732A37 Multivariate Statistical Methods, Autumn Semester 2015
Computer lab 2: Inference about mean vectors
Based upon the multivariate normal distribution, we will study methods for estimating
and testing mean vectors, comparing mean vectors etc. The methods are the multivariate
generalizations of the corresponding methods in the univariate case
Learning objectives
After reading the recommended text and completing the computer lab the student shall be
able to:
 formally test outliers in a data set
 test a given mean vector
 compute a confidence region (ellipsoid) and simplifications in the form of
simultaneous confidence intervals
 compare two or more mean vectors
Recommended reading
Chapter 4-6 in Johnson-Wichern
Assignment 1: Test of outliers
Consider again the data set in table 1.9, National track records for women. In lab 1 we
studied different distance measures between an observation and the mean vector. The
most common multivariate residual is the Mahalanobis distance and we computed this
distance for all 54 observations.
a) The Mahalanobis distance has an approximate chi square distribution, if the data
come from a multivariate normal distribution and the number of observations is
fairly large. Use the approximate chi square distribution for testing each
observation at significance level 0.1 %, and conclude which countries can be
regarded as outliers.
b) One outlier is North Korea. This country is not at all an outlier with the Euclidean
distance measure. Try to explain these seemingly contradictory results.
Assignment 2: Test, confidence region and confidence intervals for a mean vector
Look at the bird data in table 5.12 and solve exercise 5.20. You may have to make your
own program in order to solve the problem.
Assignment 3: Comparison of mean vectors (one-way Manova)
Consider the Egyptian skull data in table 6.13. We want to compare the mean vectors of
the four variables between the three time periods. Use for example Minitab’s Balanced
Manova for the calculations and solve exercise 6.24
To hand in
Solutions to all three assignments
No later than Wednesday November 25