ANOVA Assumptions - Analysis of Variance Designs - page 57

detect departures from normality, but because of their extreme sensi-
tivity to sample size variations, we recommend using a stringent alpha
level of p 001 before concluding a normality violation exists. We will

demonstrate these tests with SPSS and SAS in Sections 5.5.4 and 5.6.4.

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5.3.5 SOLUTIONS TO VIOLATIONS OF NORMALITY OF ERRORS
One way to reduce nonnormality within a variable is to eliminate outliers
that are clearly not representative of the population under study. These
outliers tend to skew distributions and distort sample means. A second
approach to reducing normality violations is to trim the values of the most
extreme scores, for example, removing the top and bottom 5 percent of
a distribution (Anderson, 2001). Such a procedure reduces variability as
well as skewness and kurtosis violations. However, some investigators are
opposed to data trimming of extreme scores, arguing that such exclusion
will artificially reduce the error term in the ANOVA ( MS S / A ) and afford
the subsequent F test a positive bias (Keppel & Wickens, 2004). A third and
more common practice is to modify the original Y i scores in a distribution
by means of a mathematical transformation. Typical transformations that
can be employed with SPSS and SAS are log, square root, inverse, and
arcsine, all of which can be quite effective at reducing situation-specific,
distributional skewness but, at the same time, may increase the difficulty
of data interpretation.

5.4 HOMOGENEITY OF VARIANCE
5.4.1 NATURE OF HOMOGENEITY OF VARIANCE
The third assumption underlying the analysis of variance is the homogene-
ity of variance or homoscedasticity assumption. The homogeneity assump-
tion requires that the distribution of residual errors for each group have
equal variances. In practice, this means that the Y i scores at each level of
the independent variable vary about their respective means Y j in a similar
(though not identical) fashion.

5.4.2 SITUATIONS PRODUCING VIOLATIONS OF HOMOGENEITY
OF VARIANCE
Violation of this assumption, called heterogeneity of variance or het-
eroscedasticity, has at least three systematic causes (Keppel & Wickens,
2004). First, classification independent variables such as gender or ethnic-
ity may have unique variances associated with the scores on the depen-
dent variable. For example, because White American mental health con-
sumers report fewer incidents of perceived racism in their daily lives than
do African American consumers, we might expect greater variability for
African Americans on a measure of stress-related racism.
Second, an experimental manipulation of an independent variable
can encourage participants to behave more similarly or differently than