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The chi-squared distribution is obtained as the sum of the squares of k independent, zero-mean, unit-variance Gaussian random variables. Generalizations of this distribution can be obtained by summing the squares of other types of Gaussian random variables. Several such distributions are described below.
Chi-squared distribution, showing χ2 on the x -axis and p -value (right tail probability) on the y -axis. A chi-squared test (also chi-square or χ2 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 ...
Chi is the basis for the name literary chiastic structure and the name of chiasmus. Symbolism. In Plato's Timaeus, it is explained that the two bands that form the soul of the world cross each other like the letter Χ. Plato's analogy, along with several other examples of chi as a symbol occur in Thomas Browne's discourse The Garden of Cyrus ...
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. [2] [3]
The Pearson's chi-squared test statistic is defined as . The p-value of the test statistic is computed either numerically or by looking it up in a table. If the p-value is small enough (usually p < 0.05 by convention), then the null hypothesis is rejected, and we conclude that the observed data does not follow the multinomial distribution.
chi. 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. Equivalently, it is the distribution of the Euclidean distance between a multivariate Gaussian ...
Pearson's chi-square test. Pearson's chi-square test uses a measure of goodness of fit which is the sum of differences between observed and expected outcome frequencies (that is, counts of observations), each squared and divided by the expectation: where: Oi = an observed count for bin i. Ei = an expected count for bin i, asserted by the null ...
Test statistic is a quantity derived from the sample for statistical hypothesis testing. [1] A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test. In general, a test statistic is selected or ...