Graphical tests for Hardy-Weinberg equilibrium based on the ternary plot

Objective: We design a graphical test for Hardy- Weinberg equilibrium. This can circumvent the calculation of p values and the statistical (non)significance of a large number of bi-allelic markers can be inferred from their position in a graph. Method: By rewriting expressions for the chi(2) statistic ( with and without continuity correction) in terms of the heterozygote frequency an acceptance region for Hardy- Weinberg equilibrium is obtained that can be depicted in a ternary plot. Results: We obtain equations for curves in the ternary plot that separate markers that are out of Hardy- Weinberg equilibrium from those that are in equilibrium. The curves depend on the chosen significance level, the sample size and on a continuity correction parameter. Some examples of graphical tests using a set of 106 SNPs on the long arm of human chromosome 22 are described. Significant markers and poor markers with a lot of missing values are easily identified in the proposed plots. R software for making the diagrams is provided. Conclusion: The proposed graphs can be used as control charts for spotting problematic markers in large scale genotyping studies, and constitute an excellent tool for the graphical exploration of bi-allelic marker data. Copyright (C) 2007 S. Karger AG, Basel.