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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 ...
PGF. In probability theory and statistics, the chi-squared distribution (also chi-square or -distribution) with degrees of freedom is the distribution of a sum of the squares of independent standard normal random variables. The chi-squared distribution is a special case of the gamma distribution and the univariate Wishart distribution.
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 ...
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.
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]
SMART criteria. S.M.A.R.T. (or SMART) is an acronym used as a mnemonic device to establish criteria for effective goal-setting and objective development. This framework is commonly applied in various fields, including project management, employee performance management, and personal development.
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