# Confidence interval for effect size for a within-subjects t-test

does anyone have a suggestion for an expedient way to calculate confidence intervals on effect sizes (cohen's D) for dependent-samples (edit: within-subjects) t-tests?

For a meta-analysis, I've extracted results for multiple papers. All use the same design: within-subjects designs in which each subject receives Treatment 1 and Treatment 2. A t-test is run to determine whether there is a difference in performance between Treatment 1 and Treatment 2. I have the sample size, the t-statistic, and used that to calculate cohen's D.

Now I am looking for a fast way to calculate the 95% CI on those d values. Online calculators, Excel calculators, and R packages that I've attempted all specify independent samples designs (Group 1 vs. Group 2). The data I have are one-sample designs...

Thanks in advance for any help!

• By "dependent samples" do you mean paired samples? If, so you would treat each pair as a case and it becomes a one-sample t-test. $\qquad$ – Michael Hardy Jul 3 '16 at 3:10
• I meant a within-subjects design, so yes it is a one-sample t-test (on difference scores). So, I can get cohen's D for that t-statistic...and now I'm looking for a fast automated way to put 95% CIs on those cohen's Ds...(I have many of these one-sample t-test values and cohen's D for each)... – Altair555 Jul 3 '16 at 3:52
• The key thing I appear to need to calculate the 95% CI for d is a fast way to find the two values of the non-centrality parameter of the t-distribution, so that the observed t-value cuts off .025 in the lower and upper tails of the distribution... – Altair555 Jul 3 '16 at 5:46