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The chi-squared distribution has numerous applications in inferential statistics, for instance in chi-squared tests and in estimating variances. It enters the problem of estimating the mean of a normally distributed population and the problem of estimating the slope of a regression line via its role in Student's t-distribution.
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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 .
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. = = The following is Yates's corrected version of Pearson's chi-squared statistics:
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If X 1 and X 2 are independent chi-squared random variables with ν 1 and ν 2 degrees of freedom respectively, then (X 1 /ν 1)/(X 2 /ν 2) is an F(ν 1, ν 2) random variable. If X is a standard normal random variable and U is an independent chi-squared random variable with ν degrees of freedom, then X ( U / ν ) {\displaystyle {\frac {X ...
In probability theory and statistics, the generalized chi-squared distribution (or generalized chi-square distribution) is the distribution of a quadratic function of a multinormal variable (normal vector), or a linear combination of different normal variables and squares of normal variables.