the underlying theory if there is one, for example, for some learning theories the
response variable might be a multiplicative rather than additive function of
independent variables.)
6 Errors should be unbiased independently and normally distributed with constant
variance for significance tests to be valid. In ANOVA the errors or residuals represent
deviations of observed scores from cell means. Survey researchers are most likely to
encounter problems of response bias which gives rise to biased errors. (Verify
normality of errors by plotting residuals against the normalized score of the rank of
the residuals. A straight line plot indicates normality.)
(If an investigator is more interested in treatment mean differences than estimate
of the treatment means then any bias in errors can be assumed to be constant
across all treatments, unless there is reason to believe otherwise.)
ANOVA is moderately robust against violations of normality and homogeneity of
variance assumptions but dependencies among subjects or their responses (such as same
subjects or repeated measures within subjects) for independent ANOVA invalidates the
analysis.
Hypothesis tests are generally of the form that subgroup means or treatment means are
equal. Sample means are used to estimate these fixed population parameters.
8.7 One-way ANOVA F-test (unrelated)When to UseThis procedure is used when an investigator wants to test for differences among the
means of two or more independent groups (treatment groups in experimental designs or
subgroups in survey and comparative designs). The procedure may be viewed as an
extension of the independent t-test when there are three or more independent groups. In
an unrelated design, different subjects appear in each of the treatment conditions or
subgroups. The hypothesis tested by the F-statistic is that population subgroup (or
treatment group) means are equal. The researcher is often interested in which means
differ and in what way. A plot of the subgroup means can be very informative as well as
modified t-tests on post hoc pairwise comparisons of subgroup means. Less frequently in
educational research an investigator might specify a particular hypothesis prior to data
analysis in which case a t-test on the preplanned comparison of interest and an estimate
of the mean difference with confidence limits would be appropriate.
Example from the LiteratureThe efficacy of three different writing courses designed for postgraduate research
students, a cognitive strategies approach, a generative writing course and a product-
centred approach, is reported by Torrance, Thomas and Robinson (1993). Of 104 students
in total who participated in the study, forty-one completed the product-centred course,
thirty completed the strategies course and thirty-three completed the generative writing
course. At the end of the course a questionnaire was administered which asked five
Inferences involving continuous data 315