in each of the samples.8.8 One-way ANOVA F-test (related) 330
This is used to identify population mean differences on one-response variable
which is measured on two or more occasions with the same subjects providing the
repeated measures or observations.Two-Factors (Independent variables)^
8.9 Two-way ANOVA 2×2 factorial (unrelated) 338
Two factors with two levels for each factor. Two independent or classification
variables are used to assign subjects to four independent groups (combinations of
each factor). Different subjects are used in each cell of the design. Analysis
allows a test of hypotheses relating to main and interaction effects.8.10 Split-plot ANOVA 343
Two factors with two or more levels for a between subjects factor. and two or
more levels for the repeated measures factor. For example, a two factor design
might have one classification variable (two categories) where different subjects
are used in each category and one-related factor with three categories (within
subjects factor), the samesubjects appear in each of the three categories (repeated
measures). Analysis allows a test of hypotheses relating to main and interaction
effects.IntroductionIn this chapter parametric statistical procedures are introduced. These include linear
regression, correlation and tests for differences in location in two-sample and multiple
sample designs. Parametric statistical techniques require that a number of assumptions
about the nature of the population from which data were drawn be met and in this sense
are more restrictive than non-parametric procedures. For example, for statistical
inferences to be valid, variables should be continuous (variables measured on interval or
ratio scales) and data should be drawn at random from a population with an underlying
normal distribution. Parametric tests are based on an underlying normal probability
distribution of a statistical variable (see Chapter 4, section 4.6). For example, an
important property of sample means is that they tend to be normally distributed even
when individual scores may not be (based on the central limit theorem). This enables
parametric techniques to be used in many situations. Also, parametric procedures are
reasonably robust, that is tolerant of moderate violations of assumptions, although, as we
shall see in later sections, violation of particular assumptions, especially when in
combination, are critical and can invalidate inferences drawn.
There is much misunderstanding about what is meant by assumptions of normality.
It is often believed, for example, that to use parametric tests such as the paired t-test (for
‘before’ and ‘after’ designs) or linear regression, the response variables should be
Inferences involving continuous data 249