third row. We continue this procedure until we find a row at which the obtained pvalue in
column 4 exceeds the critical pvalue in column 5. At that point we declare that correlation
to be nonsignificant and stop testing. All correlations below that point are likewise classed
as nonsignificant. For our data, those correlations equal to or greater than .30 are declared
significant, and those below .30 are nonsignificant. The significant correlations are indi-
cated with an asterisk in the table.
Had we used a standard Bonferroni test, we would have set 5 .05 21 5 .00238, and
a correlation less than .37 would not have been significant. In this particular case the multi-
stage test made only a small difference. But often the difference is substantial in terms of
the number of coefficients that are declared significant.Trimmed Means
I want to include one more approach that is very general and can be shown to be more pow-
erful than standard procedures when the data come from long-tailed distributions. This is
the use of trimmed means. The nice thing about this approach is that it can be adapted to
carry out any of the procedures in this chapter, simply by substituting the appropriate
trimmed means and squared standard errors.
I will assume that you have reasonably large sample sizes because we will trim those
samples from each end. Wilcox recommends 20% trimming, which results in a sizable drop
in the effective sample size, but with a corresponding gain in power. For convenience, assume
that we have 40 observations in each of several groups and that we will go along with
Wilcox’s suggestion of 20% trimming. That means that we will omit the lowest (.20)(40) 58
observations and the highest 8 observations, leaving us with a sample of 24 observations for
each condition. The trimmed means will be the means of those 24 observations in each group.a¿ >12.3 A Priori Comparisons 383Table 12.5 Significance tests for correlations in Table 12.4
Pair i Correlation pvalue a/(k 2 i 1 1)
1 vs. 2 1 .69 .0000 .00238*
3 vs. 4 2 .62 .0000 .00250*
1 vs. 3 3 .48 .0000 .00263*
5 vs. 7 4 .44 .0000 .00278*
2 vs. 4 5 .42 .0000 .00294*
2 vs. 6 6 .39 .0001 .00313*
2 vs. 3 7 .38 .0001 .00333*
1 vs. 4 8 .37 .0002 .00357*
1 vs. 6 9 .30 .0028 .00385*
4 vs. 6 10 .24 .0179 .00417
6 vs. 7 11 .23 .0236 .00455
3 vs. 6 12 .22 .0302 .00500
4 vs. 7 13 .20 .0495 .00556
2 vs. 7 14 .19 .0618 .00625
2 vs. 5 15 .12 .2409 .00714
5 vs. 6 16 .11 .2829 .00833
3 vs. 5 17 .07 .4989 .01000
3 vs. 7 18 .07 .4989 .01250
1 vs. 7 19 .03 .7724 .01667
1 vs. 5 20 2 .02 .8497 .02500
4 vs. 5 21 .00 1.0000 .05000
*p,.05