9. Inferential Statistics

In Chapter 7, you learned the basic logic of . In Chapter 8, you learned why beta/power, , , and all matter.

Now we need to answer two very practical questions:

  1. Which inferential statistic should I use?
  2. Do the data meet the assumptions for that statistic?

That is the purpose of this chapter. This chapter is less about memorizing a list of tests and more about learning how to make a decision. When you are handed a dataset, you need to be able to slow down, identify the variables, think about the design, check the assumptions, and then choose the statistical test that fits the research question.

NoteFor Dana’s Students

In my courses, you will probably use this chapter in two different ways. When we first discuss BEAN and power, you will focus more on the assumption-checking material. Later, when we move into inferential statistics, you will return to this chapter to practice choosing the correct statistical test.

That is intentional. Choosing a test and checking assumptions are connected, but they are different skills. It is normal if this chapter feels like one you return to more than once.

Types of inferential statistics

There are many inferential statistical tests, but a helpful starting distinction is between and .

Parametric statistics make assumptions about the data. For example, many parametric tests assume the dependent variable is continuous, observations are independent, the data are reasonably normal, and variances are similar across groups.

Non-parametric statistics generally make fewer assumptions about the shape of the distribution. They are not assumption-free, but they are often useful when parametric assumptions are not reasonable.

Here is the important thing: non-parametric tests are not the “bad” tests or the “backup” tests in a shameful way. They are tools. Sometimes the parametric tool is appropriate. Sometimes the non-parametric tool is more appropriate. Our job is to understand the data well enough to make a defensible choice.

How this fits with the 4-step process

This chapter connects directly to the 4-step hypothesis-testing framework from Chapter 7:

  1. Look at the data.
  2. Check assumptions.
  3. Perform the test.
  4. Interpret the results.

Choosing the correct test mostly depends on Step 1. You need to know the research question, the variables, and the study design. Checking assumptions is Step 2. If the assumptions are not reasonable, that affects Step 3 because you may need to choose a different version of the test or a different test altogether.

What this chapter will cover

By the end of this chapter, you should be able to:

  • identify the dependent variable and independent variable(s) in a research question;
  • determine whether variables are categorical or continuous;
  • distinguish between between-subjects and within-subjects designs;
  • use a decision process to choose an appropriate inferential statistic;
  • explain why assumptions matter;
  • check basic parametric assumptions in jamovi;
  • describe what to do when assumptions are violated;
  • explain why assumption decisions should be reported clearly in results.

Looking ahead

This chapter prepares you for the test-specific chapters that come later. In those chapters, you will learn exactly how to run chi-square tests, t-tests, ANOVAs, correlations, and regressions in jamovi. Before you can run those tests well, though, you need to know which test fits the data and whether the assumptions are reasonable.