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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 ...
In statistics, Yates's correction for continuity (or Yates's chi-squared test) is used in certain situations when testing for independence in a contingency table.
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 ...
The name "chi-square" ultimately derives from Pearson's shorthand for the exponent in a multivariate normal distribution with the Greek letter Chi, writing −½χ 2 for what would appear in modern notation as −½x T Σ −1 x (Σ being the covariance matrix). [27]
Sample ratio mismatches also known as unbalanced sampling [1] often occur in online controlled experiments due to failures in randomization and instrumentation. [2] Sample ratio mismatches can be detected using a chi-squared test. [3] Using methods to detect SRM can help non-experts avoid making discussions using biased data. [4]
There are several methods to derive chi-squared distribution with 2 degrees of freedom. Here is one based on the distribution with 1 degree of freedom.
where and are the same as for the chi-square test, denotes the natural logarithm, and the sum is taken over all non-empty bins. Furthermore, the total observed count should be equal to the total expected count: ∑ i O i = ∑ i E i = N {\displaystyle \sum _{i}O_{i}=\sum _{i}E_{i}=N} where N {\textstyle N} is the total number of observations.
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