Advanced Statistics  Biology 6030 
Bowling Green State University, Fall 2019 
With equality of population means for dependent groups also means any linear combinations should be equal for all groups  both of these are evaluated in MANOVA. Correlations between depedent variables indicate partial redundance of information and results obtained will pertain to an overlap of concepts to be explained.
Univariate FTests obtain the ratio of variance explained by the model over the error variance. In multivariate Analysis of variance these single variance terms are replaced by a Model VarianceCovariance Matrix over an Error Variance Covariance Matrix.
In R you first need to import datafile "BodyMeasures.txt", define n to represent the sample size, and group your response variables into a set using cbind.
Perform a MANOVA, report Pillai's trace, and include univariate tests on each measure
Obtain the Matrix of error sums of squares and crossproducts (E) and the Matrix of model sums of squares and crossproducts (H) and report them
You can obtain for the Eigenvalues after solving H for E and the Eigenvectors via lda (which requires library MASS).
You can get a canonical centroid plot of this ananlysis using procedure cca (which requires library vegan).
