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In statistics, a contingency table (also known as a cross tabulation or crosstab) is a type of table in a matrix format that displays the multivariate frequency distribution of the variables. They are heavily used in survey research, business intelligence, engineering, and scientific research.
The effect of Yates's correction is to prevent overestimation of statistical significance for small data. This formula is chiefly used when at least one cell of the table has an expected count smaller than 5. = = The following is Yates's corrected version of Pearson's chi-squared statistics:
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]
In predictive analytics, a table of confusion (sometimes also called a confusion matrix) is a table with two rows and two columns that reports the number of true positives, false negatives, false positives, and true negatives. This allows more detailed analysis than simply observing the proportion of correct classifications (accuracy).
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 ...
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 Stuart–Maxwell test is different generalization of the McNemar test, used for testing marginal homogeneity in a square table with more than two rows/columns. [12] [13] [14] The Bhapkar's test (1966) is a more powerful alternative to the Stuart–Maxwell test, [15] [16] but it tends to be liberal. Competitive alternatives to the extant ...
= the number of cells in the table. The chi-squared statistic can then be used to calculate a p-value by comparing the value of the statistic to a chi-squared distribution. The number of degrees of freedom is equal to the number of cells , minus the reduction in degrees of freedom, .