Student t-Test in Biostatistics

Introduction

• Definition — The Student t-test is a parametric significance test for comparing one or two means of continuous (numerical) data, deciding whether to accept or reject a null hypothesis about means.
• Small-sample z-test — It is the small-sample modification of the z-test: with large samples a difference ≥ 1·96 SE occurs by chance ≤ 1 in 20 (P ≤ 0·05); with small samples the extra uncertainty in estimating the SE is corrected by referring to the t-distribution.
• Gosset "Student" — Devised by W. S. Gosset, who published under the pseudonym "Student" in 1908 while a statistician at the Guinness brewery, Dublin — hence "Student's t-test".
• When to use — Method of choice for a single comparison between two groups of normally-distributed data; preferred when n < 60 and certainly when ≤ 30. PG shorthand: t-test for n < 30, z-test for n > 30, F-test for a ratio of two variances.
• Four classic uses — (1) confidence interval for a sample mean; (2) one-sample t — sample mean vs a postulated population mean; (3) two-sample/unpaired t — two samples from the same population?; (4) paired t — difference between means of two paired sets.
• RGUHS / NMC — Recurring 10-mark RGUHS LAQ (4 RGUHS recurrences in past papers, plus DNB, MUHS, MPMSU, VNSGU); maps to NMC PG competency — apply appropriate biostatistical tests.