Inferential Statistics for Hypothesis Testing

This chapter discusses and illustrates inferential statistics for hypothesis testing. The procedures and fundamental concepts reviewed in this chapter can help to accomplish the following goals: (1) evaluate the statistical and practical significance of the difference between a specific statistic (e.g. a proportion, a mean, a regression weight, or a correlation coefficient) and its hypothesised value in the population; and/or (2) evaluate the statistical and practical significance of the difference between some combination of statistics (e.g. group means) and some combination of their corresponding population parameters. Such comparisons/tests may be relatively simple or multivariate in nature. In this chapter, you will explore various procedures (e.g. t-tests, analysis of variance, multiple regression, multivariate analysis of variance and covariance, discriminant analysis, logistic regression) that can be employed in different hypothesis testing situations and research designs to inform the judgments of significance. You will also learn that statistical significance is not the only way to address hypotheses—practical significance (e.g., effect size) is almost always relevant as well; in some cases, even more relevant. Finally, you will explore several fundamental concepts dealing with the logic of statistical inference, the general linear model, research design, sampling and, for complex designs, the concept of interaction.