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)...

Pearson's chi-squared test or Pearson's χ 2 {\displaystyle \chi ^{2}} test is a statistical test applied to sets of categorical data to evaluate how likely...

a chi-squared distribution:   X   ∼   χ 1 2 {\displaystyle \ X\ \sim \ \chi _{1}^{2}} . The subscript 1 indicates that this particular chi-squared distribution...

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...

analysis, the term "standard error" refers either to the square root of the reduced chi-squared statistic or the standard error for a particular regression coefficient...

That fact, and the normal and chi-squared distributions given above form the basis of calculations involving the t-statistic: T = X ¯ n − μ 0 S n / n , {\displaystyle...

Lack-of-fit sum of squares Mean squared error Reduced chi-squared statistic, RSS per degree of freedom Squared deviations Sum of squares (statistics) Archdeacon...

replaced by an estimate, the reduced chi-squared statistic, based on the minimized value of the residual sum of squares (objective function), S. The denominator...

error Mean square quantization error Reduced chi-squared statistic Mean squared displacement Mean squared prediction error Minimum mean square error Overfitting...

residuals we can estimate the sample variance s2 using the reduced chi-squared statistic: s 2 = ε ^ T ε ^ n − p = ( M y ) T M y n − p = y T M T M y n...

statistic is too large, when that statistic would have approximately a chi-square distribution if the null hypothesis is true. In minimum chi-square estimation...

proportion). Chi-squared tests use the same calculations and the same probability distribution for different applications: Chi-squared tests for variance...

statistics, Yates's correction for continuity (or Yates's chi-squared test) is a statistical test commonly used when analyzing count data organized in...

see Least squares For the "sum of squared differences", see Mean squared error For the "sum of squared error", see Residual sum of squares For the "sum...

Propagation of uncertainty Percentile Raw data Reduced chi-squared statistic Robust standard deviation Root mean square Sample size Samuelson's inequality Six...

"R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s). It is a statistic used...

observations, the score statistic is the same as the chi-squared statistic in the Pearson's chi-squared test. Fisher information Uniformly most powerful test...

of the test statistic − 2 log ⁡ ( Λ ) {\displaystyle -2\log(\Lambda )} asymptotically approaches the chi-squared ( χ 2 {\displaystyle \chi ^{2}} ) distribution...

test, a quality of fit statistic that can be used for binary data Pearson's chi-squared test, an alternative quality of fit statistic for generalized linear...

England. Although its mathematical form is similar to a chi-squared test, is not a true statistical test. Rather, it is an empirical formula that has proven...

associated with the squared lengths (or "sum of squares" of the coordinates) of such vectors, and the parameters of chi-squared and other distributions...

two degrees of freedom, follows a chi-squared distribution with 2k degrees of freedom. Dependence among statistical tests is generally[vague] positive...

samples, as in the case of Pearson's chi-squared test. Thus computing a p-value requires a null hypothesis, a test statistic (together with deciding whether...

parentheses indicates the ith order statistic of the sample. The first order statistic (or smallest order statistic) is always the minimum of the sample...

t-test could be used. A generalization of Student's t statistic, called Hotelling's t-squared statistic, allows for the testing of hypotheses on multiple...

minimum-distance estimation. The chi-square test uses as its criterion the sum, over predefined groups, of the squared difference between the increases...

cumulative distribution functions of the Poisson and chi-squared distributions. The chi-squared distribution is itself closely related to the gamma distribution...

scaled-inverse-chi-squared distribution with parameters ν {\displaystyle \nu } and   τ 2   . {\displaystyle \ \tau ^{2}~.} The scaled-inverse-chi-squared distribution...

a statistic computed on a sample dataset in relation to a parametric model of the dataset. It is opposed to the concept of an ancillary statistic. While...

observation. In any case, σ2 is approximated by the reduced chi-squared χ ν 2 {\displaystyle \chi _{\nu }^{2}} : M β = χ ν 2 ( X T W X ) − 1 , χ ν 2 =...