Statistical Analysis for Education and Psychology Researchers

in teachers’ perceptions about student misbehaviour before and after the intervention
because the correlation between pre- and post-intervention measures is low (r=.37) The t-
test only provides information about overall means and not about change in perceptions
for individual teachers. It is possible that teachers’ scores had changed in different
directions, some improved and some reduced and the effect of these changes might
cancel out—resulting in no overall average change. Perhaps supplementary analyses are
required to detect individual changes, these may be more informative than the average
effects.

5.5 Checking for Normality

Parametric statistical procedures are based on the assumption of underlying normality in
the population from which a sample is selected. Whereas many univariate test statistics
such as t- and F-tests are said to be robust (not drastically affected by moderate
departures from underlying assumptions of normality and homogeneity of variance)
Boneau (1960) and more recently Bradley (1984) have questioned this assumption of
robustness. Monte Carlo studies (repeated sampling and testing from a distribution with
known properties) have found that non-normality has only minor consequences in the
majority of research applications (Hopkins and Weeks, 1990). As a consequence of the
general robustness of t- and F-tests, many researchers do not report information about the
shape of a distribution. This is despite the fact that many distributions are novel measures
for which underlying population distributions are not well known. Newell and Hancock
(1984) point to the dangers of erroneous statistical inferences when only means and
standard deviations of distributions are reported and skewness and kurtosis is ignored
especially when either n is small or alpha is extremely small, and data is skewed.
Checking for outliers and normality should therefore be an important preliminary to
many inferential statistical procedures. The simplest way to check for departures from
underlying normality in the population is to plot the distribution of sample scores.
Outliers can be identified and the general shape of a distribution indicates whether it is
skewed and whether it has positive or negative kurtosis (see Chapter 3 section,
Describing Distributions).
As well as plotting the distribution of sample scores the values of skewness and
kurtosis can be determined routinely in many statistical packages. These values can be
used inferentially to test whether the distribution departs significantly from normality.
In SAS the basic assumption of underlying normality can be checked using the
univariate procedure with the options plot and normal. The relevant SAS code which
produced Figures 5.9, 5.10 and 5.11 is:

proc univariate plot normal;

var corrd corre vocab;

run;

The first line of code has the procedure statement followed by the two options ‘plot’ and
‘normal’. In the second line of code the three variables ‘corrd’, ‘corre’ and ‘vocab’ are
specified.

Statistical analysis for education and psychology researchers 142