This dataset contains information on six continuous dependent variables along with a single discrete variable School Type, which distinguishes between research universities and liberal arts institutions. Twenty-five of each type of school were surveyed. We will use MANOVA to determine if the school types differ across all six dependent variables simultaneously.
A plot matrix of all six dependent variables along with normal probability plots for each variable are used to determine if the dependent variables have a multivariate normal distribution. The plots show that there are normality problems with the variables $/Student, %PhD, and Grad%. An inverse transformation on $/Student corrects the problem with that variable, which we now call Students/$. Since %PhD and %Grad are both fractions, we use the Tukey Lambda family of folded power transformations in an attempt to make them more normal. First, we must divide the raw data in these variables by 100 to make their ranges 0 to 1 rather than 0 to 100. A lambda value of .41667 for each variable seems to make both variables roughly normal. This value of lambda corresponds roughly to the angular transformation.
A MANOVA of the transformed data with School Type as the factor reveals that there is a significant difference between research universities and liberal arts colleges at the 5% level. The more interesting question is: Among which dependent variables do the differences occur? To answer this question, we perform six ANOVA analyses, one for each dependent variable, against the factor School Type. These analyses show that the differences lie in the dependent variables Students/$, %PhD, and Top10%. Post-hoc tests allow us to determine the which school type has the higher mean for these variables. The results show that universities have more PhD's and Top 10% students. The liberal arts colleges have more students per $, which means that the universities spend more per student.