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For two alleles, the chi-squared goodness of fit test for Hardy–Weinberg proportions is equivalent to the test for inbreeding, =. The inbreeding coefficient is unstable as the expected value approaches zero, and thus not useful for rare and very common alleles.
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.
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. = =
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 ...
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 ...
The square of a standard normal random variable has a chi-squared distribution with one degree of freedom. If X is a Student’s t random variable with ν degree of freedom, then X 2 is an F (1,ν) random variable. If X is a double exponential random variable with mean 0 and scale λ, then |X| is an exponential random variable with mean λ.
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 .
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.