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Introductory Statistics and Analytics: A Resampling Perspective by Peter C. Bruce

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9

HYPOTHESIS TESTING—2

Thus far, we have been looking mainly at comparisons between sample A and sample B. Hypothesis testing is used in other situations as well. As with the previous chapter, the material in this chapter will be of interest primarily to researchers; data scientists will have less need of it. After completing this chapter, you should be able to:

  • test a hypothesis for a single proportion or mean,
  • test a hypothesis involving multiple samples of count data and difference from expectation under a null model.

9.1 A SINGLE PROPORTION

In medical experiments, or studies aimed at publication, experiments with a single group are relatively uncommon—we saw earlier that well-designed experiments involve a control group and a treatment group to ensure that the only effect being evaluated is the effect of the treatment.

In business, however, single-group tests may occur to determine whether a treatment produces a change from the status-quo, particularly when a fully controlled experiment is infeasible or too costly.

Example

A sports gym offers trial memberships, and historically 25% of the trials get converted to full memberships within a week after the expiration of their trial membership. Then, the gym decides to try out a new procedure in which an employee calls the new customer 1 week into the trial period to see how things are going, what the customer is interested in, and how the gym employees might help the new customer get more involved. After 3 months, 165 trials ...

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