HotellingT2One Routine

Summary

One-sample Hotelling T2 test.

Declaration

Function HotellingT2One(X: TMtx; Means: TVec; out Signif: TSample; out hRes: THypothesisResult; Alpha: TSample = 0.05): TSample;

Parameter	Description
Data	Stores test values, each row representing different case and each column representing different response variable. The assumption is data is approximately multivariate normal.
Means	Stores estimated mean for each variable. An exception is raised if Means Length is not equal to Data columns. If Means is nil, the assumption is means are equal.
Signif	(Significance level) returns the probability of observing the given result by chance given that the null hypothesis is true.
hRes	Returns the result of the null hypothesis (default assumption is variable means are equal to Means vector).
Alpha	Defines the desired significance level. If the significance probability (Signif) is bellow the desired significance (Alpha), the null hypothesis is rejected.

Result

Hotelling T2 Statistics for one-sample test.

Description

Performs one-sample Hotelling T2 test. The one-sample T2 is used to test hypotheses about a set of means simultaneously. The null hypothesis is that sample means are equal to Means vector values. The following assumptions are made when using T2:

The population follows the multivariate normal distribution.
The members of the sample are independent.

The one-sample T2 test may also be applied to the situation in which two samples are to be compared that had a natural pairing between two observation vectors. In this case the differences between the first and second measurements are formed and then used as data in unpaired Hotelling T2 test.