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  2. Chi-squared test - Wikipedia

    en.wikipedia.org/wiki/Chi-squared_test

    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 ...

  3. Chi-squared distribution - Wikipedia

    en.wikipedia.org/wiki/Chi-squared_distribution

    The simplest chi-squared distribution is the square of a standard normal distribution. So wherever a normal distribution could be used for a hypothesis test, a chi-squared distribution could be used. Suppose that Z {\displaystyle Z} is a random variable sampled from the standard normal distribution, where the mean is 0 {\displaystyle 0} and the ...

  4. Pearson's chi-squared test - Wikipedia

    en.wikipedia.org/wiki/Pearson's_chi-squared_test

    For the test of independence, also known as the test of homogeneity, a chi-squared probability of less than or equal to 0.05 (or the chi-squared statistic being at or larger than the 0.05 critical point) is commonly interpreted by applied workers as justification for rejecting the null hypothesis that the row variable is independent of the ...

  5. Contingency table - Wikipedia

    en.wikipedia.org/wiki/Contingency_table

    Interactive cross tabulation, chi-squared independent test, and tutorial; Fisher and chi-squared calculator of 2 × 2 contingency table ; More Correlation Coefficients; Nominal Association: Phi, Contingency Coefficient, Tschuprow's T, Cramer's V, Lambda, Uncertainty Coefficient, March 24, 2008, G. David Garson, North Carolina State University

  6. Chi distribution - Wikipedia

    en.wikipedia.org/wiki/Chi_distribution

    In probability theory and statistics, the chi distribution is a continuous probability distribution over the non-negative real line. It is the distribution of the positive square root of a sum of squared independent Gaussian random variables .

  7. One- and two-tailed tests - Wikipedia

    en.wikipedia.org/wiki/One-_and_two-tailed_tests

    p-value of chi-squared distribution for different number of degrees of freedom. 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 ...

  8. Chi-square - Wikipedia

    en.wikipedia.org/wiki/Chi-square

    The term chi-square, chi-squared, or has various uses in statistics: chi-square distribution, a continuous probability distribution; chi-square test, name given to some tests using chi-square distribution; chi-square target models, a mathematical model used in radar cross-section

  9. Goodness of fit - Wikipedia

    en.wikipedia.org/wiki/Goodness_of_fit

    The chi-square distribution has (k − c) degrees of freedom, where k is the number of non-empty bins and c is the number of estimated parameters (including location and scale parameters and shape parameters) for the distribution plus one.