Increasingly, authors of research reports are being asked to report, not just effect sizes but confidence intervals (CIs; see e.g., Cumming, 2014, who provides a number of reasons as to why this is desirable). For means and correlations, estimation formulas for the standard errors required to compute CIS are easily found in standard statistics texts (if not always produced by standard statistical packages), but standard errors for the increases in variance accounted for when using hierarchic regression (delta R squared, also called the semipartial correlation coefficient squared) are more problematic.
Algina and colleagues (Algina, Keselman, & Penfield, 2007, 2008, 2010; see also Algina & Moulder, 2001) have shown that large sample formulas based on asymptotic principles (e.g., Olkin & Hedges, 1981; Olkin & Finn, 1995; Alf & Graf, 1999) are typically inaccurate, even with relatively large sample sizes (e.g., 200).
In contrast, they found that determining standard errors with a bootstrap (percentile) methodology (Wilcox, 2003) resulted in accurate confidence intervals even with sample sizes as small as 50 with three or fewer predictors, 100 with six or fewer predictors, “and likely with smaller sizes as well, say 75” (2007, p. 217). My own experience using “real” data (e.g., N = 60, number of predictors = 2–4) is that the percentile bootstrap CIs make sense whereas the asymptotic ones do not.
Researchers like me need an easy way to compute percentile bootstrap CIs, which is why I developed the BootCI program. A stand-alone program, it is designed to be simple and easy to use. It not only produces the CIs researchers need for their reports, it is also designed to be a bit educational. It computes the asymptotic delta R square CIs for comparison, and it also gives computed and bootstrap CIs for means and correlation coefficients so that results of the two methods can be compared for these familiar statistics. Thus users can see for themselves how bootstrapped and computed CIs differ or, as is often the case, do not.
Click here to download bootCI.zip. The ZIP file contains the executable bootCI.exe and and a PDF file that describes the program.
bootCI is written in Embarcadero® Delphi® XE2 Version 16 Pascal. It runs on a PC under Microsoft Windows or a Mac running a PC simulation program.