A guide to obtaining confidence intervals for effect sizes
Effect sizes, specify the magnitude of a statistical comparison. However, this does not tell us how precisely it is measured.
There are [http://www.latrobe.edu.au/psy/esci/ details by Geoff Cumming], Keselman et al (2008) and Steiger (2004) on combining these concepts by giving confidence intervals for effect sizes. Michael Smithson [https://www.anu.edu.au/psychology/people/smithson/details/CIstuff/CI.html has syntax] in SPSS and other statistical software to do the computations. There are also some [https://www.anu.edu.au/psychology/people/smithson/details/CIstuff/Noncoht2.pdf workshop notes] to explain what's going on. See also Smithson (2001).
There is also [http://core.ecu.edu/psyc/wuenschk/SPSS/SPSS-Programs.htm SPSS syntax], with an example, for obtaining a confidence interval for Cohen's d and [:FAQ/Rcis: R syntax] for an alternative more robust nonparametric bootstrap estimate (see for example Keselman et al (2008)) for confidence intervals for Cohens' d and correlations which come from non-Normal distributions.
Keselman et al (2008) have some [http://www.apa.org/journals/supplemental/met_13_2_110/met_13_2_110_supp.html SAS V9.1 code with examples] to produce bootstrap confidence intervals for effect sizes (ie based on repeated random sampling) for a robust (winsorised) version of Cohen's d in mixed anovas (replacing the lowest and highest 20% of outcome data by their respective least extreme values. This paper is available free to CBSUers using the APA internet link.
References
Keselman, HJ, Algina, J, Lix, LM, Wilcox, RR, Deering, KN (2008) A generally robust approach for testing hypotheses and setting confidence intervals for effect sizes Psychological Methods 13(2) 110-129.
Smithson, M (2001) Correct confidence intervals for various regression effect sizes and parameters: the importance of noncentral distributions in computing intervals. Educational and Psychological Measurement 61 605-632.
Steiger, JH (2004) Beyond the F Test: Effect Size Confidence Intervals and Tests of Close Fit in the Analysis of Variance and Contrast Analysis. Psychological Methods 9(2) 164-182.