Welch’s t-test, named for its creator, Bernard Lewis Welch, is an adaptation of Student’s t-test. Unlike the Student t-test, it doesn’t assume an equal variance in the two populations (Welch 1947). It is also based on hypothesis testing, like chi-squared test and log-likelihood ratio test, but in contrast to them, it takes not only the frequency of a feature into account. Sample mean, standard deviation and sample size are included in a calculation of the t-value. That is the reason why this measure can better deal with frequent words that occur only in one text or one part of a text in a given collection.

## References

``` 2241481 measure_t-test items 1 0 date desc 591 %7B%22status%22%3A%22success%22%2C%22updateneeded%22%3Afalse%2C%22instance%22%3A%22zotpress-720170bcfab1636d6938a6ae6adeaf55%22%2C%22meta%22%3A%7B%22request_last%22%3A0%2C%22request_next%22%3A0%2C%22used_cache%22%3Atrue%7D%2C%22data%22%3A%5B%7B%22key%22%3A%22BFMBZJ5T%22%2C%22library%22%3A%7B%22id%22%3A2241481%7D%2C%22meta%22%3A%7B%22lastModifiedByUser%22%3A%7B%22id%22%3A5206995%2C%22username%22%3A%22roettgermann%22%2C%22name%22%3A%22%22%2C%22links%22%3A%7B%22alternate%22%3A%7B%22href%22%3A%22https%3A%5C%2F%5C%2Fwww.zotero.org%5C%2Froettgermann%22%2C%22type%22%3A%22text%5C%2Fhtml%22%7D%7D%7D%2C%22creatorSummary%22%3A%22Paquot%20and%20Bestgen%22%2C%22parsedDate%22%3A%222009-01-01%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%201.35%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EPaquot%2C%20Magali%2C%20and%20Yves%20Bestgen%2C%20%26%23x2018%3BDistinctive%20Words%20in%20Academic%20Writing%3A%20A%20Comparison%20of%20Three%20Statistical%20Tests%20for%20Keyword%20Extraction%26%23x2019%3B%2C%20in%20%3Ci%3ECorpora%3A%20Pragmatics%20and%20Discourse%3C%5C%2Fi%3E%2C%20ed.%20by%20Andreas%20H.%20Jucker%2C%20Daniel%20Schreier%2C%20and%20Marianne%20Hundt%20%28Brill%20%7C%20Rodopi%2C%202009%29%20%26lt%3Bhttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1163%5C%2F9789042029101_014%26gt%3B%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22bookSection%22%2C%22title%22%3A%22Distinctive%20words%20in%20academic%20writing%3A%20A%20comparison%20of%20three%20statistical%20tests%20for%20keyword%20extraction%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22editor%22%2C%22firstName%22%3A%22Andreas%20H.%22%2C%22lastName%22%3A%22Jucker%22%7D%2C%7B%22creatorType%22%3A%22editor%22%2C%22firstName%22%3A%22Daniel%22%2C%22lastName%22%3A%22Schreier%22%7D%2C%7B%22creatorType%22%3A%22editor%22%2C%22firstName%22%3A%22Marianne%22%2C%22lastName%22%3A%22Hundt%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Magali%22%2C%22lastName%22%3A%22Paquot%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Yves%22%2C%22lastName%22%3A%22Bestgen%22%7D%5D%2C%22abstractNote%22%3A%22Most%20studies%20that%20make%20use%20of%20keyword%20analysis%20rely%20on%20log-likelihood%20ratio%20or%20chi-square%20tests%20to%20extract%20words%20that%20are%20particularly%20characteristic%20of%20a%20corpus%20%28e.g.%20Scott%20and%20Tribble%202006%29.%20These%20measures%20are%20computed%20on%20the%20basis%20of%20absolute%20frequencies%20and%20cannot%20account%20for%20the%20fact%20that%20%5Cu201ccorpora%20are%20inherently%20variable%20internally%5Cu201d%20%28Gries%202006%3A%20110%29.%20To%20overcome%20this%20limitation%2C%20measures%20of%20dispersion%20are%20sometimes%20used%20in%20combination%20with%20keyness%20values%20%28e.g.%20Rayson%202003%3B%20Oakes%20and%20Farrow%202007%29.%20Some%20scholars%20have%20also%20suggested%20using%20other%20statistical%20measures%20%28e.g.%20Wilcoxon-Mann-Whitney%20test%29%20but%20these%20techniques%20have%20not%20gained%20corpus%20linguists%5Cu2019%20favour%20%28yet%3F%29.%20One%20possible%20explanation%20for%20this%20lack%20of%20enthusiasm%20is%20that%20statistical%20tests%20for%20keyword%20extraction%20have%20rarely%20been%20compared.%20In%20this%20article%2C%20we%20make%20use%20of%20the%20log-likelihood%20ratio%2C%20the%20t-test%20and%20the%20Wilcoxon-Mann-Whitney%20test%20in%20turn%20to%20compare%20the%20academic%20and%20the%20fiction%20sub-corpora%20of%20the%20British%20National%20Corpus%20and%20extract%20words%20that%20are%20typical%20of%20academic%20discourse.%20We%20compare%20the%20three%20lists%20of%20academic%20keywords%20on%20a%20number%20of%20criteria%20%28e.g.%20number%20of%20keywords%20extracted%20by%20each%20measure%2C%20percentage%20of%20keywords%20that%20are%20shared%20in%20the%20three%20lists%2C%20frequency%20and%20distribution%20of%20academic%20keywords%20in%20the%20two%20corpora%29%20and%20explore%20the%20specificities%20of%20the%20three%20statistical%20measures.%20We%20also%20assess%20the%20advantages%20and%20disadvantages%20of%20these%20measures%20for%20the%20extraction%20of%20general%20academic%20words.%22%2C%22bookTitle%22%3A%22Corpora%3A%20Pragmatics%20and%20Discourse%22%2C%22date%22%3A%222009-01-01%22%2C%22language%22%3A%22%22%2C%22ISBN%22%3A%22978-90-420-2910-1%20978-90-420-2592-9%22%2C%22url%22%3A%22https%3A%5C%2F%5C%2Fbrill.com%5C%2Fview%5C%2Fbook%5C%2Fedcoll%5C%2F9789042029101%5C%2FB9789042029101-s014.xml%22%2C%22collections%22%3A%5B%222CZHD96W%22%2C%224MZ8ZP2B%22%5D%2C%22dateModified%22%3A%222024-02-20T09%3A05%3A29Z%22%7D%7D%2C%7B%22key%22%3A%22PUCJ6MVT%22%2C%22library%22%3A%7B%22id%22%3A2241481%7D%2C%22meta%22%3A%7B%22lastModifiedByUser%22%3A%7B%22id%22%3A228821%2C%22username%22%3A%22christof.s%22%2C%22name%22%3A%22Christof%20Sch%5Cu00f6ch%22%2C%22links%22%3A%7B%22alternate%22%3A%7B%22href%22%3A%22https%3A%5C%2F%5C%2Fwww.zotero.org%5C%2Fchristof.s%22%2C%22type%22%3A%22text%5C%2Fhtml%22%7D%7D%7D%2C%22creatorSummary%22%3A%22Smucker%20et%20al.%22%2C%22parsedDate%22%3A%222007%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%201.35%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3ESmucker%2C%20Mark%20D.%2C%20James%20Allan%2C%20and%20Ben%20Carterette%2C%20%26%23x2018%3BA%20Comparison%20of%20Statistical%20Significance%20Tests%20for%20Information%20Retrieval%20Evaluation%26%23x2019%3B%2C%20in%20%3Ci%3EProceedings%20of%20the%20Sixteenth%20ACM%20Conference%20on%20Conference%20on%20Information%20and%20Knowledge%20Management%3C%5C%2Fi%3E%2C%20CIKM%20%26%23x2019%3B07%20%28New%20York%2C%20NY%2C%20USA%3A%20ACM%2C%202007%29%2C%20pp.%20623%26%23x2013%3B32%20%26lt%3B%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1145%5C%2F1321440.1321528%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1145%5C%2F1321440.1321528%3C%5C%2Fa%3E%26gt%3B%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22conferencePaper%22%2C%22title%22%3A%22A%20Comparison%20of%20Statistical%20Significance%20Tests%20for%20Information%20Retrieval%20Evaluation%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Mark%20D.%22%2C%22lastName%22%3A%22Smucker%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22James%22%2C%22lastName%22%3A%22Allan%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Ben%22%2C%22lastName%22%3A%22Carterette%22%7D%5D%2C%22abstractNote%22%3A%22Information%20retrieval%20%28IR%29%20researchers%20commonly%20use%20three%20tests%20of%20statistical%20significance%3A%20the%20Student%27s%20paired%20t-test%2C%20the%20Wilcoxon%20signed%20rank%20test%2C%20and%20the%20sign%20test.%20Other%20researchers%20have%20previously%20proposed%20using%20both%20the%20bootstrap%20and%20Fisher%27s%20randomization%20%28permutation%29%20test%20as%20non-parametric%20significance%20tests%20for%20IR%20but%20these%20tests%20have%20seen%20little%20use.%20For%20each%20of%20these%20five%20tests%2C%20we%20took%20the%20ad-hoc%20retrieval%20runs%20submitted%20to%20TRECs%203%20and%205-8%2C%20and%20for%20each%20pair%20of%20runs%2C%20we%20measured%20the%20statistical%20significance%20of%20the%20difference%20in%20their%20mean%20average%20precision.%20We%20discovered%20that%20there%20is%20little%20practical%20difference%20between%20the%20randomization%2C%20bootstrap%2C%20and%20t%20tests.%20Both%20the%20Wilcoxon%20and%20sign%20test%20have%20a%20poor%20ability%20to%20detect%20significance%20and%20have%20the%20potential%20to%20lead%20to%20false%20detections%20of%20significance.%20The%20Wilcoxon%20and%20sign%20tests%20are%20simplified%20variants%20of%20the%20randomization%20test%20and%20their%20use%20should%20be%20discontinued%20for%20measuring%20the%20significance%20of%20a%20difference%20between%20means.%22%2C%22date%22%3A%222007%22%2C%22proceedingsTitle%22%3A%22Proceedings%20of%20the%20Sixteenth%20ACM%20Conference%20on%20Conference%20on%20Information%20and%20Knowledge%20Management%22%2C%22conferenceName%22%3A%22%22%2C%22language%22%3A%22%22%2C%22DOI%22%3A%2210.1145%5C%2F1321440.1321528%22%2C%22ISBN%22%3A%22978-1-59593-803-9%22%2C%22url%22%3A%22http%3A%5C%2F%5C%2Fdoi.acm.org%5C%2F10.1145%5C%2F1321440.1321528%22%2C%22collections%22%3A%5B%224MZ8ZP2B%22%5D%2C%22dateModified%22%3A%222020-02-14T14%3A36%3A54Z%22%7D%7D%2C%7B%22key%22%3A%22C428QV33%22%2C%22library%22%3A%7B%22id%22%3A2241481%7D%2C%22meta%22%3A%7B%22lastModifiedByUser%22%3A%7B%22id%22%3A5206995%2C%22username%22%3A%22roettgermann%22%2C%22name%22%3A%22%22%2C%22links%22%3A%7B%22alternate%22%3A%7B%22href%22%3A%22https%3A%5C%2F%5C%2Fwww.zotero.org%5C%2Froettgermann%22%2C%22type%22%3A%22text%5C%2Fhtml%22%7D%7D%7D%2C%22creatorSummary%22%3A%22Welch%22%2C%22parsedDate%22%3A%221947%22%2C%22numChildren%22%3A0%7D%2C%22bib%22%3A%22%3Cdiv%20class%3D%5C%22csl-bib-body%5C%22%20style%3D%5C%22line-height%3A%201.35%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%5C%22%3E%5Cn%20%20%3Cdiv%20class%3D%5C%22csl-entry%5C%22%3EWelch%2C%20Bernard%20Lewis%2C%20%26%23x2018%3BThe%20Generalization%20of%20Student%26%23x2019%3Bs%20Probem%20When%20Several%20Different%20Population%20Variances%20Are%20Involved%26%23x2019%3B%2C%20%3Ci%3EBiometrika%3C%5C%2Fi%3E%2C%2034.1%26%23x2013%3B2%20%281947%29%2C%2028%26%23x2013%3B35%20%26lt%3B%3Ca%20href%3D%27https%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1093%5C%2Fbiomet%5C%2F34.1-2.28%27%3Ehttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1093%5C%2Fbiomet%5C%2F34.1-2.28%3C%5C%2Fa%3E%26gt%3B%3C%5C%2Fdiv%3E%5Cn%3C%5C%2Fdiv%3E%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22The%20generalization%20of%20Student%27s%20probem%20when%20several%20different%20population%20variances%20are%20involved%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22Bernard%20Lewis%22%2C%22lastName%22%3A%22Welch%22%7D%5D%2C%22abstractNote%22%3A%22%22%2C%22date%22%3A%221947%22%2C%22language%22%3A%22en%22%2C%22DOI%22%3A%2210.1093%5C%2Fbiomet%5C%2F34.1-2.28%22%2C%22ISSN%22%3A%220006-3444%2C%201464-3510%22%2C%22url%22%3A%22https%3A%5C%2F%5C%2Facademic.oup.com%5C%2Fbiomet%5C%2Farticle-lookup%5C%2Fdoi%5C%2F10.1093%5C%2Fbiomet%5C%2F34.1-2.28%22%2C%22collections%22%3A%5B%22IUKRIB7T%22%5D%2C%22dateModified%22%3A%222024-02-20T09%3A15%3A53Z%22%7D%7D%5D%7D Paquot, Magali, and Yves Bestgen, ‘Distinctive Words in Academic Writing: A Comparison of Three Statistical Tests for Keyword Extraction’, in Corpora: Pragmatics and Discourse, ed. by Andreas H. Jucker, Daniel Schreier, and Marianne Hundt (Brill | Rodopi, 2009) <https://doi.org/10.1163/9789042029101_014> Smucker, Mark D., James Allan, and Ben Carterette, ‘A Comparison of Statistical Significance Tests for Information Retrieval Evaluation’, in Proceedings of the Sixteenth ACM Conference on Conference on Information and Knowledge Management, CIKM ’07 (New York, NY, USA: ACM, 2007), pp. 623–32 <https://doi.org/10.1145/1321440.1321528> Welch, Bernard Lewis, ‘The Generalization of Student’s Probem When Several Different Population Variances Are Involved’, Biometrika, 34.1–2 (1947), 28–35 <https://doi.org/10.1093/biomet/34.1-2.28> ```
``` ```