Data were initially screened for normality and homogeneity of variance prior to analysis of variance (ANOVA).
Data were screened for normality of distribution and homogeneity of variances using a Shapiro-Wilk normality test and the Barlett's test, respectively.
The data for both groups was screened for normality of distribution using Wilks-Shapiro W statistics.
Prior to analysis all measures were screened for normality and no significant violations found.
Groups were pre-screened for normality and compared with either a Student's t test or Mann-Whitney U test.
This procedure was repeated until 10,000 pairs of samples had passed the preliminary screening for normality (either Strategy I or II, with α pre = .100,.050,.010,.005, or no pretest).
Further, all outcome data will be screened for normality and, if necessary, logarithmic transformations or non-parametric methods of analysis will be applied.
Surprisingly and in remarkable contrast to the results observed for Strategy I, samples from the uniform distribution that had passed screening for normality of residuals also led to conditional Type I error rates that were far above 5%.
The first strategy required both samples to pass the preliminary screening for normality to proceed with the two-sample t test; otherwise, we used Mann-Whitney's U test.
In a second run, sample generation was repeated until 10,000 pairs were collected that had failed preliminary screening for normality (Strategy I or II), and the conditional Type I error was estimated for Mann-Whitney's U test (right part of Additional file 1).
