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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, . The chi-squared statistic can be also calculated as
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 p-value was first formally introduced by Karl Pearson, in his Pearson's chi-squared test, [39] using the chi-squared distribution and notated as capital P. [39] The p-values for the chi-squared distribution (for various values of χ 2 and degrees of freedom), now notated as P, were calculated in (Elderton 1902), collected in (Pearson 1914 ...
Just as extreme values of the normal distribution have low probability (and give small p-values), extreme values of the chi-squared distribution have low probability. An additional reason that the chi-squared distribution is widely used is that it turns up as the large sample distribution of generalized likelihood ratio tests (LRT). [8]
The p-value was introduced by Karl Pearson [6] in the Pearson's chi-squared test, where he defined P (original notation) as the probability that the statistic would be at or above a given level. This is a one-tailed definition, and the chi-squared distribution is asymmetric, only assuming positive or zero values, and has only one tail, the ...
Modern significance testing is largely the product of Karl Pearson (p-value, Pearson's chi-squared test), William Sealy Gosset (Student's t-distribution), and Ronald Fisher ("null hypothesis", analysis of variance, "significance test"), while hypothesis testing was developed by Jerzy Neyman and Egon Pearson (son of Karl).
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This reduces the chi-squared value obtained and thus increases its p-value. 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. = =