ANOVA Assumptions - Analysis of Variance Designs - page 58

a control condition, thus producing differences in group variances. That
is, motivation to participate in the study, and floor or ceiling effects (i.e.,
where participants cannot score any lower or higher on the dependent
measure because of intrinsic or extrinsic constraints) can produce extreme
variability between and within independent variable groups.
Third, variability on some dependent variables may be related to group
size. Heterogeneity can become a serious issue with unequal sample sizes.
For example, large group variances associated with small sample sizes tend
to produce a liberal F statistic whose nominal alpha level such as .05 is
actually operating at a less stringent level such as .10. Conversely, when
the situation arises where large sample sizes and large group variances
are associated, we produce a conservative F statistic, where the nominal
alpha level such as .05 is actually more stringent, for example, .01 (Stevens,
2002).

5.4.3 ASSESSING FOR VIOLATIONS OF HOMOGENEITY OF VARIANCE
There are a variety of ways to detect the presence of heterogeneity of
variance. We will review a few of the most popular approaches. Hartley
(1950) proposed a simple and elegant test statistic called “ F MAX ”togauge
the level of homoscedasticity. F MAX is simply a ratio of the largest group
variance to the smallest group variance. Thus the formula for F MAX is

s largest
s smallest .

F MAX = (5.2)

Large values of F MAX are indicative of heterogeneity. Keppel et al.
(1992) lobbied for a simple but very conservative assessment criterion
(for the introductory statistics curriculum) that identified any F MAX value
greater than 3.0 as indicative of heterogeneity; if this was obtained, a more
stringent alpha level of .025 was to be applied to the subsequent F value.
As Keppel et al. (1992) note,

research has shown that when F MAX is greater than 3.0, the sampling distribution
of F begins to become sufficiently distorted to seriously affect the decision rule
based on the undistorted theoretical sampling distribution of F .Wecancorrect
for this distortion by selecting a new critical value of F , which we will call F ADJ
at a slightly more stringent significance level, namely,

α = . 025. (pp. 119-120)

A less conservative assessment of the F MAX statistic is to use the critical
values of F MAX developed by Pearson and Hartley (1970, 1972) and is rou-
tinely employed by computer programs, such as SPSS and SAS. Recent dis-
cussions by Keppel and Wickens (2004) and Stevens (2002) offer caution
concerning the use of the F MAX statistic because of its extreme sensitivity
to distributional nonnormality.
More robust detectors of heterogeneity can be found with the test
statistics developed by Levene (1960) and Brown and Forsythe (1974). In
these measures, the original Y i scores are converted into absolute deviation