For Patterson's estimator, Figure 2 shows the 5% family–wise error threshold and effective number of tests compared to the permutation procedure, over a uniform grid of 20 marker densities. There is clearly a wide discrepancy and at the current marker density the estimate is an order of magnitude too low: 33,279 compared to 227,838 for the permutation scheme, even though the latter allowed for correlation between chromosomes. The use of P–value thresholds based on this estimator will therefore inflate the false–positive rate. This result is not entirely surprising, as we have previously noted that the effective number of tests, if it exists, is a function of both the significance threshold and also of the type of analysis [Dudbridge and Koeleman, 2004]. Thus, it is not unexpected that an estimator that works well for analysis of population structure is not accurate for Bonferroni corrections.
