Stat 407 Lab 14 MANOVA Fall 2001
In this lab we examine the use S-Plus for multivariate analysis of variance (MANOVA) of the crabs data,
that we studied early on in the course.
1. Based on your memory of previous analyses of this data, guess the relative magnitude of Wilks Λ∗ . Would
you expect it to be close to 0 or close to 1 or in half-way between?
2. Generate histograms of the variables, conditioned on species. Comment on the multivariate normality of
the data, and the homogeneity or lack of it of the group variance-covariance.
3. Compute the overall sample mean, and the means for each Sp.Sex group.
X̄ = [15.6 12.7 32.1 36.4 14.0]0
X̄1 = [14.8 11.7 32.0 36.8 13.4]0
X̄2 = [13.3 12.1 28.1 32.6 11.8]0
X̄3 = [16.6 12.3 33.7 37.2 15.3]0
X̄4 = [17.6 14.8 34.6 39.0 15.6]0
4. Run the MANOVA analysis. Report the results. What hypothesis is this statistic testing? (You will
need to make the variable Sp.Sex a factor, by changing its variable type. Then choose the Statistics− >
Multivariate − > MANOVA. In the MANOVA control panel select FL, RW, CW,CL, BD as the response
variables, and S.Sex as the main effect. In the results tab, choose Wilks as the test statistic, and check the
boxes Short Output, ANOVA table, Estimated Effects. Save the fitted values into a new data set.)
5. What are the Estimated effects, that are computed in the MANOVA analysis?
6. What are the fitted values that are computed in the MANOVA table?
7. Run univariate ANOVA analyses comparing the means on each variable. Report the results. Why is
ANOVA inadequate for comparing the multivariate means? Which variables are the most important in the
mean difference based on the univariate ANOVAs?
8. Write down the numbers to compute the between (B) sums of squares matrix without actually computing
it.
9. Explain how you would compute the within (W) sums of squares matrix, without actually calculating it.
1