manova1
One-way multivariate analysis of variance (MANOVA).
d = manova1 (x, group, alpha) performs a
one-way MANOVA for comparing the mean vectors of two or more groups of
multivariate data.
x is a matrix with each row representing a multivariate observation, and each column representing a variable.
group is a numeric vector, string array, or cell array of strings with the same number of rows as x. x values are in the same group if they correspond to the same value of GROUP.
alpha is the scalar significance level and is 0.05 by default.
d is an estimate of the dimension of the group means. It is the smallest dimension such that a test of the hypothesis that the means lie on a space of that dimension is not rejected. If d = 0 for example, we cannot reject the hypothesis that the means are the same. If d = 1, we reject the hypothesis that the means are the same but we cannot reject the hypothesis that they lie on a line.
[d, p] = manova1 (…) returns P, a vector of p-values
for testing the null hypothesis that the mean vectors of the groups lie on
various dimensions. P(1) is the p-value for a test of dimension 0, P(2) for
dimension 1, etc.
[d, p, stats] = manova1 (…) returns a STATS
structure with the following fields:
| "W" | within-group sum of squares and products matrix | |
| "B" | between-group sum of squares and products matrix | |
| "T" | total sum of squares and products matrix | |
| "dfW" | degrees of freedom for WSSP matrix | |
| "dfB" | degrees of freedom for BSSP matrix | |
| "dfT" | degrees of freedom for TSSP matrix | |
| "lambda" | value of Wilk’s lambda (the test statistic) | |
| "chisq" | transformation of lambda to a chi-square distribution | |
| "chisqdf" | degrees of freedom for chisq | |
| "eigenval" | eigenvalues of (WSSP^-1) * BSSP | |
| "eigenvec" | eigenvectors of (WSSP^-1) * BSSP; these are the coefficients for canonical variables, and they are scaled so the within-group variance of C is 1 | |
| "canon" | canonical variables, equal to XC*eigenvec, where XC is X with columns centered by subtracting their means | |
| "mdist" | Mahalanobis distance from each point to its group mean | |
| "gmdist" | Mahalanobis distances between each pair of group means | |
| "gnames" | Group names |
The canonical variables C have the property that C(:,1) is the linear combination of the x columns that has the maximum separation between groups, C(:,2) has the maximum separation subject to it being orthogonal to C(:,1), and so on.
Source Code: manova1
load carbig
[d,p] = manova1([MPG, Acceleration, Weight, Displacement], Origin)
d = 3
p =
0
0.0000
0.0075
0.1934
|