Introduction

This chapter discusses the statistical procedures that can be used to make inferences and to test hypotheses about differences among groups and relationships among variables. In the previous chapter I discussed the logic of statistical inference and hypothesis testing. Two statistical concepts that underlie these procedures are those of the sampling distribution – in particular the sampling distribution of the mean and the standard error of the mean – and the properties of the normal probability distribution. In this chapter I will discuss procedures for using sample statistics for making inferences about population parameters, as well as for testing for the statistical significance of differences between means and of correlations among sets of scores.

In this chapter I will discuss the following topics:

• how to estimate the standard error of the mean from sample statistics;

• the use of this estimate to establish confidence intervals for testing hypotheses about differences between two means in the case of large samples;

• the t-ratio for testing statistical hypotheses about differences between the means in the case of small samples;

• a procedure – the analysis of variance – for comparing the means of more than two groups;

• the statistical significance of correlation coefficients.

In addition, several related statistical analyses will be briefly introduced and references for further reading about the following will be provided:

• effect size

• nonparametric tests of significance

• N-way, multivariate and repeated measures analysis of variance.