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Chi-squared distribution, showing χ2 on the x -axis and p -value (right tail probability) on the y -axis. A chi-squared test (also chi-square or χ2 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 ...
Usage. Pearson's chi-squared test is used to assess three types of comparison: goodness of fit, homogeneity, and independence. A test of goodness of fit establishes whether an observed frequency distribution differs from a theoretical distribution. A test of homogeneity compares the distribution of counts for two or more groups using the same ...
The p-value for the significance of V is the same one that is calculated using the Pearson's chi-squared test. [citation needed] The formula for the variance of V=φ c is known. [3] In R, the function cramerV() from the package rcompanion [4] calculates V using the chisq.test function from the stats package.
In probability theory and statistics, the chi-squared distribution (also chi-square or -distribution) with degrees of freedom is the distribution of a sum of the squares of independent standard normal random variables. The chi-squared distribution is a special case of the gamma distribution and the univariate Wishart distribution.
p. -value. In null-hypothesis significance testing, the -value[note 1] is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. [2][3] A very small p -value means that such an extreme observed outcome would be very unlikely under the null hypothesis.
Reduced chi-squared statistic. In statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD) in isotopic dating [1] and variance of unit weight in the context of weighted least squares. [2][3] Its square root is called regression standard error, [4 ...
The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. Such measures can be used in statistical hypothesis testing, e.g. to test for normality of residuals, to test ...
Chi-square automatic interaction detection (CHAID) [1][2][3] is a decision tree technique based on adjusted significance testing (Bonferroni correction, Holm-Bonferroni testing). The technique was developed in South Africa in 1975 and was published in 1980 by Gordon V. Kass, who had completed a PhD thesis on this topic.