# Outlier-Robust Evidence for the Expectation Hypothesis

The test for homogeneity, on the other hand, is designed to test the null hypothesis that two or more , according to some criterion of classification applied to the samples.

## Outlier-Robust Evidence for the Expectation Hypothesis …

### Author Page for Christina V. Atanasova :: SSRN

Smith and Kronforst proposed that the alternative explanations of introgression or ancestral polymorphism could be distinguished by considering absolute divergence within and outside of the loci of interest. Both hypotheses predict an excess of shared derived alleles at affected loci, but introgression should lead to reduced absolute divergence due to more recent coalescence at these loci, whereas the locus-specific population structure hypothesis predicts no reduction in absolute divergence at these loci compared with other loci in the genome. Loci with an excess of shared derived alleles, and therefore showing evidence of shared ancestry, were located by calculating the *D* statistic in nonoverlapping 5-kb windows across genomic regions of interest, and identifying outliers using an arbitrary cutoff (the 10% of windows with the highest *D* values). The mean absolute genetic divergence (*d _{XY}*) was then compared between the outliers and nonoutliers, and found to be significantly lower in outlier windows, consistent with recent introgression (). This method makes two assumptions. First, that the

*D*statistic can accurately identify regions that carry a significant excess of shared variation, and second, that

*D*outliers do not have inherent biases leading to their cooccurrence with regions of low absolute divergence. These assumptions, which extend the use of

*D*beyond its original definition, may be made by other researchers for similar purposes, but they remain to be tested.

### A Random Thought on Outliers and Science | …

This analysis indicates that rejection of the null hypothesis is appropriate because the p-value is lower than 0.05. The probability values for the test of homogeneity of variances indicates that there is not enough information to reject the null hypothesis of equality of variances. No pattern or outlier data are apparent in either the “residuals versus order of the data” or “residuals versus fitted values .” The normal probability plot and histogram indicate that the residuals may not be normally distributed. Perhaps a transformation of the data could improve this fit; however, it is doubtful that any difference would be large enough to be of practical importance .