Chi‐Square, Partition of

摘要: A chi-square statistic suitable for testing a primary hypothesis can be partitioned into components such that each component gives test corresponding secondary hypothesis. Some partitionings are exact and some approximate. The theory is based on the Fisher–Cochran theorem about decomposing quadratic functions of normal variables. history this technique surveyed. Applications described contingency tables, with main focus two-way table likelihood-ratio statistics. Brief mention also made partitioning non-chi-square components, as decomposition forms basis correspondence analysis. Keywords: contingency tables; correspondence analysis; R. A. Fisher; independence; likelihood-ratio statistic; Pearson statistic; quadratic form