Statistical Analysis for Education and Psychology Researchers

distributions, for example, binomial and χ^2 distributions. The remaining chapters in this
book introduce various statistical tests and are sequenced on the basis of the type of
inference and the type of underlying data distribution. Inferences about count data
including binomial and χ^2 distributions are presented in Chapter 6. Inferences based on
ranked data are presented in Chapter 7, and statistical inferences and associated test
statistics based on the normal distribution are presented in Chapter 8.
When data is classified as binomial all data values are categorized into one of only two
possible values, this is sometimes referred to as binary data. Nominal data is when data
values can be classified into two or more groups. It can be thought of as an expansion of
the binomial situation. A useful statistic for nominally classified data is the χ^2 statistic
based on the χ^2 distribution. If a response variable is rank ordered, or the distribution of a
continuous variable is asymmetrical, then the continuous variable can be treated as a
ranked variable and nonparametric or distribution free statistics should be considered.
This class of statistics makes very few distributional assumptions. All that is required for
some tests is that scores can be identified as being different, other tests require that scores
or values can be ranked. It is possible that scores may have a joint rank, in these
circumstances the majority of tests do not include these tied scores in the computation of
the test statistic. The value of initial data analysis in identifying possible underlying
statistical models for the data can not be overemphasized.
In many circumstances, probably too many, data is assumed to be normally
distributed. When this assumption is made, either implicitly or explicitly, then it follows
that scores should have a mean and a standard deviation. If either a mean or a standard
deviation does not make sense, for example, a standard deviation of 0.6 ‘blue eyes’, then
you are probably applying a continuous measure when you should not. Clearly blue eyes
represents a discrete and probably nominal value. Apart from simple plots there are
inferential procedures that can be used to check for normality assumptions. These are
presented in section ‘Checking for normality’, p. 143.

Using the Statistical Test Decision Chart

The decisions chart shown in Figure 5.1 incorporates the three main criteria outlined in
this section: research questions; research design; and data distributions. The chart can
be thought of as a map with grid references consisting of statements about study design
and research questions down the left hand side and statements relating to inferences and
data type along the top of the chart.
To use the chart you should first consider the research design and research
questions(s); decisions about these are located under the column heading design on the
left of the chart. If you move down this column you are presented first with one sample
(group) designs, subdivided into research questions about association/ relationships,
differences and prediction, then two sample (group) designs and research questions
related to comparisons/differences and associations. The final choice is between types of
multiple sample (group) designs involving questions about differences and associations
between samples.
Along the top of the chart under the general heading statistical inferences there are two
main columns headed count data and continuous data. Inferences about count data are
further subdivided into inferences relating to binomial/nominal data and inferences

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