## ABSTRACT

The previous chapter introduced descriptive statistics. This chapter moves to inferential statistics, those statistics that enable researchers to make inferences about the wider population (discussed in Chapter 34). Here we introduce difference tests, regression and multiple regression, and, arising from both difference testing and regression analysis, the need for standardized scores, and how they can be calculated. The chapter covers:

measures of difference between groupsOO the t-test (a test of difference for parametric data)OO analysis of variance (a test of difference for para-OO metric data) the chi-square test (a test of difference and a test of OO goodness of fit for non-parametric data) degrees of freedom (a statistic that is used in calcu-OO lating statistical significance in considering difference tests) the Mann-Whitney and Wilcoxon tests (tests of dif-OO ference for non-parametric data) the Kruskal-Wallis and Friedman tests (tests of dif-OO ference for non-parametric data) regression analysis (prediction tests for parametric OO data) simple linear regression (predicting the value of one OO variable from the known value of another variable) multiple regression (calculating the different weight-OO ings of independent variables on a dependent variable) standardized scores (used in calculating regressions OO and comparing sets of data with different means and standard deviations)

Both separately and together, these statistics constitute powerful tools in the arsenal of statistics for analysing numerical data. We give several worked examples for clarification, and take the novice reader by the hand through these.