Chapter 5 M5: Extending Inference

In this module, we continue our exploration of inference. We see that there’s a common framework/procedure for things like hypothesis tests and confidence intervals, and that we can make a few key changes in order to do inference for new kinds of parameters and questions. Once we’ve encountered several of these variations, it becomes important to know which one to use in which situation! Some key skills are:

• Write out the general framework for doing a hypothesis test and/or confidence interval
• Follow that framework! And make sure that each step both matches up with the kind of parameter you’re looking at, and makes sense in context. This includes things like:
  • State proper null and alternative hypotheses
  • Choose an \(\alpha\)/confidence level and explain your choice
  • Write the appropriate point estimate/sample statistic
  • Check the relevant assumptions/conditions for inference
  • Write the appropriate test statistic and its distribution if the null is true
    • (…and explain what that means)
  • Show how to use the test stat and null distribution to obtain a p-value
  • Use the p-value to make a decision about the null hypothesis
  • Set up a confidence interval for your parameter of interest, using a point estimate, critical value, and standard error of the point estimate
  • Interpret your hypothesis decision, p-value, and confidence interval in context
• Identify what type of parameter a question/application is about, and adjust the inference procedure accordingly. The types of parameters/tests discussed include:
  • One proportion
  • One mean
  • A difference between two proportions
  • A difference between two means
    • …in either paired or independent groups, which is different!
  • Chi-square tests (one-way for goodness of fit, two-way for independence)
• Given a description of a variable/problem/study/dataset, determine what kind of test is appropriate
  • …then carry out the test :)
  • It’s especially important to think about what the null and alternative hypotheses would be based on the context, and what it would mean to reject (or fail to reject) the null hypothesis.
• Given a general topic or research question, come up with a specific way to answer that question by measuring variable(s) and doing the appropriate test

As usual, the focus here isn’t on arithmetic. (Unless it’s, like, “20 minus 10” levels of arithmetic.) It’s always sufficient to set up a formula and plug in any values you know from the problem description, then leave it at that.