On the P: drive is a data set called "crabs.csv" with morphological measurements of crabs Leptograpsus variegatus, of two color morphs (orange, or 0, and blue, or B) sampled off the coast of West Australia. The five morphometric measurements taken on each crab were: frontal lobe length (FL), rear width (RW), carapace length (CW), carapace width (CL), and body depth (BD). Each crab was also sexed.
1. Run a MANOVA relating all five of the morphological variables to species, sex, and the interaction between species and sex. Use the residuals from this model to check the assumptions of MANOVA. Specifically, graphically check for nonlinearities, skewness, and use Mahalanobis' distances to check for multivariate outliers.
2. Interpret the results of your MANOVA. Which main effects were significant? Was the interaction significant? What does the interaction tell you about the nature of the differences in morphology between sexes and between species?
3. Conduct a thorough post-hoc procedure. Include both multivariate post-hocs and univariate post-hocs. Remember that if your interaction is significant you need to do these comparisons among combinations of species and sex.
4. Conduct a discriminant analysis on the combinations of color morph and sex, based on the five morphological variables.
5. Interpret the LDA. How many axes were needed to separate the groups? Which groups separate on which axis, and what do the loadings tell you about how they differ (i.e. use the loadings to interpret what the crabs look like on either end of each LD axis)? Present histograms of scores and biplots to support your interpretation.
6. How well did the groups separate? Use a "confusion matrix" to address the degree of non-overlap between the groups. Were there any groups that were completely non-overlapping with the others, or were all of them sometimes misclassified as another group? How much better than random chance were you able to predict the groups based on their morphologies? Where were the misclassifications, and what do they tell you about which groups are the least distinct?
7. Discuss how your DFA and MANOVA results were complementary ways of understanding the data. What did DFA tell you that MANOVA didn't, and vice versa?
Attachment:- crabs.rar