BIO 510/710 Biostatistics Frederick
Testing for Normality: SAS Proc Univariate and Analyst
Objective: To complete home work problems 6.1 (parts a and b ) and 6.5 (Kolmogorov-
Smirnov: an alternative to the D’Agostino - Pearson test).
Introduction: Because common parametric statistical analyses require data be
distributed normally, it is common to test data for their adherence to the normal
distribution before the parametric tests and their associated probabilities are relied
upon. In Chapter 6 of the Zar text, we find we can calculate the g1 statistic for
symmetry (estimates the “gamma one” parameter), where a value near 0 indicates
symmetry, a negative value indicates data skewed to the left (mean less than median),
and a positive value indicates data skewed to the right (see figure 3.2). The g2 statistic
indicates kurtosis (0 = mesokurtic, <0 = platykurtic, >0 = leptokurtic). The hand
calculation for g1 is somewhat tedious, and g2 is even worse. Luckily, SAS will calculate
these values easily under Proc Univariate, which can also be done via the Analyst
utility.
Significant asymmetry or significant deviations from mesokurtosis result in data
unsuitable for parametric analysis. A single test statistic for how well data fit the normal
distribution is a more popular means than the individual tests for symmetry or kurtosis.
Zar recommends the D’Agostino - Pearson test, but SAS uses other tests, like the
Kolmogorov - Smirnov test instead. Data are considered no different than normal
unless we have significant reason to reject that null hypothesis (e.g., P<0.05).
Homework Exercise 6.1 a and b, and Exercise 6.5: Calculate the g1 and g2 statistics
and the SAS tests for normality by using Proc Univariate. You may use the frequencies
of observations in Proc Univariate by using the Freq command. Enter the program
below into the editor window and submit it. The Normal and Plot options will produce
the tests for normality and will provide some standard plots of your data. Find the g1
and g2 statistics and circle and label them as your answers to 6.1 a and b. Compare
the results from the SAS tests for normality with the answer to exercise 6.5 given by Zar
(note the two do NOT use the same test).
data weight;
title Exercise 6.1 and 6.5 in Zar - <your name here>;
input mass numobs;
cards;
4.0 2
4.3 3
4.5 5
4.6 8
4.7 6
4.8 5
4.9 4
5.0 3
5.1 1
;
proc univariate normal plot;
freq numobs;
run;
Enter the data in the Analyst table, then use Statistics, Descriptive, and Distributions to
do the same test.
