Statistical Analysis for Education and Psychology Researchers

Introduction

Educational researchers may be less familiar with nonparametric methods and in
particular rank test procedures than with parametric methods. Use of nonparametric rank
procedures is more common among research psychologists. In this chapter, six
nonparametric or distribution free statistics that make use of rank scores are introduced:
Spearman’s correlation, Run’s test, Wilcoxon M-W test, Signed ranks test, Kruskal
Wallis ANOVA and Friedman’s ANOVA. The term distribution free is strictly not
accurate. Whereas parametric statistical procedures are dependent upon distributional
theory, they make certain specific assumptions about patterns of variability in the
population (referred to as statistical test assumptions). Nonparametric tests do not rely on
population distributional assumptions. Nonparametric procedures are not entirely
distributional free. Whilst not making use of distribution theory in the same way that
parametric procedures do, (mathematical descriptions of patterns of variation are used to
make inferences about population parameters or constants based on sample data) they
nevertheless definitely do make use of the distribution of sample observations. In this
sense they are not distribution free.
Nonparametric statistical tests are generally less powerful than parametric tests and are
also less likely to mislead investigators because they are not dependent upon certain
restrictive measurement and distributional assumptions. Nonparametric procedures are
also well suited to small sample sizes, and rank tests are particularly helpful when
outliers are present in a data set since ranks of raw scores are not affected by extreme
values. Data may naturally form ranks, or ranks may be assigned on the basis of
measurement (or combinations of different measures) or subjective judgment.
Many introductory statistical textbooks relegate nonparametric procedures to the later
chapters and promulgate the view that they should be used when assumptions of
normality and homogeneity of variance (equal population variances) are not met.
Whereas nonparametric tests are useful for solving certain statistical difficulties (small
sample sizes, unrealistic measurement and distributional assumptions), they are not a
panacea for all problems. They are subject to assumptions of independence of
observations (groups are comprised of random samples and successive observations
within samples are independent) and are also sensitive to unequal variances especially in
combination with unequal sample sizes. As Zimmerman and Zumbo (1993) point out,
psychologists (and probably educational researchers) are not yet fully appreciative of this.
Therefore, general advice is that nonparametric procedures are sometimes an effective
way of dealing with non-normal or unknown distributions but are not always the answer
to unequal variances. What can be done when assumptions of homogeneity of variance
are violated? What is referred to in the statistical literature as the Behrens-Fisher
problem. Strategies are discussed in Chapter 8, but essentially the answer involves using
a modified test procedure with estimated degrees of freedom.

7.1 Correlation an overview

In psychological and educational research many questions are concerned with the extent
of covariation between two variables. In a review of two journals, the British Educational

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