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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 ...
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 ...
The chi-squared test, when used with the standard approximation that a chi-squared distribution is applicable, has the following assumptions: Simple random sample The sample data is a random sampling from a fixed distribution or population where every collection of members of the population of the given sample size has an equal probability of ...
The chi-square distribution has (k − c) degrees of freedom, where k is the number of non-empty cells and c is the number of estimated parameters (including location and scale parameters and shape parameters) for the distribution plus one.
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 inverse-chi-squared distribution (or inverted-chi-square distribution) is the probability distribution of a random variable whose multiplicative inverse (reciprocal) has a chi-squared distribution. It is also often defined as the distribution of a random variable whose reciprocal divided by its degrees of freedom is a chi-squared distribution.
Relative fit indices (also called “incremental fit indices” and “comparative fit indices”) compare the chi-square for the hypothesized model to one from a “null”, or “baseline” model. This null model almost always contains a model in which all of the variables are uncorrelated, and as a result, has a very large chi-square ...
In statistics, minimum chi-square estimation is a method of estimation of unobserved quantities based on observed data. 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.