= Sample size for a one sample t-test =

This [[attachment:onesamp.xls|spreadsheet]] computes the total sample size for a one sample t-test with given power. 

This can also be done using this [[http://www.stat.ubc.ca/~rollin/stats/ssize/n1.html|on-line calculator.]] Both these programs use the more liberal normal quantiles as opposed to t quantiles for sample size evaluation.

The web calculator [[http://www.sample-size.net/sample-size-study-paired-t-test/ | 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 [[http://www.jerrydallal.com/LHSP/sizenotes.htm | 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.