Null Hypothesis Statistical Significance Testing and z-Tests

Abstract

In the previous chapter, we learned about the theory of statistical inference. This theory provides statisticians, researchers, and students with the background information they need to make inferences about a population based on sample data. This chapter builds upon that theoretical foundation by teaching about the simplest possible inferential statistics procedure: the z -test. Although z-tests are not common in social science research, learning the z -test is still important. Mastering a z -test will make the more complicated procedures discussed in later chapters easier to learn because those procedures are variations of a z -test that have been adapted to other types of data and research situations. Learning Goals • Execute the eight steps of null hypothesis statistical significance testing (NHST). • Conduct a z-test and explain how it fits into the general linear model (GLM). • Recognize how effect sizes can compensate for some of the weaknesses of the decision to reject or retain a null hypothesis. • Calculate and interpret Cohen's d for a z -test. • Define Type I and Type II errors and explain why it is always possible to commit one or the other when conducting a null hypothesis statistical significance test. Null Hypothesis Statistical Significance Testing The main purpose of this chapter is to transition from the theory of inferential statistics to the application of inferential statistics. The fundamental process of inferential statistics is called null hypothesis statistical significance testing (NHST) . All procedures in the rest of this textbook are a form of NHST, so it is best to think of NHSTs as statistical procedures used to draw conclusions about a population based on sample data. There are eight steps to NHST procedures: 1. Form groups in the data. 2. Define the null hypothesis (H0). The null hypothesis is always that there is no difference between groups or that there is no relationship between independent and dependent variables. 3. Set alpha (α). The default alpha = .05. 4. Choose a one-tailed or a two-tailed test. This determines the alternative hypothesis (H1). 5. Find the critical value, which is used to define the rejection region. 6. Calculate the observed value. 7. Compare the observed value and the critical value. If the observed value is more extreme than the critical value, then the null hypothesis should be rejected. Otherwise, it should be retained. 8. Calculate an effect size.