Sample Size Estimation for Longitudinal Studies

Sample Size Estimation for Longitudinal Studies Don Hedeker

University of Illinois at Chicago uic.edu/hedeker

Hedeker, Gibbons, & Waternaux (1999). Sample size estimation for longitudinal designs with attrition. Journal of Educational and Behavioral Statistics, 24:70-93

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Comparison of two groups at a single timepoint

Number of subjects (N ) in each of two groups (Fleiss, 1986):

N

=

2(z + z)22 (?1 - ?2)2

=

2(z + z)2 [(?1 - ?2)/]2

? z is the value of the standardized score cutting off /2 proportion of each tail of a standard normal distribution (for a two-tailed hypothesis test)

? z is the value of the standardized score cutting off the upper proportion

? 2 is the assumed common variance in the two groups

? ?1 - ?2 is the difference in means of the two groups

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Some common choices: ? z = 1.645, 1.96, 2.576 for 2-tailed .10, .05, and .01 test ? z = .842, 1.036, 1.282 for power = .8, .85. and .90 ? effect size = (?1 - ?2)/ = .2, .5, .8 for "small," "medium,"

and "large" effects (Cohen, 1988)

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Example

? z = 1.96 2-tailed .05 hypothesis test ? z = .842 power = .8 ? effect size (?1 - ?2)/ = .5

2(1.96 + .842)2

N=

(.5)2

= 15.7/.25 = 62.8

need 63 subjects in each group

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Rule of thumb: N (4/)2, where = effect size (for power = .8 for a 2-tailed .05 test)

effect size () .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

N per group 1571 394 176 100 64 45 34 26 21 17

(4/)2 1600 400 178 100 64 44 33 25 20 16

Amaze your friends with your sample size determination abilities!

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