Two Sided Tests

Chapter 14

Case Study: opportunity cost

Will a prompt about saving money for future purchases would lead students to spend less?

  • \(H_0\) Null hypothesis Reminding students that they can save money for later purchases will not have any impact on spending decisions.

  • \(H_A\) Alternatve hypothesis Reminding students that they can save money for later purchases will reduce the chance they will continue w/ purchase.

p-value

probability of observing difference of 0.2 or larger (more extreme)

Alternative Alternatives

\(H_A\) Alternatve hypothesis Reminding students that they can save money for later purchases will reduce the chance they will continue w/ purchase.


But why is this the alternative hypothesis? Couldn’t we also imagine that the prompt would increase the chance that students buy the item?

  • Probably not
  • And that’s not the research question!

Danger of One-Sided Hypotheses

  1. Framing \(H_A\) to match the data elevates risk of Type I error.
  2. Framing \(H_A\) to match what we think elevates risk of confirmation bias

Two-Sided Test

Research question: does administering blood thinning medication have an impact on survival rate of patients that have undergone CPR?

  • \(H_0\) Null hypothesis Blood thinners do not have an effect on survival rates.

  • \(H_A\) Alternatve hypothesis Blood thinners do have an impact on survival rates.

Data

Difference in proportions: \[ \hat{p_T} - \hat{p_C} = \frac{14}{40} - \frac{11}{50} = 0.13 \]

Randomized null distribution

Observations that are at least as large as 0.13

Randomized null distribution

Observations that are at least as extreme as \(\pm 0.13\), in either direction!

Two-sided tests

p-value for two-sided test

First find p-value for one tail and then double it!


Default to two-sided test

Only use a one-sided hypothesis test if you have a reason to focus on one direction in the alternative