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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%.
This evaluation was additionally motivated by the anticipation that, although the observed conditional Type I error rates of both the main parametric test and the nonparametric test were seriously altered by screening for normality, these results will rarely occur in practice because the Shapiro-Wilk test is very powerful in large samples.
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.
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).
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).
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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.
Further, all outcome data will be screened for normality and, if necessary, logarithmic transformations or non-parametric methods of analysis will be applied.
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