Introductory Statistics and Analytics: A Resampling Perspective

8

HYPOTHESIS TESTS

In this chapter, we move from confidence intervals to hypothesis tests, which are used in research community mainly because peer reviewers and regulators typically require evidence of statistical significance prior to publishing or approving results. Data scientists will encounter them in what marketers call A–B testing. After completing this chapter, you should be able to

• describe the difference between a hypothesis test and a confidence interval,
• correctly use the vocabulary of hypothesis testing,
• test hypotheses for
  • a single proportion
  • two proportions
  • two means
• distinguish when to use one-way and two-way hypothesis tests.

8.1 REVIEW OF TERMINOLOGY

Previously, we introduced these two concepts:

1. A study or an experiment to compare one treatment with another.
2. Effective design of sample surveys to accurately reveal characteristics of populations.

We also saw that variation comes from two random sources:

1. Which subjects get assigned to which treatments, and
2. Which individuals or elements get selected for the sample.

We saw that resampling methods, or the corresponding formulas, could be used to quantify this random variability.

Definition: Statistical inference

Statistical inference is the process of accounting for random variation in data as you draw conclusions.

Confidence Intervals and Hypothesis Tests

Inference procedures, which are designed to protect you from being fooled by random variation, fall into two categories.

Confidence Intervals Confidence ...