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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.
For small sample sizes, might be significantly lower than 5%. [13] [14] [15] While this effect occurs for any discrete statistic (not just in contingency tables, or for Fisher's test), it has been argued that the problem is compounded by the fact that Fisher's test conditions on the marginals. [18]
This formula is chiefly used when at least one cell of the table has an expected count smaller than 5. ∑ i = 1 N O i = 20 {\displaystyle \sum _{i=1}^{N}O_{i}=20\,} The following is Yates's corrected version of Pearson's chi-squared statistics :
Chi-squared distribution, showing χ 2 on the x-axis and p-value (right tail probability) on the y-axis. 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.
The sample odds ratio n 11 n 00 / n 10 n 01 is easy to calculate, and for moderate and large samples performs well as an estimator of the population odds ratio. When one or more of the cells in the contingency table can have a small value, the sample odds ratio can be biased and exhibit high variance.
The sample data is a random sampling from a fixed distribution or population where every collection of members of the population of the given sample size has an equal probability of selection. Variants of the test have been developed for complex samples, such as where the data is weighted.
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").
Four bits of information determine all the entries in the contingency table, including its marginal totals. For example, if we know H, M, F, and C, then we can compute all the marginal totals for any threshold. Alternatively, if we know H/P, F/Q, P, and Q, then we can compute all the entries in the table. [1]
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