title: Graphical tests for Hardy-Weinberg equilibrium based on the ternary plot.
abstract: 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.
  
  
  METHODS
  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.
  
  
  CONCLUSIONS
  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.
authors: Department of Statistics and Operations Research, Universitat Politècnica de Catalunya, Barcelona, Spain. jan.graffelman@upc.edu
authors: Jan
authors: J
authors: Graffelman
authors: Jair Morales
authors: JM
authors: Camarena
mesh_terms: D002892:Chromosomes, Human, Pair 22 / Q000235:genetics; D005787:Gene Frequency; D005838:Genotype; D006579:Heterozygote; D006801:Humans; D015810:Linkage Disequilibrium; D008957:Models, Genetic; D015233:Models, Statistical; D020641:Polymorphism, Single Nucleotide