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

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. 623–632 <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>