# Sample size for a one sample t-test

This spreadsheet computes the total sample size for a one sample t-test with given power.

This can also be done using this on-line calculator. Both these programs use the more liberal normal quantiles as opposed to t quantiles for sample size evaluation.

The web calculator here computes the number of subjects for a paired t-test using the formula on page 221 of

Rosner B. Fundamentals of Biostatistics. 4th ed. Duxbury Press; 1995. Page 221. See also here.

Note This formula is also incorrectly given on page 39 of

Kraemer HC and Thiemann S (1987) How many subjects? Statistical power analysis in research. Sage.:London. (There should be a copy of this book in the CBU library). The formula should be (z(a) + z(P)) and not (z(a) - z(P) as in Kraemer and Thiemann (1987) for type I error, a, and power, P and z-value, z.

The formula is: N for paired t-test = (1.96+0.842)^{2 } / (difference in paired means / sd of the DIFFERENCE in the means)^{2 } for 80% power and two-tailed type I error of 5% so

Example Using the above formula if the raw paired subject difference is 0.303 and the sd of this difference equals 0.266 then we require 7.85 / (0.303/0.266)^{2 } = 6 subjects.