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effectsize:paired-t-test

Effect size and confidence interval for paired-t-test

We implemented the method by Algina, J., & Keselman, H. J. (2003). Approximate confidence intervals for effect sizes. Educational and Psychological Measurement, 63, 537-553.

The sample effect size is calculated as

d=ˉy1ˉy2(s21+s22)/2

where ˉy1 and ˉy1 are sample means, and s21 and s22 are sample variances of under two different conditions, respectively.

Algina and Keselman (2003) constructed a confidence interval for the population effect size based on a non-central t-distribution. In the method, one first gets the lower and upper bounds of the non-centrality parameter as λL and λU with

λL=t1ncp(t,df=n1,1α/2)

and

λU=t1ncp(t,df=n1,α/2)

where

t=ˉy1ˉy2(s21+s222rs1s2)/n

with r being the correlation.

Now the confidence interval is given by

[λL2(s21+s222rs1s2)n(s21+s22),λU2(s21+s222rs1s2)n(s21+s22)]

effectsize/paired-t-test.txt · Last modified: 2024/09/19 12:24 (external edit)