Statistics: hotelling_t2test

### Function Reference: `hotelling_t2test`

statistics: [h, pval, stats] = hotelling_t2test (x)
statistics: […] = hotelling_t2test (x, m)
statistics: […] = hotelling_t2test (x, y)
statistics: […] = hotelling_t2test (x, m, Name, Value)
statistics: […] = hotelling_t2test (x, y, Name, Value)

Compute Hotelling’s T^2 ("T-squared") test for a single sample or two dependent samples (paired-samples).

For a sample x from a multivariate normal distribution with unknown mean and covariance matrix, test the null hypothesis that `mean (x) == m`.

For two dependent samples x and y from a multivariate normal distributions with unknown means and covariance matrices, test the null hypothesis that `mean (x - y) == 0`.

`hotelling_t2test` treats NaNs as missing values, and ignores the corresponding rows.

Name-Value pair arguments can be used to set statistical significance. `"alpha"` can be used to specify the significance level of the test (the default value is 0.05).

If h is 1 the null hypothesis is rejected, meaning that the tested sample does not come from a multivariate distribution with mean m, or in case of two dependent samples that they do not come from the same multivariate distribution. If h is 0, then the null hypothesis cannot be rejected and it can be assumed that it holds true.

The p-value of the test is returned in pval.

stats is a structure containing the value of the Hotelling’s T^2 test statistic in the field "Tsq", and the degrees of freedom of the F distribution in the fields "df1" and "df2". Under the null hypothesis, (n-p) T^2 / (p(n-1)) has an F distribution with p and n-p degrees of freedom, where n and p are the numbers of samples and variables, respectively.

See also: hotelling_t2test2

Source Code: hotelling_t2test