{ "id": "epcrwwtqht", "slug": "location-test", "title": "Location test", "updated": "2026-10-25", "topic_path": [ { "id": "physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical" }, { "id": "physical.math", "label": "Mathematics and statistics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math" }, { "id": "physical.math.statistics", "label": "Statistics and probability", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math.statistics" }, { "id": "physical.math.statistics.stats_statistical_inference", "label": "Statistical inference, estimation, sampling, and testing", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math.statistics.stats_statistical_inference" }, { "id": "physical.math.statistics.stats_statistical_inference.hypothesis_testing", "label": "Hypothesis testing", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math.statistics.stats_statistical_inference.hypothesis_testing" } ], "geo": [ { "id": "geo.nongeo.t1800.physical.math.statistics.stats_statistical_inference.hypothesis_testing", "label": "Non-geographic · 1800 to 1945: Hypothesis testing", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1800.physical.math.statistics.stats_statistical_inference.hypothesis_testing", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t1800", "label": "Non-geographic · 1800 to 1945", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1800" }, { "id": "geo.nongeo.t1800.physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1800.physical" }, { "id": "geo.nongeo.t1800.physical.math", "label": "Mathematics and statistics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1800.physical.math" }, { "id": "geo.nongeo.t1800.physical.math.statistics", "label": "Statistics and probability", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1800.physical.math.statistics" }, { "id": "geo.nongeo.t1800.physical.math.statistics.stats_statistical_inference", "label": "Statistical inference, estimation, sampling, and testing", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1800.physical.math.statistics.stats_statistical_inference" }, { "id": "geo.nongeo.t1800.physical.math.statistics.stats_statistical_inference.hypothesis_testing", "label": "Hypothesis testing", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1800.physical.math.statistics.stats_statistical_inference.hypothesis_testing" } ] }, { "id": "geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference.hypothesis_testing", "label": "Non-geographic · 1946 to 2000: Hypothesis testing", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference.hypothesis_testing", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t1946", "label": "Non-geographic · 1946 to 2000", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946" }, { "id": "geo.nongeo.t1946.physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical" }, { "id": "geo.nongeo.t1946.physical.math", "label": "Mathematics and statistics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math" }, { "id": "geo.nongeo.t1946.physical.math.statistics", "label": "Statistics and probability", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics" }, { "id": "geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference", "label": "Statistical inference, estimation, sampling, and testing", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference" }, { "id": "geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference.hypothesis_testing", "label": "Hypothesis testing", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference.hypothesis_testing" } ] } ], "excerpt": "A location test is a statistical hypothesis test that compares the location parameter, such as the mean or median, of distributions, using parametric tests like the t-test or nonparametric rank tests.", "snippet": "A location test is a statistical hypothesis test that compares the location parameter, such as the mean or median, of distributions, using parametric tests like the t-test or nonparametric rank tests.", "node": "physical.math.statistics.stats_statistical_inference.hypothesis_testing", "markdown": "# Location test\n\nA location test is a statistical hypothesis test that compares the location parameter, such as the mean or median, of one or more distributions. Parametric versions assume a distributional form: the t-test targets the mean, with the pooled two-sample Student t-test assuming independent samples and a common variance, while Welch's two-sample t-test does not require the assumption of equal variances between populations. Nonparametric versions, the core of the subject, target the median or the pseudomedian (the median of \\( (u+v)/2 \\) for independent \\( u, v \\) drawn from the same distribution; the two coincide when the distribution is symmetric).[1](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/wilcox.test.html) Named location tests include the sign test, the [Wilcoxon signed-rank test](https://www.edgepedia.org/wilcoxon-signed-rank-test), the [Mann–Whitney U test](https://www.edgepedia.org/mann-whitney-u-test) (Wilcoxon rank-sum), the two-sample median test, and the k-sample Kruskal–Wallis and Friedman tests.[2](https://reference.wolfram.com/language/ref/LocationTest.en.md) • [3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2743502/) Software such as R's wilcox.test, Wolfram's LocationTest, and the nptest package expose these as routine calls.[1](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/wilcox.test.html) • [2](https://reference.wolfram.com/language/ref/LocationTest.en.md) • [4](https://www.rdocumentation.org/packages/nptest/versions/1.2/topics/np.loc.test)\n\n| Fact | Detail |\n|---|---|\n| Null vs alternative (two-sample shift model) | \\( H_{0}: F(x) = G(x) \\) versus \\( H_{1}: F(x) = G(x + \\Delta) \\)[5](https://journals.plos.org/plosone/article/file?id=10.1371%2Fjournal.pone.0195894&type=printable) |\n| Efficiency vs t-test | Wilcoxon rank-sum ARE 0.955 under normality; at least about 0.864 for all continuous distributions[3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2743502/) • [6](https://link.springer.com/article/10.1007/s42952-024-00262-7) |\n| Origin papers | Wilcoxon (1945)[7](https://doi.org/10.2307/3001968), Mann & Whitney (1947)[8](https://doi.org/10.1214/aoms/1177730491), Kruskal & Wallis (1952)[9](https://doi.org/10.1080/01621459.1952.10483441) |\n| What U measures | \\( \\varphi(F,G) = \\Pr[Y_{F} > Y_{G}] + \\tfrac{1}{2}\\Pr[Y_{F} = Y_{G}] \\)[10](https://pmc.ncbi.nlm.nih.gov/articles/PMC2857732/) |\n| Exact p-values | Default in R below 50 finite values; tie-handling via the Streitberg–Röhmel shift algorithm[1](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/wilcox.test.html) |\n| Main failure mode | Invalid under unequal variances alone when only equal means are assumed[10](https://pmc.ncbi.nlm.nih.gov/articles/PMC2857732/) |\n\n## How it works\n\nNonparametric location tests replace the data with ranks or signs, so the null distribution of the statistic can be computed without assuming a data-generating distribution. Under the null with exchangeable data, the rank vector is uniform over all \\( n! \\) permutations of \\( \\{1, \\dots, n\\} \\), which makes the tests distribution-free.[11](https://juliastats.org/HypothesisTests.jl/latest/specs/rank_tests/)\n\nThe two-sample rank-sum test is defined through the Mann–Whitney functional \\( \\varphi(F,G) = \\Pr[Y_{F} > Y_{G}] + \\tfrac{1}{2}\\Pr[Y_{F} = Y_{G}] \\); the null \\( \\varphi = 1/2 \\) is rejected when one sample tends to produce larger values.[10](https://pmc.ncbi.nlm.nih.gov/articles/PMC2857732/) Mann and Whitney proved the test is consistent against the stochastic-ordering alternative \\( F(x) \\leq G(x) \\) for every \\( x \\) with strict inequality for some \\( x \\).[12](https://projecteuclid.org/journalArticle/Download?urlId=10.1214%2Faoms%2F1177730491&isResultClick=False) This is broader than a location shift: the procedure tests location only under the shift model of parallel cumulative distribution functions, and describing it as a test of \"differences in distribution\" in general has been shown misleading by counterexample.[13](https://doi.org/10.1111/bmsp.12162) • [14](https://onlinelibrary.wiley.com/doi/10.1002/bimj.4710240102) Under the shift model, inverting the test gives a confidence interval for \\( \\Delta \\), the Hodges–Lehmann estimate; the two-sample estimator estimates the median of the difference between samples, not the difference of medians, a distinction the R documentation calls a common misconception.[1](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/wilcox.test.html)\n\n## How it is done\n\n**Sign test.** Count observations above and below the hypothesized value \\( m_{0} \\). Under \\( H_{0} \\) the counts follow a binomial distribution with parameters \\( n \\) and \\( p = 1/2 \\); a two-sided test rejects when the smaller count is too small.[15](https://online.stat.psu.edu/stat415/book/export/html/836)\n\n**Wilcoxon signed-rank test.** Discard zero differences, rank the absolute differences (midranks for ties), and compute \\( W = \\sum_{i=1}^{n} Z_{i} R_{i} \\), where \\( Z_{i} \\) indicates a positive difference and \\( R_{i} \\) is the rank; \\( W \\) ranges from 0 to \\( n(n+1)/2 \\).[15](https://online.stat.psu.edu/stat415/book/export/html/836) • [11](https://juliastats.org/HypothesisTests.jl/latest/specs/rank_tests/) For large \\( n \\), \\( W' = (W - n(n+1)/4) / \\sqrt{n(n+1)(2n+1)/24} \\) is approximately standard normal.[15](https://online.stat.psu.edu/stat415/book/export/html/836) Each group of \\( t \\) tied ranks reduces the null variance by \\( (t^{3} - t)/48 \\).[16](https://www.jhanley.biostat.mcgill.ca/c607/ch14/jh_ch_14.pdf)\n\n**Mann–Whitney U / Wilcoxon rank-sum.** Pool the samples, rank them, and either sum one group's ranks or count cross-group pairs with ties counting one half. \\( U \\) has \\( E(U) = 0.5 \\cdot n_{1} \\cdot n_{2} \\) and \\( \\mathrm{Var}(U) = n_{1} \\cdot n_{2}(n_{1} + n_{2} + 1)/12 \\), and \\( U_{1} = T_{1} - n_{1}(n_{1}+1)/2 \\), so the two formulations are exactly equivalent.[17](https://people.stat.sc.edu/hansont/stat704/notes3.pdf) • [16](https://www.jhanley.biostat.mcgill.ca/c607/ch14/jh_ch_14.pdf) • [11](https://juliastats.org/HypothesisTests.jl/latest/specs/rank_tests/)\n\n**Median test.** Count values in one sample exceeding the global median of all \\( m + n \\) observations; this count follows a hypergeometric distribution under \\( H_{0} \\), and randomization gives exact significance levels.[18](https://eldorado.tu-dortmund.de/server/api/core/bitstreams/bb7cba51-51e7-46c5-902f-89d694300a6d/content)\n\nExact null distributions can be computed two ways: a lattice recursion for untied samples at \\( O(n^{3}) \\) cost and full permutation enumeration at \\( O(2^{n}) \\); in addition, a normal approximation at \\( O(n) \\) is available but is not an exact computation.[11](https://juliastats.org/HypothesisTests.jl/latest/specs/rank_tests/)\n\nIn software, R's wilcox.test computes an exact p-value by default when samples contain fewer than 50 finite values and otherwise uses a normal approximation; with ties, an exact p-value is not generally used by default; the Streitberg–Röhmel shift algorithm computes exact conditional p-values for both tied and untied samples when the exact calculation is requested.[1](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/wilcox.test.html) Wolfram's LocationTest offers \"Sign\", \"SignedRank\", \"MannWhitney\", and t- and z-tests, choosing by default the most powerful test that applies.[2](https://reference.wolfram.com/language/ref/LocationTest.en.md) The R package nptest performs [randomization tests](https://www.edgepedia.org/randomization-test) with eight statistics, including Welch's t and the studentized Wilcoxon[4](https://www.rdocumentation.org/packages/nptest/versions/1.2/topics/np.loc.test), and robnptests implements the Fried–Dehling robust tests with permutation, randomization, or asymptotic p-values.[19](https://s-abbas.r-universe.dev/robnptests/doc/manual.pdf)\n\n## Origin\n\nFrank Wilcoxon's 1945 paper *Individual Comparisons by Ranking Methods* in *Biometrics Bulletin* introduced the rank-sum test, substituting rank scores \\( 1, 2, 3, \\dots, n \\) for the data to obtain rapid approximate significance in paired and unpaired experiments, with exact tables for 5 to 10 replicates[7](https://doi.org/10.2307/3001968) • [20](https://sci-hub.ru/storage/moscow/1867/6cf7c23f788de9858d4bd1639bb59275/wilcoxon1945.pdf); the same paper presented the signed-rank procedure for paired data.[7](https://doi.org/10.2307/3001968) H. B. Mann and D. R. Whitney's 1947 paper in *The Annals of Mathematical Statistics* proposed the U statistic, computed exact probabilities by a recurrence relation up to \\( n = m = 8 \\), and proved the limit distribution is normal as \\( m, n \\) grow.[8](https://doi.org/10.1214/aoms/1177730491) • [12](https://projecteuclid.org/journalArticle/Download?urlId=10.1214%2Faoms%2F1177730491&isResultClick=False) William H. Kruskal and W. Allen Wallis extended the rank approach to [one-way analysis of variance](https://www.edgepedia.org/one-way-analysis-of-variance) by ranks in 1952 in the *Journal of the American Statistical Association*.[9](https://doi.org/10.1080/01621459.1952.10483441)\n\n## Variants\n\nThe one-sample forms are the sign test and the signed-rank test; the paired form applies the signed-rank test to within-pair differences, replacing the paired t-test when differences are severely non-normal.[21](http://estat.me/estat/eLearning/en/eStatU/chapter10.html) • [22](https://stats.libretexts.org/Courses/Las_Positas_College/Math_40%3A_Statistics_and_Probability/12%3A_Nonparametric_Statistics/12.10%3A_Wilcoxon_Signed-Rank_Test) The two-sample forms are the rank-sum (Mann–Whitney) test and the median test.[18](https://eldorado.tu-dortmund.de/server/api/core/bitstreams/bb7cba51-51e7-46c5-902f-89d694300a6d/content) The Kruskal–Wallis test generalizes the rank-sum comparison to \\( k \\) independent groups and is the nonparametric counterpart of one-way ANOVA; the [Friedman test](https://www.edgepedia.org/friedman-test) handles \\( k \\) related samples.[3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2743502/) • [21](http://estat.me/estat/eLearning/en/eStatU/chapter10.html) Robust two-sample tests based on sample medians and Hodges–Lehmann estimators were introduced by Roland Fried and Herold Dehling in 2011.[23](https://doi.org/10.1007/s10260-011-0164-1) Multivariate extensions use component-wise medians and Hodges–Lehmann estimators for the shift hypothesis \\( H_{0}: F(x) = G(x) \\) versus \\( H_{1}: F(x) = G(x + \\Delta) \\).[5](https://journals.plos.org/plosone/article/file?id=10.1371%2Fjournal.pone.0195894&type=printable) A maximum-type statistic pairs Wilcoxon-type location scores with the Ansari–Bradley scale statistic for one-sided location-scale alternatives in a two-stage design.[24](https://link.springer.com/article/10.1007/s10260-024-00775-9)\n\n## Applications\n\nAgainst the t-test under normality, the Wilcoxon rank-sum test has ARE 0.955 (equal to \\( 3/\\pi \\)), and Kruskal–Wallis has the same 0.955 against ANOVA, so little power is lost even when parametric assumptions hold.[3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2743502/) • [10](https://pmc.ncbi.nlm.nih.gov/articles/PMC2857732/) For all continuous distributions the ARE is at least about 0.864, while the normal scores test has ARE 1 relative to the t-test.[6](https://link.springer.com/article/10.1007/s42952-024-00262-7) For heavy-tailed or very skewed distributions the WMW procedure can be more powerful than the t-test, and the ARE can become infinite.[10](https://pmc.ncbi.nlm.nih.gov/articles/PMC2857732/) • [3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2743502/) Practical guidance is to use the t-test for approximately normal data (where it has more power), the signed-rank test for symmetric but non-normal data, and the sign test for highly skewed data.[17](https://people.stat.sc.edu/hansont/stat704/notes3.pdf)\n\n## Limitations and alternatives\n\nThe WMW test is invalid if only equality of means is assumed, because a difference in variances alone can make the statistic significant; validity requires \\( F = G \\) under the null.[10](https://pmc.ncbi.nlm.nih.gov/articles/PMC2857732/) In simulation studies combining non-normality with variance heterogeneity, all methods protected the type I error rate except Mann–Whitney, which inflated it.[25](https://li01.tci-thaijo.org/index.php/cast/article/view/249633) The classical t-test is comparatively robust: it retains asymptotic validity when normality is violated[10](https://pmc.ncbi.nlm.nih.gov/articles/PMC2857732/), and the two-sample t-test is asymptotically valid when a common variance exists.[18](https://eldorado.tu-dortmund.de/server/api/core/bitstreams/bb7cba51-51e7-46c5-902f-89d694300a6d/content) Ties and zeros require care: zeros are discarded before ranking, ties force midranks and permutation-based inference, and adding small random noise (jittering) can hold the significance level on discrete data.[11](https://juliastats.org/HypothesisTests.jl/latest/specs/rank_tests/) • [19](https://s-abbas.r-universe.dev/robnptests/doc/manual.pdf) Alternatives include permutation and bootstrap procedures, which approximate the statistic's distribution from the pooled sample[5](https://journals.plos.org/plosone/article/file?id=10.1371%2Fjournal.pone.0195894&type=printable), the studentized Wilcoxon test for unequal variances[4](https://www.rdocumentation.org/packages/nptest/versions/1.2/topics/np.loc.test), and robust median-based tests.[23](https://doi.org/10.1007/s10260-011-0164-1) Because the WMW procedure tests location only under the shift model, effect size is better reported as the probability of superiority than as a single median shift.[13](https://doi.org/10.1111/bmsp.12162)\n\n## References\n\n1. [R: Wilcoxon Rank Sum and Signed Rank Tests (wilcox.test)](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/wilcox.test.html)\n2. [LocationTest, Wolfram Language Reference](https://reference.wolfram.com/language/ref/LocationTest.en.md)\n3. [Nonparametric versus parametric tests of location in biomedical research](https://pmc.ncbi.nlm.nih.gov/articles/PMC2743502/)\n4. [np.loc.test function - RDocumentation (nptest package)](https://www.rdocumentation.org/packages/nptest/versions/1.2/topics/np.loc.test)\n5. [Robust multivariate nonparametric tests for detection of two-sample location shift in clinical trials (PLoS ONE, 2018)](https://journals.plos.org/plosone/article/file?id=10.1371%2Fjournal.pone.0195894&type=printable)\n6. [Nonparametric tests for combined location-scale and Lehmann alternatives using adaptive approach and max-type metric (Journal of the Korean Statistical Society, 2024)](https://link.springer.com/article/10.1007/s42952-024-00262-7)\n7. [Frank Wilcoxon (1945). Individual Comparisons by Ranking Methods. Biometrics Bulletin.](https://doi.org/10.2307/3001968)\n8. [H. B. Mann, D. R. Whitney (1947). On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other. The Annals of Mathematical Statistics.](https://doi.org/10.1214/aoms/1177730491)\n9. [William H. Kruskal, W. Allen Wallis (1952). Use of Ranks in One-Criterion Variance Analysis. Journal of the American Statistical Association.](https://doi.org/10.1080/01621459.1952.10483441)\n10. [Fay & Proschan (2010), 'Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules', Statistics in Medicine](https://pmc.ncbi.nlm.nih.gov/articles/PMC2857732/)\n11. [Rank-based location inference · HypothesisTests.jl](https://juliastats.org/HypothesisTests.jl/latest/specs/rank_tests/)\n12. [Mann, H. B. & Whitney, D. R. (1947) 'On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other', Annals of Mathematical Statistics 18(1):50–60](https://projecteuclid.org/journalArticle/Download?urlId=10.1214%2Faoms%2F1177730491&isResultClick=False)\n13. [When is the Wilcoxon–Mann–Whitney procedure a test of location? Implications for effect-size measures](https://doi.org/10.1111/bmsp.12162)\n14. [Hilgers (1982), 'On the Wilcoxon-Mann-Whitney Test as Nonparametric Analogue and Extension of t-Test', Biometrical Journal 24(1):1–15](https://onlinelibrary.wiley.com/doi/10.1002/bimj.4710240102)\n15. [Lesson 20: The Wilcoxon Tests (Penn State STAT 415)](https://online.stat.psu.edu/stat415/book/export/html/836)\n16. [\"Distribution-Free\" or \"Non-parametric\" Methods (McGill C607 course notes)](https://www.jhanley.biostat.mcgill.ca/c607/ch14/jh_ch_14.pdf)\n17. [Nonparametric tests (Timothy Hanson, Stat 704, University of South Carolina)](https://people.stat.sc.edu/hansont/stat704/notes3.pdf)\n18. [Robust nonparametric tests for the two-sample location problem (Fried & Dehling)](https://eldorado.tu-dortmund.de/server/api/core/bitstreams/bb7cba51-51e7-46c5-902f-89d694300a6d/content)\n19. [robnptests: Robust Nonparametric Two-Sample Tests for Location/Scale (R package manual)](https://s-abbas.r-universe.dev/robnptests/doc/manual.pdf)\n20. [Wilcoxon, F. (1945) 'Individual Comparisons by Ranking Methods', Biometrics Bulletin 1(6):80–83](https://sci-hub.ru/storage/moscow/1867/6cf7c23f788de9858d4bd1639bb59275/wilcoxon1945.pdf)\n21. [Chapter 10 Nonparametric tests (eStat)](http://estat.me/estat/eLearning/en/eStatU/chapter10.html)\n22. [12.10: Wilcoxon Signed-Rank Test (McDonald, Statistics LibreTexts)](https://stats.libretexts.org/Courses/Las_Positas_College/Math_40%3A_Statistics_and_Probability/12%3A_Nonparametric_Statistics/12.10%3A_Wilcoxon_Signed-Rank_Test)\n23. [Roland Fried, Herold Dehling (2011). Robust nonparametric tests for the two-sample location problem. Statistical Methods & Applications.](https://doi.org/10.1007/s10260-011-0164-1)\n24. [A maximum statistic for the one-sided location-scale alternative in the two-stage design (Statistical Methods & Applications, 2024)](https://link.springer.com/article/10.1007/s10260-024-00775-9)\n25. [Two-sample Location Tests under Violation of the Normality and Variance Homogeneity Assumptions](https://li01.tci-thaijo.org/index.php/cast/article/view/249633)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Mathematics and statistics › Statistics and probability › Statistical inference, estimation, sampling, and testing › Hypothesis testing*\n\n*Initially written Sep 29, 2026 · Edited: Oct 15, 2026; Oct 25, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [], "url": "https://www.edgepedia.org/location-test", "markdown_url": "https://www.edgepedia.org/location-test.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"Location test\", Edgepedia (EdgeChat), https://www.edgepedia.org/location-test. Edgepedia Community License 1.0.", "credit_md": "\"[Location test](https://www.edgepedia.org/location-test)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/location-test](https://www.edgepedia.org/location-test). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"Location test\", Edgepedia (EdgeChat), https://www.edgepedia.org/location-test. Edgepedia Community License 1.0.", "speakable": "A location test is a statistical hypothesis test that compares the location parameter, such as the mean or median, of distributions, using parametric tests like the t-test or nonparametric rank tests." }