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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. Proofs related to chi-squared distribution - Wikipedia

    en.wikipedia.org/wiki/Proofs_related_to_chi...

    There are several methods to derive chi-squared distribution with 2 degrees of freedom. ... The chi square distribution for k degrees of freedom will then be given by ...

  4. Pearson's chi-squared test - Wikipedia

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

    Pearson's chi-squared test or Pearson's test is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance. It is the most widely used of many chi-squared tests (e.g., Yates , likelihood ratio , portmanteau test in time series , etc.) – statistical ...

  5. 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 ...

  6. Yates's correction for continuity - Wikipedia

    en.wikipedia.org/wiki/Yates's_correction_for...

    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.

  7. Goodness of fit - Wikipedia

    en.wikipedia.org/wiki/Goodness_of_fit

    The resulting value can be compared with a chi-square distribution to determine the 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

  8. Reduced chi-squared statistic - Wikipedia

    en.wikipedia.org/wiki/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 .

  9. Minimum chi-square estimation - Wikipedia

    en.wikipedia.org/wiki/Minimum_chi-square_estimation

    In statistics, minimum chi-square estimation is a method of estimation of unobserved quantities based on observed data. [1]In certain chi-square tests, one rejects a null hypothesis about a population distribution if a specified test statistic is too large, when that statistic would have approximately a chi-square distribution if the null hypothesis is true.