2) {
+            return Double.NaN;
+        }
+        long n = stats.count - 1;
+        double meanDiff = stats.sum / stats.count;
+        double variance = (stats.sumOfSqrs - ((stats.sum * stats.sum) / stats.count)) / stats.count;
+        if (variance <= 0.0) {
+            return meanDiff == 0.0 ? Double.NaN : 0.0;
+        }
+        double stdDiv = Math.sqrt(variance);
+        double stdErr = stdDiv / Math.sqrt(n);
+        double t = Math.abs(meanDiff / stdErr);
+        TDistribution dist = new TDistribution(n);
+        return dist.cumulativeProbability(-t) * tails;
+    }
+
+    @Override
+    public TTestState reduce(Stream<TTestState> states) {
+        TTestStats.Reducer reducer = new TTestStats.Reducer();
+        states.forEach(tTestState -> {
+            PairedTTestState state = (PairedTTestState) tTestState;
+            reducer.accept(state.stats);
+            if (state.tails != tails) {
+                throw new IllegalStateException("Incompatible tails value in the reduce. Expected "
+                    + state.tails + " reduced with " + tails);
+            }
+        });
+        return new PairedTTestState(reducer.result(), tails);
+    }
+
+    @Override
+    public String getWriteableName() {
+        return NAME;
+    }
+
+    @Override
+    public boolean equals(Object o) {
+        if (this == o) return true;
+        if (o == null || getClass() != o.getClass()) return false;
+        PairedTTestState that = (PairedTTestState) o;
+        return tails == that.tails &&
+            stats.equals(that.stats);
+    }
+
+    @Override
+    public int hashCode() {
+        return Objects.hash(stats, tails);
+    }
+}

x-pack/plugin/analytics/src/main/java/org/elasticsearch/xpack/analytics/ttest/TTest.java

@@ -0,0 +1,15 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+
+package org.elasticsearch.xpack.analytics.ttest;
+
+import org.elasticsearch.search.aggregations.metrics.NumericMetricsAggregation;
+
+public interface TTest extends NumericMetricsAggregation.SingleValue {
+
+    double getValue();
+
+}

x-pack/plugin/analytics/src/main/java/org/elasticsearch/xpack/analytics/ttest/TTestAggregationBuilder.java

@@ -0,0 +1,140 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+
+package org.elasticsearch.xpack.analytics.ttest;
+
+import org.elasticsearch.common.ParseField;
+import org.elasticsearch.common.io.stream.StreamInput;
+import org.elasticsearch.common.io.stream.StreamOutput;
+import org.elasticsearch.common.xcontent.ObjectParser;
+import org.elasticsearch.common.xcontent.ToXContent;
+import org.elasticsearch.common.xcontent.XContentBuilder;
+import org.elasticsearch.index.query.QueryShardContext;
+import org.elasticsearch.search.DocValueFormat;
+import org.elasticsearch.search.aggregations.AggregationBuilder;
+import org.elasticsearch.search.aggregations.AggregatorFactories;
+import org.elasticsearch.search.aggregations.AggregatorFactory;
+import org.elasticsearch.search.aggregations.support.CoreValuesSourceType;
+import org.elasticsearch.search.aggregations.support.MultiValuesSourceAggregationBuilder;
+import org.elasticsearch.search.aggregations.support.MultiValuesSourceAggregatorFactory;
+import org.elasticsearch.search.aggregations.support.MultiValuesSourceFieldConfig;
+import org.elasticsearch.search.aggregations.support.MultiValuesSourceParseHelper;
+import org.elasticsearch.search.aggregations.support.ValueType;
+import org.elasticsearch.search.aggregations.support.ValuesSourceConfig;
+import org.elasticsearch.search.aggregations.support.ValuesSourceType;
+
+import java.io.IOException;
+import java.util.Map;
+import java.util.Objects;
+
+public class TTestAggregationBuilder extends MultiValuesSourceAggregationBuilder.LeafOnly<TTestAggregationBuilder> {
+    public static final String NAME = "t_test";
+    public static final ParseField A_FIELD = new ParseField("a");
+    public static final ParseField B_FIELD = new ParseField("b");
+    public static final ParseField TYPE_FIELD = new ParseField("type");
+    public static final ParseField TAILS_FIELD = new ParseField("tails");
+
+    public static final ObjectParser<TTestAggregationBuilder, String> PARSER =
+        ObjectParser.fromBuilder(NAME, TTestAggregationBuilder::new);
+
+    static {
+        MultiValuesSourceParseHelper.declareCommon(PARSER, true, ValueType.NUMERIC);
+        MultiValuesSourceParseHelper.declareField(A_FIELD.getPreferredName(), PARSER, true, false);
+        MultiValuesSourceParseHelper.declareField(B_FIELD.getPreferredName(), PARSER, true, false);
+        PARSER.declareString(TTestAggregationBuilder::testType, TYPE_FIELD);
+        PARSER.declareInt(TTestAggregationBuilder::tails, TAILS_FIELD);
+
+    }
+
+    private TTestType testType = TTestType.HETEROSCEDASTIC;
+
+    private int tails = 2;
+
+    public TTestAggregationBuilder(String name) {
+        super(name);
+    }
+
+    public TTestAggregationBuilder(TTestAggregationBuilder clone,
+                                   AggregatorFactories.Builder factoriesBuilder,
+                                   Map<String, Object> metadata) {
+        super(clone, factoriesBuilder, metadata);
+    }
+
+    public TTestAggregationBuilder a(MultiValuesSourceFieldConfig valueConfig) {
+        field(A_FIELD.getPreferredName(), Objects.requireNonNull(valueConfig, "Configuration for field [" + A_FIELD + "] cannot be null"));
+        return this;
+    }
+
+    public TTestAggregationBuilder b(MultiValuesSourceFieldConfig weightConfig) {
+        field(B_FIELD.getPreferredName(), Objects.requireNonNull(weightConfig, "Configuration for field [" + B_FIELD + "] cannot be null"));
+        return this;
+    }
+
+    public TTestAggregationBuilder testType(String testType) {
+        return testType(TTestType.resolve(Objects.requireNonNull(testType, "Test type cannot be null")));
+    }
+
+    public TTestAggregationBuilder testType(TTestType testType) {
+        this.testType = Objects.requireNonNull(testType, "Test type cannot be null");
+        return this;
+    }
+
+    public TTestAggregationBuilder tails(int tails) {
+        if (tails < 1 || tails > 2) {
+            throw new IllegalArgumentException(
+                "[tails] must be 1 or 2. Found [" + tails + "] in [" + name + "]");
+        }
+        this.tails = tails;
+        return this;
+    }
+
+    public TTestAggregationBuilder(StreamInput in) throws IOException {
+        super(in);
+        testType = in.readEnum(TTestType.class);
+        tails = in.readVInt();
+    }
+
+    @Override
+    protected AggregationBuilder shallowCopy(AggregatorFactories.Builder factoriesBuilder, Map<String, Object> metadata) {
+        return new TTestAggregationBuilder(this, factoriesBuilder, metadata);
+    }
+
+    @Override
+    public BucketCardinality bucketCardinality() {
+        return BucketCardinality.NONE;
+    }
+
+    @Override
+    protected void innerWriteTo(StreamOutput out) throws IOException {
+        out.writeEnum(testType);
+        out.writeVInt(tails);
+    }
+
+    @Override
+    protected ValuesSourceType defaultValueSourceType() {
+        return CoreValuesSourceType.NUMERIC;
+    }
+
+    @Override
+    protected MultiValuesSourceAggregatorFactory innerBuild(
+        QueryShardContext queryShardContext,
+        Map<String, ValuesSourceConfig> configs,
+        DocValueFormat format,
+        AggregatorFactory parent,
+        AggregatorFactories.Builder subFactoriesBuilder) throws IOException {
+        return new TTestAggregatorFactory(name, configs, testType, tails, format, queryShardContext, parent, subFactoriesBuilder, metadata);
+    }
+
+    @Override
+    public XContentBuilder doXContentBody(XContentBuilder builder, ToXContent.Params params) throws IOException {
+        return builder;
+    }
+
+    @Override
+    public String getType() {
+        return NAME;
+    }
+}

x-pack/plugin/analytics/src/main/java/org/elasticsearch/xpack/analytics/ttest/TTestAggregator.java

@@ -0,0 +1,67 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+
+package org.elasticsearch.xpack.analytics.ttest;
+
+import org.apache.lucene.search.ScoreMode;
+import org.elasticsearch.search.DocValueFormat;
+import org.elasticsearch.search.aggregations.Aggregator;
+import org.elasticsearch.search.aggregations.InternalAggregation;
+import org.elasticsearch.search.aggregations.metrics.NumericMetricsAggregator;
+import org.elasticsearch.search.aggregations.pipeline.PipelineAggregator;
+import org.elasticsearch.search.aggregations.support.MultiValuesSource;
+import org.elasticsearch.search.internal.SearchContext;
+
+import java.io.IOException;
+import java.util.List;
+import java.util.Map;
+
+
+public abstract class TTestAggregator<T extends TTestState> extends NumericMetricsAggregator.SingleValue {
+
+    protected final MultiValuesSource.NumericMultiValuesSource valuesSources;
+    protected final int tails;
+
+    private DocValueFormat format;
+
+    TTestAggregator(String name, MultiValuesSource.NumericMultiValuesSource valuesSources, int tails, DocValueFormat format,
+                    SearchContext context, Aggregator parent,
+                    List<PipelineAggregator> pipelineAggregators, Map<String, Object> metadata) throws IOException {
+        super(name, context, parent, pipelineAggregators, metadata);
+        this.valuesSources = valuesSources;
+        this.tails = tails;
+        this.format = format;
+    }
+
+    @Override
+    public ScoreMode scoreMode() {
+        return valuesSources != null && valuesSources.needsScores() ? ScoreMode.COMPLETE : ScoreMode.COMPLETE_NO_SCORES;
+    }
+
+    protected abstract T getState(long bucket);
+
+    protected abstract T getEmptyState();
+
+    protected abstract long size();
+
+    @Override
+    public InternalAggregation buildAggregation(long bucket) {
+        if (valuesSources == null || bucket >= size()) {
+            return buildEmptyAggregation();
+        }
+        return new InternalTTest(name, getState(bucket), format, metadata());
+    }
+
+    @Override
+    public InternalAggregation buildEmptyAggregation() {
+        return new InternalTTest(name, getEmptyState(), format, metadata());
+    }
+
+    @Override
+    public double metric(long owningBucketOrd) {
+        return getState(owningBucketOrd).getValue();
+    }
+}

x-pack/plugin/analytics/src/main/java/org/elasticsearch/xpack/analytics/ttest/TTestAggregatorFactory.java

@@ -0,0 +1,81 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+
+package org.elasticsearch.xpack.analytics.ttest;
+
+import org.elasticsearch.index.query.QueryShardContext;
+import org.elasticsearch.search.DocValueFormat;
+import org.elasticsearch.search.aggregations.Aggregator;
+import org.elasticsearch.search.aggregations.AggregatorFactories;
+import org.elasticsearch.search.aggregations.AggregatorFactory;
+import org.elasticsearch.search.aggregations.pipeline.PipelineAggregator;
+import org.elasticsearch.search.aggregations.support.MultiValuesSource;
+import org.elasticsearch.search.aggregations.support.MultiValuesSourceAggregatorFactory;
+import org.elasticsearch.search.aggregations.support.ValuesSourceConfig;
+import org.elasticsearch.search.internal.SearchContext;
+
+import java.io.IOException;
+import java.util.List;
+import java.util.Map;
+
+class TTestAggregatorFactory extends MultiValuesSourceAggregatorFactory {
+
+    private final TTestType testType;
+    private final int tails;
+
+    TTestAggregatorFactory(String name, Map<String, ValuesSourceConfig> configs, TTestType testType, int tails,
+                           DocValueFormat format, QueryShardContext queryShardContext, AggregatorFactory parent,
+                           AggregatorFactories.Builder subFactoriesBuilder,
+                           Map<String, Object> metadata) throws IOException {
+        super(name, configs, format, queryShardContext, parent, subFactoriesBuilder, metadata);
+        this.testType = testType;
+        this.tails = tails;
+    }
+
+    @Override
+    protected Aggregator createUnmapped(SearchContext searchContext,
+                                        Aggregator parent,
+                                        List<PipelineAggregator> pipelineAggregators,
+                                        Map<String, Object> metadata) throws IOException {
+        switch (testType) {
+            case PAIRED:
+                return new PairedTTestAggregator(name, null, tails, format, searchContext, parent, pipelineAggregators, metadata);
+            case HOMOSCEDASTIC:
+                return new UnpairedTTestAggregator(name, null, tails, true, format, searchContext, parent, pipelineAggregators, metadata);
+            case HETEROSCEDASTIC:
+                return new UnpairedTTestAggregator(name, null, tails, false, format, searchContext, parent, pipelineAggregators, metadata);
+            default:
+                throw new IllegalArgumentException("Unsupported t-test type " + testType);
+        }
+    }
+
+    @Override
+    protected Aggregator doCreateInternal(SearchContext searchContext,
+                                          Map<String, ValuesSourceConfig> configs,
+                                          DocValueFormat format,
+                                          Aggregator parent,
+                                          boolean collectsFromSingleBucket,
+                                          List<PipelineAggregator> pipelineAggregators,
+                                          Map<String, Object> metadata) throws IOException {
+        MultiValuesSource.NumericMultiValuesSource numericMultiVS
+            = new MultiValuesSource.NumericMultiValuesSource(configs, queryShardContext);
+        if (numericMultiVS.areValuesSourcesEmpty()) {
+            return createUnmapped(searchContext, parent, pipelineAggregators, metadata);
+        }
+        switch (testType) {
+            case PAIRED:
+                return new PairedTTestAggregator(name, numericMultiVS, tails, format, searchContext, parent, pipelineAggregators, metadata);
+            case HOMOSCEDASTIC:
+                return new UnpairedTTestAggregator(name, numericMultiVS, tails, true, format, searchContext, parent, pipelineAggregators,
+                    metadata);
+            case HETEROSCEDASTIC:
+                return new UnpairedTTestAggregator(name, numericMultiVS, tails, false, format, searchContext, parent, pipelineAggregators,
+                    metadata);
+            default:
+                throw new IllegalArgumentException("Unsupported t-test type " + testType);
+        }
+    }
+}

x-pack/plugin/analytics/src/main/java/org/elasticsearch/xpack/analytics/ttest/TTestState.java

@@ -0,0 +1,20 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+
+package org.elasticsearch.xpack.analytics.ttest;
+
+import org.elasticsearch.common.io.stream.NamedWriteable;
+
+import java.util.stream.Stream;
+
+/**
+ * Base class for t-test aggregation state
+ */
+public interface TTestState extends NamedWriteable {
+    double getValue();
+
+    TTestState reduce(Stream<TTestState> states);
+}

x-pack/plugin/analytics/src/main/java/org/elasticsearch/xpack/analytics/ttest/TTestStats.java

@@ -0,0 +1,85 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+
+package org.elasticsearch.xpack.analytics.ttest;
+
+import org.elasticsearch.common.io.stream.StreamInput;
+import org.elasticsearch.common.io.stream.StreamOutput;
+import org.elasticsearch.common.io.stream.Writeable;
+import org.elasticsearch.search.aggregations.metrics.CompensatedSum;
+
+import java.io.IOException;
+import java.util.Objects;
+import java.util.function.Consumer;
+
+/**
+ * Collects basic stats that are needed to perform t-test
+ */
+public class TTestStats implements Writeable {
+    public final long count;
+    public final double sum;
+    public final double sumOfSqrs;
+
+    public TTestStats(long count, double sum, double sumOfSqrs) {
+        this.count = count;
+        this.sum = sum;
+        this.sumOfSqrs = sumOfSqrs;
+    }
+
+    public TTestStats(StreamInput in) throws IOException {
+        count = in.readVLong();
+        sum = in.readDouble();
+        sumOfSqrs = in.readDouble();
+    }
+
+    @Override
+    public void writeTo(StreamOutput out) throws IOException {
+        out.writeVLong(count);
+        out.writeDouble(sum);
+        out.writeDouble(sumOfSqrs);
+    }
+
+    public double variance() {
+        double v = (sumOfSqrs - ((sum * sum) / count)) / (count - 1);
+        return v < 0 ? 0 : v;
+    }
+
+    public double average() {
+        return sum / count;
+    }
+
+    public static class Reducer implements Consumer<TTestStats> {
+        private long count = 0;
+        CompensatedSum compSum = new CompensatedSum(0, 0);
+        CompensatedSum compSumOfSqrs = new CompensatedSum(0, 0);
+
+        @Override
+        public void accept(TTestStats stat) {
+            count += stat.count;
+            compSum.add(stat.sum);
+            compSumOfSqrs.add(stat.sumOfSqrs);
+        }
+
+        public TTestStats result() {
+            return new TTestStats(count, compSum.value(), compSumOfSqrs.value());
+        }
+    }
+
+    @Override
+    public boolean equals(Object o) {
+        if (this == o) return true;
+        if (o == null || getClass() != o.getClass()) return false;
+        TTestStats that = (TTestStats) o;
+        return count == that.count &&
+            Double.compare(that.sum, sum) == 0 &&
+            Double.compare(that.sumOfSqrs, sumOfSqrs) == 0;
+    }
+
+    @Override
+    public int hashCode() {
+        return Objects.hash(count, sum, sumOfSqrs);
+    }
+}

x-pack/plugin/analytics/src/main/java/org/elasticsearch/xpack/analytics/ttest/TTestStatsBuilder.java

@@ -0,0 +1,78 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+
+package org.elasticsearch.xpack.analytics.ttest;
+
+import org.elasticsearch.common.lease.Releasable;
+import org.elasticsearch.common.lease.Releasables;
+import org.elasticsearch.common.util.BigArrays;
+import org.elasticsearch.common.util.DoubleArray;
+import org.elasticsearch.common.util.LongArray;
+import org.elasticsearch.search.aggregations.metrics.CompensatedSum;
+
+public class TTestStatsBuilder implements Releasable {
+
+    private LongArray counts;
+    private DoubleArray sums;
+    private DoubleArray compensations;
+    private DoubleArray sumOfSqrs;
+    private DoubleArray sumOfSqrCompensations;
+
+    TTestStatsBuilder(BigArrays bigArrays) {
+        counts = bigArrays.newLongArray(1, true);
+        sums = bigArrays.newDoubleArray(1, true);
+        compensations = bigArrays.newDoubleArray(1, true);
+        sumOfSqrs = bigArrays.newDoubleArray(1, true);
+        sumOfSqrCompensations = bigArrays.newDoubleArray(1, true);
+    }
+
+    public TTestStats get(long bucket) {
+        return new TTestStats(counts.get(bucket), sums.get(bucket), sumOfSqrs.get(bucket));
+    }
+
+    public long build(long bucket) {
+        return counts.get(bucket);
+    }
+
+    public long getSize() {
+        return counts.size();
+    }
+
+    public void grow(BigArrays bigArrays, long buckets) {
+        if (buckets >= counts.size()) {
+            long overSize = BigArrays.overSize(buckets);
+            counts = bigArrays.resize(counts, overSize);
+            sums = bigArrays.resize(sums, overSize);
+            compensations = bigArrays.resize(compensations, overSize);
+            sumOfSqrs = bigArrays.resize(sumOfSqrs, overSize);
+            sumOfSqrCompensations = bigArrays.resize(sumOfSqrCompensations, overSize);
+        }
+    }
+
+    public void addValue(CompensatedSum compSum, CompensatedSum compSumOfSqr, long bucket, double val) {
+        counts.increment(bucket, 1);
+        double sum = sums.get(bucket);
+        double compensation = compensations.get(bucket);
+        compSum.reset(sum, compensation);
+
+        double sumOfSqr = sumOfSqrs.get(bucket);
+        double sumOfSqrCompensation = sumOfSqrCompensations.get(bucket);
+        compSumOfSqr.reset(sumOfSqr, sumOfSqrCompensation);
+
+        compSum.add(val);
+        compSumOfSqr.add(val * val);
+
+        sums.set(bucket, compSum.value());
+        compensations.set(bucket, compSum.delta());
+        sumOfSqrs.set(bucket, compSumOfSqr.value());
+        sumOfSqrCompensations.set(bucket, compSumOfSqr.delta());
+    }
+
+    @Override
+    public void close() {
+        Releasables.close(counts, sums, compensations, sumOfSqrs, sumOfSqrCompensations);
+    }
+}

x-pack/plugin/analytics/src/main/java/org/elasticsearch/xpack/analytics/ttest/TTestType.java

@@ -0,0 +1,25 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+
+package org.elasticsearch.xpack.analytics.ttest;
+
+import java.util.Locale;
+
+/**
+ * T-test type, paired, unpaired equal variance, unpaired unequal variance
+ */
+public enum TTestType {
+    PAIRED, HOMOSCEDASTIC, HETEROSCEDASTIC;
+
+    public static TTestType resolve(String name) {
+        return TTestType.valueOf(name.toUpperCase(Locale.ROOT));
+    }
+
+    public String value() {
+        return name().toLowerCase(Locale.ROOT);
+    }
+
+}

x-pack/plugin/analytics/src/main/java/org/elasticsearch/xpack/analytics/ttest/UnpairedTTestAggregator.java

@@ -0,0 +1,99 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+
+package org.elasticsearch.xpack.analytics.ttest;
+
+import org.apache.lucene.index.LeafReaderContext;
+import org.elasticsearch.common.lease.Releasables;
+import org.elasticsearch.common.util.BigArrays;
+import org.elasticsearch.index.fielddata.SortedNumericDoubleValues;
+import org.elasticsearch.search.DocValueFormat;
+import org.elasticsearch.search.aggregations.Aggregator;
+import org.elasticsearch.search.aggregations.LeafBucketCollector;
+import org.elasticsearch.search.aggregations.LeafBucketCollectorBase;
+import org.elasticsearch.search.aggregations.metrics.CompensatedSum;
+import org.elasticsearch.search.aggregations.pipeline.PipelineAggregator;
+import org.elasticsearch.search.aggregations.support.MultiValuesSource;
+import org.elasticsearch.search.internal.SearchContext;
+
+import java.io.IOException;
+import java.util.List;
+import java.util.Map;
+
+import static org.elasticsearch.xpack.analytics.ttest.TTestAggregationBuilder.A_FIELD;
+import static org.elasticsearch.xpack.analytics.ttest.TTestAggregationBuilder.B_FIELD;
+
+public class UnpairedTTestAggregator extends TTestAggregator<UnpairedTTestState> {
+    private final TTestStatsBuilder a;
+    private final TTestStatsBuilder b;
+    private final boolean homoscedastic;
+
+    UnpairedTTestAggregator(String name, MultiValuesSource.NumericMultiValuesSource valuesSources, int tails, boolean homoscedastic,
+                            DocValueFormat format, SearchContext context, Aggregator parent, List<PipelineAggregator> pipelineAggregators,
+                            Map<String, Object> metadata) throws IOException {
+        super(name, valuesSources, tails, format, context, parent, pipelineAggregators, metadata);
+        BigArrays bigArrays = context.bigArrays();
+        a = new TTestStatsBuilder(bigArrays);
+        b = new TTestStatsBuilder(bigArrays);
+        this.homoscedastic = homoscedastic;
+    }
+
+    @Override
+    protected UnpairedTTestState getState(long bucket) {
+        return new UnpairedTTestState(a.get(bucket), b.get(bucket), homoscedastic, tails);
+    }
+
+    @Override
+    protected UnpairedTTestState getEmptyState() {
+        return new UnpairedTTestState(new TTestStats(0, 0, 0), new TTestStats(0, 0, 0), homoscedastic, tails);
+    }
+
+    @Override
+    protected long size() {
+        return a.getSize();
+    }
+
+    @Override
+    public LeafBucketCollector getLeafCollector(LeafReaderContext ctx,
+                                                final LeafBucketCollector sub) throws IOException {
+        if (valuesSources == null) {
+            return LeafBucketCollector.NO_OP_COLLECTOR;
+        }
+        final BigArrays bigArrays = context.bigArrays();
+        final SortedNumericDoubleValues docAValues = valuesSources.getField(A_FIELD.getPreferredName(), ctx);
+        final SortedNumericDoubleValues docBValues = valuesSources.getField(B_FIELD.getPreferredName(), ctx);
+        final CompensatedSum compSumA = new CompensatedSum(0, 0);
+        final CompensatedSum compSumOfSqrA = new CompensatedSum(0, 0);
+        final CompensatedSum compSumB = new CompensatedSum(0, 0);
+        final CompensatedSum compSumOfSqrB = new CompensatedSum(0, 0);
+
+        return new LeafBucketCollectorBase(sub, docAValues) {
+
+            private void processValues(int doc, long bucket, SortedNumericDoubleValues docValues, CompensatedSum compSum,
+                                       CompensatedSum compSumOfSqr, TTestStatsBuilder builder) throws IOException {
+                if (docValues.advanceExact(doc)) {
+                    final int numValues = docValues.docValueCount();
+                    for (int i = 0; i < numValues; i++) {
+                        builder.addValue(compSum, compSumOfSqr, bucket, docValues.nextValue());
+                    }
+                }
+            }
+
+            @Override
+            public void collect(int doc, long bucket) throws IOException {
+                a.grow(bigArrays, bucket + 1);
+                b.grow(bigArrays, bucket + 1);
+                processValues(doc, bucket, docAValues, compSumA, compSumOfSqrA, a);
+                processValues(doc, bucket, docBValues, compSumB, compSumOfSqrB, b);
+            }
+        };
+    }
+
+    @Override
+    public void doClose() {
+        Releasables.close(a, b);
+    }
+}

x-pack/plugin/analytics/src/main/java/org/elasticsearch/xpack/analytics/ttest/UnpairedTTestState.java

@@ -0,0 +1,120 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+
+package org.elasticsearch.xpack.analytics.ttest;
+
+import org.apache.commons.math3.distribution.TDistribution;
+import org.elasticsearch.common.io.stream.StreamInput;
+import org.elasticsearch.common.io.stream.StreamOutput;
+
+import java.io.IOException;
+import java.util.Objects;
+import java.util.stream.Stream;
+
+public class UnpairedTTestState implements TTestState {
+
+    public static final String NAME = "U";
+
+    private final TTestStats a;
+    private final TTestStats b;
+    private boolean homoscedastic;
+    private int tails;
+
+    public UnpairedTTestState(TTestStats a, TTestStats b, boolean homoscedastic, int tails) {
+        this.a = a;
+        this.b = b;
+        this.homoscedastic = homoscedastic;
+        this.tails = tails;
+    }
+
+    public UnpairedTTestState(StreamInput in) throws IOException {
+        a = new TTestStats(in);
+        b = new TTestStats(in);
+        homoscedastic = in.readBoolean();
+        tails = in.readVInt();
+    }
+
+    @Override
+    public double getValue() {
+        if (a.count < 2 || b.count < 2) {
+            return Double.NaN;
+        }
+
+        if (homoscedastic) {
+            long n = a.count + b.count - 2;
+            double variance = ((a.count - 1) * a.variance() + (b.count - 1) * b.variance()) / n;
+            double nn = (1.0 / a.count + 1.0 / b.count);
+            return p(variance * nn, n);
+        } else {
+            double s2an = a.variance() / a.count;
+            double s2bn = b.variance() / b.count;
+            double variance = s2an + s2bn;
+            double degreeOfFreedom = variance * variance / (s2an * s2an / (a.count - 1) + s2bn * s2bn / (b.count - 1));
+            return p(variance, degreeOfFreedom);
+        }
+    }
+
+    private double p(double sd2, double degreesOfFreedom) {
+        if (degreesOfFreedom < 0) {
+            return Double.NaN;
+        }
+        double sd = Math.sqrt(sd2);
+        double meanDiff = a.average() - b.average();
+        double t = Math.abs(meanDiff / sd);
+        TDistribution dist = new TDistribution(degreesOfFreedom);
+        return dist.cumulativeProbability(-t) * tails;
+    }
+
+
+    @Override
+    public TTestState reduce(Stream<TTestState> states) {
+        TTestStats.Reducer reducerA = new TTestStats.Reducer();
+        TTestStats.Reducer reducerB = new TTestStats.Reducer();
+        states.forEach(tTestState -> {
+            UnpairedTTestState state = (UnpairedTTestState) tTestState;
+            if (state.homoscedastic != homoscedastic) {
+                throw new IllegalStateException("Incompatible homoscedastic mode in the reduce. Expected "
+                    + state.homoscedastic + " reduced with " + homoscedastic);
+            }
+            if (state.tails != tails) {
+                throw new IllegalStateException("Incompatible tails value in the reduce. Expected "
+                    + state.tails + " reduced with " + tails);
+            }
+            reducerA.accept(state.a);
+            reducerB.accept(state.b);
+        });
+        return new UnpairedTTestState(reducerA.result(), reducerB.result(), homoscedastic, tails);
+    }
+
+    @Override
+    public void writeTo(StreamOutput out) throws IOException {
+        a.writeTo(out);
+        b.writeTo(out);
+        out.writeBoolean(homoscedastic);
+        out.writeVInt(tails);
+    }
+
+    @Override
+    public String getWriteableName() {
+        return NAME;
+    }
+
+    @Override
+    public boolean equals(Object o) {
+        if (this == o) return true;
+        if (o == null || getClass() != o.getClass()) return false;
+        UnpairedTTestState that = (UnpairedTTestState) o;
+        return homoscedastic == that.homoscedastic &&
+            tails == that.tails &&
+            a.equals(that.a) &&
+            b.equals(that.b);
+    }
+
+    @Override
+    public int hashCode() {
+        return Objects.hash(a, b, homoscedastic, tails);
+    }
+}

x-pack/plugin/analytics/src/test/java/org/elasticsearch/xpack/analytics/ttest/InternalTTestTests.java

@@ -0,0 +1,131 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+
+package org.elasticsearch.xpack.analytics.ttest;
+
+import org.elasticsearch.common.ParseField;
+import org.elasticsearch.common.io.stream.BytesStreamOutput;
+import org.elasticsearch.common.io.stream.NamedWriteableAwareStreamInput;
+import org.elasticsearch.common.io.stream.NamedWriteableRegistry;
+import org.elasticsearch.common.io.stream.StreamInput;
+import org.elasticsearch.common.io.stream.Writeable;
+import org.elasticsearch.common.settings.Settings;
+import org.elasticsearch.common.xcontent.NamedXContentRegistry;
+import org.elasticsearch.search.DocValueFormat;
+import org.elasticsearch.search.SearchModule;
+import org.elasticsearch.search.aggregations.Aggregation;
+import org.elasticsearch.search.aggregations.ParsedAggregation;
+import org.elasticsearch.search.aggregations.pipeline.PipelineAggregator;
+import org.elasticsearch.test.InternalAggregationTestCase;
+import org.elasticsearch.xpack.analytics.AnalyticsPlugin;
+
+import java.io.IOException;
+import java.util.ArrayList;
+import java.util.HashMap;
+import java.util.List;
+import java.util.Map;
+
+import static java.util.Collections.emptyList;
+
+public class InternalTTestTests extends InternalAggregationTestCase<InternalTTest> {
+
+    private TTestType type = randomFrom(TTestType.values());
+    private int tails = randomIntBetween(1, 2);
+
+    @Override
+    protected InternalTTest createTestInstance(String name, Map<String, Object> metadata) {
+        TTestState state = randomState();
+        DocValueFormat formatter = randomNumericDocValueFormat();
+        return new InternalTTest(name, state, formatter, metadata);
+    }
+
+    private TTestState randomState() {
+        if (type == TTestType.PAIRED) {
+            return new PairedTTestState(randomStats(), tails);
+        } else {
+            return new UnpairedTTestState(randomStats(), randomStats(), type == TTestType.HOMOSCEDASTIC, tails);
+        }
+    }
+
+    private TTestStats randomStats() {
+        return new TTestStats(randomNonNegativeLong(), randomDouble(), randomDouble());
+    }
+
+    @Override
+    protected Writeable.Reader<InternalTTest> instanceReader() {
+        return InternalTTest::new;
+    }
+
+    @Override
+    protected void assertReduced(InternalTTest reduced, List<InternalTTest> inputs) {
+        TTestState expected = reduced.state.reduce(inputs.stream().map(a -> a.state));
+        assertNotNull(expected);
+        assertEquals(expected.getValue(), reduced.getValue(), 0.00001);
+    }
+
+    @Override
+    protected void assertFromXContent(InternalTTest min, ParsedAggregation parsedAggregation) {
+        // There is no ParsedTTest yet so we cannot test it here
+    }
+
+    @Override
+    protected InternalTTest mutateInstance(InternalTTest instance) {
+        String name = instance.getName();
+        TTestState state;
+        try (BytesStreamOutput output = new BytesStreamOutput()) {
+            output.writeNamedWriteable(instance.state);
+            try (StreamInput in = new NamedWriteableAwareStreamInput(output.bytes().streamInput(), getNamedWriteableRegistry())) {
+                state = in.readNamedWriteable(TTestState.class);
+            }
+        } catch (IOException ex) {
+            throw new IllegalStateException(ex);
+        }
+        DocValueFormat formatter = instance.format();
+        List<PipelineAggregator> pipelineAggregators = instance.pipelineAggregators();
+        Map<String, Object> metadata = instance.getMetadata();
+        switch (between(0, 2)) {
+            case 0:
+                name += randomAlphaOfLength(5);
+                break;
+            case 1:
+                state = randomState();
+                break;
+            case 2:
+                if (metadata == null) {
+                    metadata = new HashMap<>(1);
+                } else {
+                    metadata = new HashMap<>(instance.getMetadata());
+                }
+                metadata.put(randomAlphaOfLength(15), randomInt());
+                break;
+            default:
+                throw new AssertionError("Illegal randomisation branch");
+        }
+        return new InternalTTest(name, state, formatter, metadata);
+    }
+
+    @Override
+    protected List<NamedXContentRegistry.Entry> getNamedXContents() {
+        List<NamedXContentRegistry.Entry> extendedNamedXContents = new ArrayList<>(super.getNamedXContents());
+        extendedNamedXContents.add(new NamedXContentRegistry.Entry(Aggregation.class,
+            new ParseField(TTestAggregationBuilder.NAME),
+            (p, c) -> {
+                assumeTrue("There is no ParsedTTest yet", false);
+                return null;
+            }
+        ));
+        return extendedNamedXContents;
+    }
+
+    @Override
+    protected NamedWriteableRegistry getNamedWriteableRegistry() {
+        List<NamedWriteableRegistry.Entry> entries = new ArrayList<>();
+        entries.addAll(new SearchModule(Settings.EMPTY, emptyList()).getNamedWriteables());
+        entries.addAll(new AnalyticsPlugin().getNamedWriteables());
+        return new NamedWriteableRegistry(entries);
+    }
+
+}

x-pack/plugin/analytics/src/test/java/org/elasticsearch/xpack/analytics/ttest/TTestAggregationBuilderTests.java

@@ -0,0 +1,84 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+
+package org.elasticsearch.xpack.analytics.ttest;
+
+import org.elasticsearch.common.ParseField;
+import org.elasticsearch.common.io.stream.Writeable;
+import org.elasticsearch.common.xcontent.NamedXContentRegistry;
+import org.elasticsearch.common.xcontent.XContentParser;
+import org.elasticsearch.script.Script;
+import org.elasticsearch.search.aggregations.AggregatorFactories;
+import org.elasticsearch.search.aggregations.BaseAggregationBuilder;
+import org.elasticsearch.search.aggregations.support.MultiValuesSourceFieldConfig;
+import org.elasticsearch.test.AbstractSerializingTestCase;
+import org.junit.Before;
+
+import java.io.IOException;
+
+import static java.util.Collections.singletonList;
+import static org.hamcrest.Matchers.hasSize;
+
+public class TTestAggregationBuilderTests extends AbstractSerializingTestCase<TTestAggregationBuilder> {
+    String aggregationName;
+
+    @Before
+    public void setupName() {
+        aggregationName = randomAlphaOfLength(10);
+    }
+
+    @Override
+    protected NamedXContentRegistry xContentRegistry() {
+        return new NamedXContentRegistry(singletonList(new NamedXContentRegistry.Entry(
+            BaseAggregationBuilder.class,
+            new ParseField(TTestAggregationBuilder.NAME),
+            (p, n) -> TTestAggregationBuilder.PARSER.apply(p, (String) n))));
+    }
+
+    @Override
+    protected TTestAggregationBuilder doParseInstance(XContentParser parser) throws IOException {
+        assertSame(XContentParser.Token.START_OBJECT, parser.nextToken());
+        AggregatorFactories.Builder parsed = AggregatorFactories.parseAggregators(parser);
+        assertThat(parsed.getAggregatorFactories(), hasSize(1));
+        assertThat(parsed.getPipelineAggregatorFactories(), hasSize(0));
+        TTestAggregationBuilder agg = (TTestAggregationBuilder) parsed.getAggregatorFactories().iterator().next();
+        assertNull(parser.nextToken());
+        assertNotNull(agg);
+        return agg;
+    }
+
+    @Override
+    protected TTestAggregationBuilder createTestInstance() {
+        MultiValuesSourceFieldConfig aConfig;
+        if (randomBoolean()) {
+            aConfig = new MultiValuesSourceFieldConfig.Builder().setFieldName("a_field").build();
+        } else {
+            aConfig = new MultiValuesSourceFieldConfig.Builder().setScript(new Script(randomAlphaOfLength(10))).build();
+        }
+        MultiValuesSourceFieldConfig bConfig;
+        if (randomBoolean()) {
+            bConfig = new MultiValuesSourceFieldConfig.Builder().setFieldName("b_field").build();
+        } else {
+            bConfig = new MultiValuesSourceFieldConfig.Builder().setScript(new Script(randomAlphaOfLength(10))).build();
+        }
+        TTestAggregationBuilder aggregationBuilder = new TTestAggregationBuilder(aggregationName)
+            .a(aConfig)
+            .b(bConfig);
+        if (randomBoolean()) {
+            aggregationBuilder.tails(randomIntBetween(1, 2));
+        }
+        if (randomBoolean()) {
+            aggregationBuilder.testType(randomFrom(TTestType.values()));
+        }
+        return aggregationBuilder;
+    }
+
+    @Override
+    protected Writeable.Reader<TTestAggregationBuilder> instanceReader() {
+        return TTestAggregationBuilder::new;
+    }
+}
+

x-pack/plugin/analytics/src/test/java/org/elasticsearch/xpack/analytics/ttest/TTestAggregatorTests.java

@@ -0,0 +1,558 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the Elastic License;
+ * you may not use this file except in compliance with the Elastic License.
+ */
+
+package org.elasticsearch.xpack.analytics.ttest;
+
+import org.apache.lucene.document.NumericDocValuesField;
+import org.apache.lucene.document.SortedNumericDocValuesField;
+import org.apache.lucene.index.DirectoryReader;
+import org.apache.lucene.index.IndexReader;
+import org.apache.lucene.index.RandomIndexWriter;
+import org.apache.lucene.search.IndexSearcher;
+import org.apache.lucene.search.MatchAllDocsQuery;
+import org.apache.lucene.search.Query;
+import org.apache.lucene.store.Directory;
+import org.elasticsearch.common.CheckedConsumer;
+import org.elasticsearch.common.settings.Settings;
+import org.elasticsearch.index.fielddata.ScriptDocValues;
+import org.elasticsearch.index.mapper.KeywordFieldMapper;
+import org.elasticsearch.index.mapper.MappedFieldType;
+import org.elasticsearch.index.mapper.NumberFieldMapper;
+import org.elasticsearch.script.MockScriptEngine;
+import org.elasticsearch.script.Script;
+import org.elasticsearch.script.ScriptEngine;
+import org.elasticsearch.script.ScriptModule;
+import org.elasticsearch.script.ScriptService;
+import org.elasticsearch.script.ScriptType;
+import org.elasticsearch.search.aggregations.AggregationBuilder;
+import org.elasticsearch.search.aggregations.AggregationExecutionException;
+import org.elasticsearch.search.aggregations.AggregatorTestCase;
+import org.elasticsearch.search.aggregations.InternalAggregation;
+import org.elasticsearch.search.aggregations.bucket.global.GlobalAggregationBuilder;
+import org.elasticsearch.search.aggregations.bucket.global.InternalGlobal;
+import org.elasticsearch.search.aggregations.bucket.histogram.HistogramAggregationBuilder;
+import org.elasticsearch.search.aggregations.bucket.histogram.InternalHistogram;
+import org.elasticsearch.search.aggregations.support.AggregationInspectionHelper;
+import org.elasticsearch.search.aggregations.support.CoreValuesSourceType;
+import org.elasticsearch.search.aggregations.support.MultiValuesSourceFieldConfig;
+import org.elasticsearch.search.aggregations.support.ValuesSourceType;
+import org.elasticsearch.search.lookup.LeafDocLookup;
+
+import java.io.IOException;
+import java.util.Collections;
+import java.util.HashMap;
+import java.util.List;
+import java.util.Map;
+import java.util.function.Consumer;
+import java.util.function.Function;
+
+import static java.util.Arrays.asList;
+import static java.util.Collections.singleton;
+
+public class TTestAggregatorTests extends AggregatorTestCase {
+
+    /**
+     * Script to return the {@code _value} provided by aggs framework.
+     */
+    public static final String ADD_HALF_SCRIPT = "add_one";
+
+    @Override
+    protected AggregationBuilder createAggBuilderForTypeTest(MappedFieldType fieldType, String fieldName) {
+        return new TTestAggregationBuilder("foo")
+            .a(new MultiValuesSourceFieldConfig.Builder().setFieldName(fieldName).build())
+            .b(new MultiValuesSourceFieldConfig.Builder().setFieldName(fieldName).build());
+    }
+
+    @Override
+    protected List<ValuesSourceType> getSupportedValuesSourceTypes() {
+        return List.of(CoreValuesSourceType.NUMERIC);
+    }
+
+    @Override
+    protected ScriptService getMockScriptService() {
+        Map<String, Function<Map<String, Object>, Object>> scripts = new HashMap<>();
+
+        scripts.put(ADD_HALF_SCRIPT, vars -> {
+            LeafDocLookup leafDocLookup = (LeafDocLookup) vars.get("doc");
+            String fieldname = (String) vars.get("fieldname");
+            ScriptDocValues<?> scriptDocValues = leafDocLookup.get(fieldname);
+            double val = ((Number) scriptDocValues.get(0)).doubleValue();
+            if (val == 1) {
+                val += 0.0000001;
+            }
+            return val + 0.5;
+        });
+
+        MockScriptEngine scriptEngine = new MockScriptEngine(MockScriptEngine.NAME,
+            scripts,
+            Collections.emptyMap());
+        Map<String, ScriptEngine> engines = Collections.singletonMap(scriptEngine.getType(), scriptEngine);
+
+        return new ScriptService(Settings.EMPTY, engines, ScriptModule.CORE_CONTEXTS);
+    }
+
+    public void testNoMatchingField() throws IOException {
+        testCase(new MatchAllDocsQuery(), randomFrom(TTestType.values()), iw -> {
+            iw.addDocument(asList(new NumericDocValuesField("wrong_a", 102), new NumericDocValuesField("wrong_b", 89)));
+            iw.addDocument(asList(new NumericDocValuesField("wrong_a", 99), new NumericDocValuesField("wrong_b", 93)));
+        }, tTest -> assertEquals(Double.NaN, tTest.getValue(), 0));
+    }
+
+    public void testNotEnoughRecords() throws IOException {
+        testCase(new MatchAllDocsQuery(), randomFrom(TTestType.values()), iw -> {
+            iw.addDocument(asList(new NumericDocValuesField("a", 102), new NumericDocValuesField("b", 89)));
+        }, tTest -> assertEquals(Double.NaN, tTest.getValue(), 0));
+    }
+
+    public void testSameValues() throws IOException {
+        TTestType tTestType = randomFrom(TTestType.values());
+        testCase(new MatchAllDocsQuery(), tTestType, iw -> {
+            iw.addDocument(asList(new NumericDocValuesField("a", 102), new NumericDocValuesField("b", 102)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 99), new NumericDocValuesField("b", 99)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 111), new NumericDocValuesField("b", 111)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 97), new NumericDocValuesField("b", 97)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 101), new NumericDocValuesField("b", 101)));
+        }, tTest -> assertEquals(tTestType == TTestType.PAIRED ? Double.NaN : 1, tTest.getValue(), 0));
+    }
+
+    public void testMatchesSortedNumericDocValues() throws IOException {
+        testCase(new MatchAllDocsQuery(), TTestType.PAIRED, iw -> {
+            iw.addDocument(asList(new SortedNumericDocValuesField("a", 102), new SortedNumericDocValuesField("b", 89)));
+            iw.addDocument(asList(new SortedNumericDocValuesField("a", 99), new SortedNumericDocValuesField("b", 93)));
+            iw.addDocument(asList(new SortedNumericDocValuesField("a", 111), new SortedNumericDocValuesField("b", 72)));
+            iw.addDocument(asList(new SortedNumericDocValuesField("a", 97), new SortedNumericDocValuesField("b", 98)));
+            iw.addDocument(asList(new SortedNumericDocValuesField("a", 101), new SortedNumericDocValuesField("b", 102)));
+            iw.addDocument(asList(new SortedNumericDocValuesField("a", 99), new SortedNumericDocValuesField("b", 98)));
+        }, tTest -> assertEquals(0.09571844217 * 2, tTest.getValue(), 0.000001));
+    }
+
+    public void testMultiplePairedValues() {
+        AggregationExecutionException ex = expectThrows(AggregationExecutionException.class, () ->
+            testCase(new MatchAllDocsQuery(), TTestType.PAIRED, iw -> {
+                iw.addDocument(asList(new SortedNumericDocValuesField("a", 102), new SortedNumericDocValuesField("a", 103),
+                    new SortedNumericDocValuesField("b", 89)));
+                iw.addDocument(asList(new SortedNumericDocValuesField("a", 99), new SortedNumericDocValuesField("b", 93)));
+            }, tTest -> fail("Should have thrown exception"))
+        );
+        assertEquals(
+            "Encountered more than one value for a single document. Use a script to combine multiple values per doc into a single value.",
+            ex.getMessage());
+    }
+
+    public void testMultipleUnpairedValues() throws IOException {
+        TTestType tTestType = randomFrom(TTestType.HETEROSCEDASTIC, TTestType.HOMOSCEDASTIC);
+        testCase(new MatchAllDocsQuery(), tTestType, iw -> {
+            iw.addDocument(asList(new SortedNumericDocValuesField("a", 102), new SortedNumericDocValuesField("a", 103),
+                new SortedNumericDocValuesField("b", 89)));
+            iw.addDocument(asList(new SortedNumericDocValuesField("a", 99), new SortedNumericDocValuesField("b", 93)));
+        }, tTest -> assertEquals(tTestType == TTestType.HETEROSCEDASTIC ? 0.0607303911 : 0.01718374671, tTest.getValue(), 0.000001));
+    }
+
+    public void testMissingValues() throws IOException {
+        TTestType tTestType = randomFrom(TTestType.values());
+        testCase(new MatchAllDocsQuery(), tTestType, iw -> {
+            iw.addDocument(asList(new SortedNumericDocValuesField("a", 102), new SortedNumericDocValuesField("b", 89)));
+            iw.addDocument(asList(new SortedNumericDocValuesField("a1", 99), new SortedNumericDocValuesField("b", 93)));
+            iw.addDocument(asList(new SortedNumericDocValuesField("a", 111), new SortedNumericDocValuesField("b1", 72)));
+            iw.addDocument(asList(new SortedNumericDocValuesField("a", 97), new SortedNumericDocValuesField("b", 98)));
+            iw.addDocument(asList(new SortedNumericDocValuesField("a", 101), new SortedNumericDocValuesField("b", 102)));
+            iw.addDocument(asList(new SortedNumericDocValuesField("a", 99), new SortedNumericDocValuesField("b", 98)));
+        }, tTest -> {
+            switch (tTestType) {
+                case PAIRED:
+                    assertEquals(0.4385093524, tTest.getValue(), 0.000001);
+                    break;
+                case HOMOSCEDASTIC:
+                    assertEquals(0.1066843841, tTest.getValue(), 0.000001);
+                    break;
+                case HETEROSCEDASTIC:
+                    assertEquals(0.1068382282, tTest.getValue(), 0.000001);
+                    break;
+                default:
+                    fail("unknown t-test type " + tTestType);
+            }
+        });
+    }
+
+    public void testUnmappedWithMissingField() throws IOException {
+        TTestType tTestType = randomFrom(TTestType.values());
+        boolean missA = randomBoolean();
+        boolean missB = missA == false || randomBoolean(); // at least one of the fields should be missing
+        MappedFieldType fieldType1 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType1.setName(missA ? "not_a" : "a");
+        MappedFieldType fieldType2 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType2.setName(missB ? "not_b" : "b");
+        TTestAggregationBuilder aggregationBuilder = new TTestAggregationBuilder("t_test")
+            .a(new MultiValuesSourceFieldConfig.Builder().setFieldName("a").setMissing(100).build())
+            .b(new MultiValuesSourceFieldConfig.Builder().setFieldName("b").setMissing(100).build())
+            .testType(tTestType);
+        testCase(aggregationBuilder, new MatchAllDocsQuery(), iw -> {
+            iw.addDocument(asList(new NumericDocValuesField("a", 102), new NumericDocValuesField("b", 89)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 99), new NumericDocValuesField("b", 93)));
+        }, (Consumer<InternalTTest>) tTest -> {
+            if (missA && missB) {
+                assertEquals(Double.NaN, tTest.getValue(), 0);
+            } else {
+                if (missA) {
+                    switch (tTestType) {
+                        case PAIRED:
+                            assertEquals(0.1392089745, tTest.getValue(), 0.000001);
+                            break;
+                        case HOMOSCEDASTIC:
+                            assertEquals(0.04600190799, tTest.getValue(), 0.000001);
+                            break;
+                        case HETEROSCEDASTIC:
+                            assertEquals(0.1392089745, tTest.getValue(), 0.000001);
+                            break;
+                        default:
+                            fail("unknown t-test type " + tTestType);
+                    }
+                } else {
+                    switch (tTestType) {
+                        case PAIRED:
+                            assertEquals(0.7951672353, tTest.getValue(), 0.000001);
+                            break;
+                        case HOMOSCEDASTIC:
+                            assertEquals(0.7705842661, tTest.getValue(), 0.000001);
+                            break;
+                        case HETEROSCEDASTIC:
+                            assertEquals(0.7951672353, tTest.getValue(), 0.000001);
+                            break;
+                        default:
+                            fail("unknown t-test type " + tTestType);
+                    }
+                }
+            }
+        }, fieldType1, fieldType2);
+    }
+
+    public void testUnsupportedType() {
+        TTestType tTestType = randomFrom(TTestType.values());
+        boolean wrongA = randomBoolean();
+        boolean wrongB = wrongA == false || randomBoolean(); // at least one of the fields should have unsupported type
+        MappedFieldType fieldType1;
+        if (wrongA) {
+            fieldType1 = new KeywordFieldMapper.KeywordFieldType();
+            fieldType1.setHasDocValues(true);
+        } else {
+            fieldType1 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        }
+        fieldType1.setName("a");
+        MappedFieldType fieldType2;
+        if (wrongB) {
+            fieldType2 = new KeywordFieldMapper.KeywordFieldType();
+            fieldType2.setHasDocValues(true);
+        } else {
+            fieldType2 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        }
+        fieldType2.setName("b");
+        TTestAggregationBuilder aggregationBuilder = new TTestAggregationBuilder("t_test")
+            .a(new MultiValuesSourceFieldConfig.Builder().setFieldName("a").build())
+            .b(new MultiValuesSourceFieldConfig.Builder().setFieldName("b").build())
+            .testType(tTestType);
+
+        IllegalArgumentException ex = expectThrows(IllegalArgumentException.class, () ->
+            testCase(aggregationBuilder, new MatchAllDocsQuery(), iw -> {
+                iw.addDocument(asList(new SortedNumericDocValuesField("a", 102), new SortedNumericDocValuesField("a", 103),
+                    new SortedNumericDocValuesField("b", 89)));
+                iw.addDocument(asList(new SortedNumericDocValuesField("a", 99), new SortedNumericDocValuesField("b", 93)));
+            }, tTest -> fail("Should have thrown exception"), fieldType1, fieldType2)
+        );
+        assertEquals(
+            "Expected numeric type on field [" + (wrongA ? "a" : "b") + "], but got [keyword]",
+            ex.getMessage());
+    }
+
+    public void testBadMissingField() {
+        TTestType tTestType = randomFrom(TTestType.values());
+        boolean missA = randomBoolean();
+        boolean missB = missA == false || randomBoolean(); // at least one of the fields should be have bad missing
+        MappedFieldType fieldType1 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType1.setName("a");
+        MultiValuesSourceFieldConfig.Builder a = new MultiValuesSourceFieldConfig.Builder().setFieldName("a");
+        if (missA) {
+            a.setMissing("bad_number");
+        }
+        MappedFieldType fieldType2 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType2.setName("b");
+        MultiValuesSourceFieldConfig.Builder b = new MultiValuesSourceFieldConfig.Builder().setFieldName("b");
+        if (missB) {
+            b.setMissing("bad_number");
+        }
+        TTestAggregationBuilder aggregationBuilder = new TTestAggregationBuilder("t_test").a(a.build()).b(b.build()).testType(tTestType);
+
+        NumberFormatException ex = expectThrows(NumberFormatException.class, () ->
+            testCase(aggregationBuilder, new MatchAllDocsQuery(), iw -> {
+                iw.addDocument(asList(new SortedNumericDocValuesField("a", 102), new SortedNumericDocValuesField("b", 89)));
+                iw.addDocument(asList(new SortedNumericDocValuesField("a", 99), new SortedNumericDocValuesField("b", 93)));
+            }, tTest -> fail("Should have thrown exception"), fieldType1, fieldType2)
+        );
+        assertEquals("For input string: \"bad_number\"", ex.getMessage());
+    }
+
+
+    public void testUnmappedWithBadMissingField() {
+        TTestType tTestType = randomFrom(TTestType.values());
+        boolean missA = randomBoolean();
+        boolean missB = missA == false || randomBoolean(); // at least one of the fields should be have bad missing
+        MappedFieldType fieldType1 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType1.setName("a");
+        MultiValuesSourceFieldConfig.Builder a = new MultiValuesSourceFieldConfig.Builder();
+        if (missA) {
+            a.setFieldName("not_a").setMissing("bad_number");
+        } else {
+            a.setFieldName("a");
+        }
+        MappedFieldType fieldType2 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+
+        MultiValuesSourceFieldConfig.Builder b = new MultiValuesSourceFieldConfig.Builder();
+        if (missB) {
+            b.setFieldName("not_b").setMissing("bad_number");
+        } else {
+            b.setFieldName("b");
+        }
+        TTestAggregationBuilder aggregationBuilder = new TTestAggregationBuilder("t_test").a(a.build()).b(b.build()).testType(tTestType);
+
+        NumberFormatException ex = expectThrows(NumberFormatException.class, () ->
+            testCase(aggregationBuilder, new MatchAllDocsQuery(), iw -> {
+                iw.addDocument(asList(new SortedNumericDocValuesField("a", 102), new SortedNumericDocValuesField("b", 89)));
+                iw.addDocument(asList(new SortedNumericDocValuesField("a", 99), new SortedNumericDocValuesField("b", 93)));
+            }, tTest -> fail("Should have thrown exception"), fieldType1, fieldType2)
+        );
+        assertEquals("For input string: \"bad_number\"", ex.getMessage());
+    }
+
+    public void testEmptyBucket() throws IOException {
+        TTestType tTestType = randomFrom(TTestType.values());
+        MappedFieldType fieldType1 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType1.setName("a");
+        MappedFieldType fieldType2 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType2.setName("b");
+        MappedFieldType fieldTypePart = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldTypePart.setName("part");
+        HistogramAggregationBuilder histogram = new HistogramAggregationBuilder("histo").field("part").interval(10).minDocCount(0)
+            .subAggregation(new TTestAggregationBuilder("t_test")
+                .a(new MultiValuesSourceFieldConfig.Builder().setFieldName("a").build())
+                .b(new MultiValuesSourceFieldConfig.Builder().setFieldName("b").build())
+                .testType(tTestType));
+
+        testCase(histogram, new MatchAllDocsQuery(), iw -> {
+            iw.addDocument(asList(new NumericDocValuesField("a", 102), new NumericDocValuesField("b", 89),
+                new NumericDocValuesField("part", 1)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 99), new NumericDocValuesField("b", 93),
+                new NumericDocValuesField("part", 1)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 111), new NumericDocValuesField("b", 72),
+                new NumericDocValuesField("part", 1)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 97), new NumericDocValuesField("b", 98),
+                new NumericDocValuesField("part", 21)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 101), new NumericDocValuesField("b", 102),
+                new NumericDocValuesField("part", 21)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 99), new NumericDocValuesField("b", 98),
+                new NumericDocValuesField("part", 21)));
+        }, (Consumer<InternalHistogram>) histo -> {
+            assertEquals(3, histo.getBuckets().size());
+            assertNotNull(histo.getBuckets().get(0).getAggregations().asMap().get("t_test"));
+            InternalTTest tTest = (InternalTTest) histo.getBuckets().get(0).getAggregations().asMap().get("t_test");
+            assertEquals(tTestType == TTestType.PAIRED ? 0.1939778614 :
+                tTestType == TTestType.HOMOSCEDASTIC ? 0.05878871029 : 0.07529006595, tTest.getValue(), 0.000001);
+
+            assertNotNull(histo.getBuckets().get(1).getAggregations().asMap().get("t_test"));
+            tTest = (InternalTTest) histo.getBuckets().get(1).getAggregations().asMap().get("t_test");
+            assertEquals(Double.NaN, tTest.getValue(), 0.000001);
+
+            assertNotNull(histo.getBuckets().get(2).getAggregations().asMap().get("t_test"));
+            tTest = (InternalTTest) histo.getBuckets().get(2).getAggregations().asMap().get("t_test");
+            assertEquals(tTestType == TTestType.PAIRED ? 0.6666666667 :
+                tTestType == TTestType.HOMOSCEDASTIC ? 0.8593081179 : 0.8594865044, tTest.getValue(), 0.000001);
+
+        }, fieldType1, fieldType2, fieldTypePart);
+    }
+
+    @AwaitsFix(bugUrl = "https://github.com/elastic/elasticsearch/issues/54365")
+    public void testFormatter() throws IOException {
+        TTestType tTestType = randomFrom(TTestType.values());
+        MappedFieldType fieldType1 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType1.setName("a");
+        MappedFieldType fieldType2 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType2.setName("b");
+        TTestAggregationBuilder aggregationBuilder = new TTestAggregationBuilder("t_test")
+            .a(new MultiValuesSourceFieldConfig.Builder().setFieldName("a").build())
+            .b(new MultiValuesSourceFieldConfig.Builder().setFieldName("b").build())
+            .testType(tTestType).format("0.00%");
+
+        testCase(aggregationBuilder, new MatchAllDocsQuery(), iw -> {
+            iw.addDocument(asList(new NumericDocValuesField("a", 102), new NumericDocValuesField("b", 89)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 99), new NumericDocValuesField("b", 93)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 111), new NumericDocValuesField("b", 72)));
+        }, (Consumer<InternalTTest>) tTest -> {
+            assertEquals(tTestType == TTestType.PAIRED ? 0.1939778614 :
+                tTestType == TTestType.HOMOSCEDASTIC ? 0.05878871029 : 0.07529006595, tTest.getValue(), 0.000001);
+            assertEquals(tTestType == TTestType.PAIRED ? "19.40%" :
+                tTestType == TTestType.HOMOSCEDASTIC ? "5.88%" : "7.53%", tTest.getValueAsString());
+        }, fieldType1, fieldType2);
+    }
+
+    public void testGetProperty() throws IOException {
+        MappedFieldType fieldType1 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType1.setName("a");
+        MappedFieldType fieldType2 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType2.setName("b");
+        GlobalAggregationBuilder globalBuilder = new GlobalAggregationBuilder("global")
+            .subAggregation(new TTestAggregationBuilder("t_test")
+                .a(new MultiValuesSourceFieldConfig.Builder().setFieldName("a").build())
+                .b(new MultiValuesSourceFieldConfig.Builder().setFieldName("b").build())
+                .testType(TTestType.PAIRED));
+
+        testCase(globalBuilder, new MatchAllDocsQuery(), iw -> {
+            iw.addDocument(asList(new NumericDocValuesField("a", 102), new NumericDocValuesField("b", 89)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 99), new NumericDocValuesField("b", 93)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 111), new NumericDocValuesField("b", 72)));
+        }, (Consumer<InternalGlobal>) global -> {
+            assertEquals(3, global.getDocCount());
+            assertTrue(AggregationInspectionHelper.hasValue(global));
+            assertNotNull(global.getAggregations().asMap().get("t_test"));
+            InternalTTest tTest = (InternalTTest) global.getAggregations().asMap().get("t_test");
+            assertEquals(tTest, global.getProperty("t_test"));
+            assertEquals(0.1939778614, (Double) global.getProperty("t_test.value"), 0.000001);
+        }, fieldType1, fieldType2);
+    }
+
+    public void testScript() throws IOException {
+        boolean fieldInA = randomBoolean();
+        TTestType tTestType = randomFrom(TTestType.values());
+
+        MappedFieldType fieldType = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType.setName("field");
+
+        MultiValuesSourceFieldConfig a = new MultiValuesSourceFieldConfig.Builder().setFieldName("field").build();
+        MultiValuesSourceFieldConfig b = new MultiValuesSourceFieldConfig.Builder().setScript(
+            new Script(ScriptType.INLINE, MockScriptEngine.NAME, ADD_HALF_SCRIPT, Collections.singletonMap("fieldname", "field"))).build();
+        TTestAggregationBuilder aggregationBuilder = new TTestAggregationBuilder("t_test").
+            a(fieldInA ? a : b).b(fieldInA ? b : a).testType(tTestType);
+
+        testCase(aggregationBuilder, new MatchAllDocsQuery(), iw -> {
+                iw.addDocument(singleton(new NumericDocValuesField("field", 1)));
+                iw.addDocument(singleton(new NumericDocValuesField("field", 2)));
+                iw.addDocument(singleton(new NumericDocValuesField("field", 3)));
+            }, (Consumer<InternalTTest>) tTest -> {
+                assertEquals(tTestType == TTestType.PAIRED ? 0 : 0.5733922538, tTest.getValue(), 0.000001);
+            }, fieldType);
+    }
+
+    public void testPaired() throws IOException {
+        MappedFieldType fieldType1 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType1.setName("a");
+        MappedFieldType fieldType2 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType2.setName("b");
+        TTestAggregationBuilder aggregationBuilder = new TTestAggregationBuilder("t_test")
+            .a(new MultiValuesSourceFieldConfig.Builder().setFieldName("a").build())
+            .b(new MultiValuesSourceFieldConfig.Builder().setFieldName("b").build())
+            .testType(TTestType.PAIRED);
+        int tails = randomIntBetween(1, 2);
+        if (tails == 1 || randomBoolean()) {
+            aggregationBuilder.tails(tails);
+        }
+        testCase(aggregationBuilder, new MatchAllDocsQuery(), iw -> {
+            iw.addDocument(asList(new NumericDocValuesField("a", 102), new NumericDocValuesField("b", 89)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 99), new NumericDocValuesField("b", 93)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 111), new NumericDocValuesField("b", 72)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 97), new NumericDocValuesField("b", 98)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 101), new NumericDocValuesField("b", 102)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 99), new NumericDocValuesField("b", 98)));
+        }, (Consumer<InternalTTest>) ttest -> {
+            assertEquals(0.09571844217 * tails, ttest.getValue(), 0.00001);
+        }, fieldType1, fieldType2);
+    }
+
+    public void testHomoscedastic() throws IOException {
+        MappedFieldType fieldType1 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType1.setName("a");
+        MappedFieldType fieldType2 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType2.setName("b");
+        TTestAggregationBuilder aggregationBuilder = new TTestAggregationBuilder("t_test")
+            .a(new MultiValuesSourceFieldConfig.Builder().setFieldName("a").build())
+            .b(new MultiValuesSourceFieldConfig.Builder().setFieldName("b").build())
+            .testType(TTestType.HOMOSCEDASTIC);
+        int tails = randomIntBetween(1, 2);
+        if (tails == 1 || randomBoolean()) {
+            aggregationBuilder.tails(tails);
+        }
+        testCase(aggregationBuilder, new MatchAllDocsQuery(), iw -> {
+            iw.addDocument(asList(new NumericDocValuesField("a", 102), new NumericDocValuesField("b", 89)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 99), new NumericDocValuesField("b", 93)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 111), new NumericDocValuesField("b", 72)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 97), new NumericDocValuesField("b", 98)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 101), new NumericDocValuesField("b", 102)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 99), new NumericDocValuesField("b", 98)));
+        }, (Consumer<InternalTTest>) ttest -> {
+            assertEquals(0.03928288693 * tails, ttest.getValue(), 0.00001);
+        }, fieldType1, fieldType2);
+    }
+
+
+    public void testHeteroscedastic() throws IOException {
+        MappedFieldType fieldType1 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType1.setName("a");
+        MappedFieldType fieldType2 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType2.setName("b");
+        TTestAggregationBuilder aggregationBuilder = new TTestAggregationBuilder("t_test")
+            .a(new MultiValuesSourceFieldConfig.Builder().setFieldName("a").build())
+            .b(new MultiValuesSourceFieldConfig.Builder().setFieldName("b").build());
+        if (randomBoolean()) {
+            aggregationBuilder.testType(TTestType.HETEROSCEDASTIC);
+        }
+        int tails = randomIntBetween(1, 2);
+        if (tails == 1 || randomBoolean()) {
+            aggregationBuilder.tails(tails);
+        }
+        testCase(aggregationBuilder, new MatchAllDocsQuery(), iw -> {
+            iw.addDocument(asList(new NumericDocValuesField("a", 102), new NumericDocValuesField("b", 89)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 99), new NumericDocValuesField("b", 93)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 111), new NumericDocValuesField("b", 72)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 97), new NumericDocValuesField("b", 98)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 101), new NumericDocValuesField("b", 102)));
+            iw.addDocument(asList(new NumericDocValuesField("a", 99), new NumericDocValuesField("b", 98)));
+        }, (Consumer<InternalTTest>) ttest -> {
+            assertEquals(0.04538666214 * tails, ttest.getValue(), 0.00001);
+        }, fieldType1, fieldType2);
+    }
+
+    private void testCase(Query query, TTestType type,
+                          CheckedConsumer<RandomIndexWriter, IOException> buildIndex,
+                          Consumer<InternalTTest> verify) throws IOException {
+        MappedFieldType fieldType1 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType1.setName("a");
+        MappedFieldType fieldType2 = new NumberFieldMapper.NumberFieldType(NumberFieldMapper.NumberType.INTEGER);
+        fieldType2.setName("b");
+
+        TTestAggregationBuilder aggregationBuilder = new TTestAggregationBuilder("t_test")
+            .a(new MultiValuesSourceFieldConfig.Builder().setFieldName("a").build())
+            .b(new MultiValuesSourceFieldConfig.Builder().setFieldName("b").build());
+        if (type != TTestType.HETEROSCEDASTIC || randomBoolean()) {
+            aggregationBuilder.testType(type);
+        }
+        testCase(aggregationBuilder, query, buildIndex, verify, fieldType1, fieldType2);
+    }
+
+    private <T extends AggregationBuilder, V extends InternalAggregation> void testCase(
+        T aggregationBuilder, Query query,
+        CheckedConsumer<RandomIndexWriter, IOException> buildIndex,
+        Consumer<V> verify, MappedFieldType... fieldType) throws IOException {
+        try (Directory directory = newDirectory()) {
+            RandomIndexWriter indexWriter = new RandomIndexWriter(random(), directory);
+            buildIndex.accept(indexWriter);
+            indexWriter.close();
+
+            try (IndexReader indexReader = DirectoryReader.open(directory)) {
+                IndexSearcher indexSearcher = newSearcher(indexReader, true, true);
+
+                V agg = searchAndReduce(indexSearcher, query, aggregationBuilder, fieldType);
+                verify.accept(agg);
+
+            }
+        }
+    }
+}

x-pack/plugin/core/src/main/java/org/elasticsearch/xpack/core/analytics/action/AnalyticsStatsAction.java

@@ -119,14 +119,16 @@ public class AnalyticsStatsAction extends ActionType<AnalyticsStatsAction.Respon
         private final long cumulativeCardinalityUsage;
         private final long stringStatsUsage;
         private final long topMetricsUsage;
+        private final long ttestUsage;
 
         public NodeResponse(DiscoveryNode node, long boxplotUsage, long cumulativeCardinalityUsage, long stringStatsUsage,
-                long topMetricsUsage) {
+                long topMetricsUsage, long ttestUsage) {
             super(node);
             this.boxplotUsage = boxplotUsage;
             this.cumulativeCardinalityUsage = cumulativeCardinalityUsage;
             this.stringStatsUsage = stringStatsUsage;
             this.topMetricsUsage = topMetricsUsage;
+            this.ttestUsage = ttestUsage;
         }
 
         public NodeResponse(StreamInput in) throws IOException {
@@ -144,6 +146,11 @@ public class AnalyticsStatsAction extends ActionType<AnalyticsStatsAction.Respon
                 stringStatsUsage = 0;
                 topMetricsUsage = 0;
             }
+            if (in.getVersion().onOrAfter(Version.V_8_0_0)) { // Will drop to 7.8.0 after backport
+                ttestUsage = in.readVLong();
+            } else {
+                ttestUsage = 0;
+            }
         }
 
         @Override
@@ -157,6 +164,9 @@ public class AnalyticsStatsAction extends ActionType<AnalyticsStatsAction.Respon
                 out.writeVLong(stringStatsUsage);
                 out.writeVLong(topMetricsUsage);
             }
+            if (out.getVersion().onOrAfter(Version.V_8_0_0)) { // Will drop to 7.8.0 after backport
+                out.writeVLong(ttestUsage);
+            }
         }
 
         @Override
@@ -185,5 +195,9 @@ public class AnalyticsStatsAction extends ActionType<AnalyticsStatsAction.Respon
         public long getTopMetricsUsage() {
             return topMetricsUsage;
         }
+
+        public long getTTestUsage() {
+            return topMetricsUsage;
+        }
     }
 }

x-pack/plugin/transform/src/main/java/org/elasticsearch/xpack/transform/transforms/pivot/Aggregations.java

@@ -78,7 +78,8 @@ public final class Aggregations {
         "string_stats", // https://github.com/elastic/elasticsearch/issues/51925
         "terms", // https://github.com/elastic/elasticsearch/issues/51073
         "top_hits",
-        "top_metrics" // https://github.com/elastic/elasticsearch/issues/52236
+        "top_metrics", // https://github.com/elastic/elasticsearch/issues/52236
+        "t_test" // https://github.com/elastic/elasticsearch/issues/54503
     );
 
     private Aggregations() {}