Tsqlim

Purpose

Calculates PCA confidence limits for Hotelling's T².

Synopsis

tsqcl = tsqlim(m,pc,cl)

tsqcl = tsqlim(model,cl)

Description

Inputs can be in one of two forms:

(a) the number of samples m, the number of principal components used pc, and the fractional confidence limit, cl (0 < cl < 1) which can be a scalar or a vector (to calculate multiple confidence limits simultaneously).

or (b) a standard model structure, model, and the fractional confidence limit, cl (0 < cl < 1).

The output tsqcl is the confidence limit based on an F distribution as shown below. See Jackson (1991).

    $T_{K,M,\alpha }^{2}={\frac {K\left(M-1\right)}{M-K}}{{F}_{K,M-K,\alpha }}$

where $K$ is the number of PCs, $M$ is the number of samples and ${{F}_{K,M-K,\alpha }}$ is the F distribution with $K$ degrees of freedom in the numberator and $M-K$ degrees of freedom in the denominator, and probability point $\alpha$.

Examples

tsqcl = tsqlim(15,2,0.95)

model = pca(data,pc); tsqcl = tsqlim(model,0.95)

See Also

analysis, ftest, pca, pcr, pls