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The example above is the simplest kind of contingency table, a table in which each variable has only two levels; this is called a 2 × 2 contingency table. In principle, any number of rows and columns may be used. There may also be more than two variables, but higher order contingency tables are difficult to represent visually.
Mid-p exact p-values and confidence limits for the odds ratio; Calculations of rate ratios and rate differences with confidence intervals and statistical tests. For stratified 2x2 tables with count data, OpenEpi provides: Mantel-Haenszel (MH) and precision-based estimates of the risk ratio and odds ratio; Precision-based adjusted risk difference
Risk difference can be estimated from a 2x2 contingency table: Group Experimental (E) Control (C) ... Value Absolute risk increase ARI EER − CER: 0.1, or 10%
Boschloo's test is a statistical hypothesis test for analysing 2x2 contingency tables. It examines the association of two Bernoulli distributed random variables and is a uniformly more powerful alternative to Fisher's exact test .
The values 1 and 0; the values 1 and −1, often simply abbreviated by + and −; A lower-case letter with the exponent 0 or 1. If these values represent "low" and "high" settings of a treatment, then it is natural to have 1 represent "high", whether using 0 and 1 or −1 and 1. This is illustrated in the accompanying table for a 2×2 experiment.
Value Absolute risk increase ARI EER − CER: 0.1, or 10% Number needed to harm: NNH 1 / (EER − CER) 10 Relative risk (risk ratio) RR EER / CER: 1.25 Relative risk increase RRI (EER − CER) / CER, or RR − 1 0.25, or 25% Attributable fraction among the exposed: AF e (EER − CER) / EER: 0.2 Odds ratio: OR (EE / EN) / (CE / CN) 1.5
The McNemar's test is a special case of the Cochran–Mantel–Haenszel test; it is equivalent to a CMH test with one stratum for each of the N pairs and, in each stratum, a 2x2 table showing the paired binary responses. [18] Multinomial confidence intervals are used for matched pairs binary data.
Under specious pressure from Fisher, Barnard retracted his test in a published paper, [8] however many researchers prefer Barnard’s exact test over Fisher's exact test for analyzing 2 × 2 contingency tables, [9] since its statistics are more powerful for the vast majority of experimental designs, whereas Fisher’s exact test statistics are conservative, meaning the significance shown by ...