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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.
where is the grand mean, is the additive main effect of level from the first factor (i-th row in the contingency table), is the additive main effect of level from the second factor (j-th column in the contingency table) and is the non-additive interaction effect of treatment (,) for samples =,..., from both factors (cell at row i and column j ...
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 ...
For hand calculations, the test is feasible only in the case of a 2 × 2 contingency table. However the principle of the test can be extended to the general case of an m × n table, [8] [9] and some statistical packages provide a calculation (sometimes using a Monte Carlo method to obtain an approximation) for the more general case. [10]
McNemar's test is a statistical test used on paired nominal data.It is applied to 2 × 2 contingency tables with a dichotomous trait, with matched pairs of subjects, to determine whether the row and column marginal frequencies are equal (that is, whether there is "marginal homogeneity").
We consider a binary outcome variable such as case status (e.g. lung cancer) and a binary predictor such as treatment status (e.g. smoking). The observations are grouped in strata. The stratified data are summarized in a series of 2 × 2 contingency tables, one for each stratum. The i-th such contingency table is:
A chi-squared test (also chi-square or χ 2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily used to examine whether two categorical variables ( two dimensions of the contingency table ) are independent in influencing the test statistic ...
The TOC curve with four boxes indicates how a point on the TOC curve reveals the hits, misses, false alarms, and correct rejections. The TOC curve is an effective way to show the total information in the contingency table for all thresholds. The data used to create this TOC curve is available for download here. This dataset has 30 observations ...