o What is the "protected F" or least significant difference (LSD) test in MANOVA? How does it relate to the use of discriminant analysis in MANCOVA?
In the second step on MANOVA, when one tests for specific group differences, having established the overall difference among groups using the F test, today the most common method relies on multiple discriminant analysis (MDA) and associated significance tests (ex., Wilks, Hotelling, Pillai-Bartlett, etc.) as discussed above. However, the earlier method, of following a significant MANOVA with a series of ANOVAs on each of the dependent variables, is still used. This traditional method is called the protected F test, the protected t test, or the least significant difference test. Using multiple univariate ANOVA tests at a nominal alpha significance level (ex., .05) is misleading -- the actual significance level will be much higher (that is, > .05), affording less protection against Type I errors (thinking you have something when you don't) than the researcher may be assuming. For this reason, the protected F or LSD method is no longer recommended.
Using discriminant analysis, the MANCOVA dependents are used as predictor variables to classify a factor (treatment) variable, and the discriminant beta weights are used to assess the relative strength of relation of the MANOVA dependents to the factor. The beta weights indicate the strength of relation of a given dependent controlling for all other dependents