10 ttest — t tests (mean-comparison tests)
You can also use ttest without the unpaired option in a regression setting because a paired
comparison includes the assumption of constant variance. The ttest with an unequal variance
assumption does not lend itself to an easy representation in regression settings and is not discussed
here. (x
j
− y
j
) = β
0
+
j
.
William Sealy Gosset (1876–1937) was born in Canterbury, England. He studied chemistry and
mathematics at Oxford and worked as a chemist with the brewers Guinness in Dublin. Gosset
became interested in statistical problems, which he discussed with Karl Pearson and later with
Fisher and Neyman. He published several important papers under the pseudonym “Student”, and
he lent that name to the t test he invented.
References
Acock, A. C. 2014. A Gentle Introduction to Stata. 4th ed. College Station, TX: Stata Press.
Boland, P. J. 2000. William Sealy Gosset—alias ‘Student’ 1876–1937. In Creators of Mathematics: The Irish Connection,
ed. K. Houston, 105–112. Dublin: University College Dublin Press.
Dixon, W. J., and F. J. Massey, Jr. 1983. Introduction to Statistical Analysis. 4th ed. New York: McGraw–Hill.
Gleason, J. R. 1999. sg101: Pairwise comparisons of means, including the Tukey wsd method. Stata Technical Bulletin
47: 31–37. Reprinted in Stata Technical Bulletin Reprints, vol. 8, pp. 225–233. College Station, TX: Stata Press.
Gosset, W. S. 1943. “Student’s” Collected Papers. London: Biometrika Office, University College.
Gosset [Student, pseud.], W. S. 1908. The probable error of a mean. Biometrika 6: 1–25.
Hamilton, L. C. 2013. Statistics with Stata: Updated for Version 12. 8th ed. Boston: Brooks/Cole.
Hoel, P. G. 1984. Introduction to Mathematical Statistics. 5th ed. New York: Wiley.
Pearson, E. S., R. L. Plackett, and G. A. Barnard. 1990. ‘Student’: A Statistical Biography of William Sealy Gosset.
Oxford: Oxford University Press.
Preece, D. A. 1982. t is for trouble (and textbooks): A critique of some examples of the paired-samples t-test.
Statistician 31: 169–195.
Satterthwaite, F. E. 1946. An approximate distribution of estimates of variance components. Biometrics Bulletin 2:
110–114.
Senn, S. J., and W. Richardson. 1994. The first t-test. Statistics in Medicine 13: 785–803.
Welch, B. L. 1947. The generalization of ‘student’s’ problem when several different population variances are involved.
Biometrika 34: 28–35.
Zelen, M. 1979. A new design for randomized clinical trials. New England Journal of Medicine 300: 1242–1245.
Also see
[R] bitest — Binomial probability test
[R] ci — Confidence intervals for means, proportions, and counts
[R] esize — Effect size based on mean comparison
[R] mean — Estimate means
[R] oneway — One-way analysis of variance
[R] prtest — Tests of proportions
[R] sdtest — Variance-comparison tests
[MV] hotelling — Hotelling’s T-squared generalized means test