Regression to the Mean Mimicking Changes in Sexual Arousal to Child Stimuli in Pedophiles

Abstract

The sexual preference for prepubertal children (pedophilia) is generally assumed to be a lifelong condition. Müller et al. (2014) challenged the notion that pedophilia was stable. Using data from phallometric testing, they found that almost half of 40 adult pedophilic men did not show a corresponding arousal pattern at retest. Critics pointed out that regression to the mean and measurement error might account for these results. Müller et al. contested these explanations. The present study shows that regression to the mean in combination with low reliability does indeed provide an exhaustive explanation for the results. Using a statistical model and an estimate of the retest correlation derived from the data, the relative frequency of cases with an allegedly non-pedophilic arousal pattern was shown to be consistent with chance expectation. A bootstrap simulation showed that this outcome was to be expected under a wide range of retest correlations. A re-analysis of the original data from the study by Müller et al. corroborated the assumption of considerable measurement error. Therefore, the original data do not challenge the view that pedophilic sexual preference is stable.

Appendix

A bootstrap test was performed in order to estimate the retest correlation in the whole sample (ρ _tt) based on which a sub-sample correlation of r _tt = .24 could be expected. For this purpose, 200 bootstrap samples of size N = 124 were drawn from a bivariate standard normal deviation with correlation ρ _tt. Values of ρ _tt were set to vary in increments of .05 ranging from .00 to 1.00. The size of the bootstrap samples was estimated from the bivariate standard normal model above: If the 40 cases selected by Müller et al. (2014; cf. Fedoroff et al., 2015) correspond to 32 % of the cumulative probability density, then about 124 cases will make up the entire sample.

The correlation coefficients between the bootstrap draws were calculated mutually (i.e., for the 19,900 non-redundant pairs for each value of ρ _tt). This was done following the restrictions applied by Müller et al. (2014; i.e., score on the first variable ≥0.25, score on the second variable ≤−0.25 or ≥0.25). Table 1 contains the bootstrap results.

Table 1 Bootstrap results: 200 draws from a bivariate standard normal probability density function at different levels of test–retest reliability ρ _tt: means and 95 % CIs of sub-group test–retest reliability r _tt

At ρ _tt = .30, for instance, the mean r _tt of the bootstrap samples was .23, with a 95 % bootstrap CI of [−.08, .50]. As Table 1 shows, however, all values of ρ _tt from .00 to .60 were in agreement with an r _tt value of .24 in the selected sub-sample. Only for ρ _tt values of .65 and above, the concomitant 95 % bootstrap CIs would not contain the value of .24 anymore.