For two samples x from multivariate normal distributions with the same number of variables (columns), unknown means and unknown equal covariance matrices, test the null hypothesis mean (x) == mean (y).

hotelling_t2test2 treats NaNs as missing values, and ignores the corresponding rows for each sample independently.

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

If h is 1 the null hypothesis is rejected, meaning that the tested samples 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 both samples come from the same multivariate distribution.

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 "t2stat", its F transform in "fstat", and the degrees of freedom of the F distribution in the fields "df1" and "df2". Under the null hypothesis, $$ {(n_x+n_y-p-1) T^2 \over p(n_x+n_y-2)} $$ has an F distribution with p and n_x+n_y-p-1 degrees of freedom, where n_x and n_y are the sample sizes and p is the number of variables.

The effect size is the Mahalanobis distance D between the two means, in the field "MahalanobisD", with its 100 (1 - alpha)% confidence interval in "MahalanobisDCI". The noncentrality of the F statistic is n_x n_y / (n_x + n_y) D^2; the distance is estimated from max (F df1 (df2 - 2) / df2 - df1, 0), unbiased for the noncentrality before its truncation at zero, and the interval inverts the noncentral F distribution. Where the interval would need a noncentrality above 10^5, where ncfcdf loses accuracy, it is NaN.

See also: hotelling_t2test

Source Code: hotelling_t2test2