# Final Study Guide

The final is Thursday Dec 7th 9:30-11:20am in LINC 368.

The final is cumulative, all content on the midterm study guide may also be tested on the final exam.

The final exam from last year is provided on canvas.

## Concepts

When does the two sample t-test have exactly a t-distribution under the null hypothesis?

Describe what happens if the equal variance two sample t-test is used in a situation where the populations do not have equal variance.

Describe what happens if Welch’s two sample t-test is used in a situation where the populations do have equal variance.

Why do some people reccomend you should always use Welch’s two sample t-test?

Describe what happens if the paired t-test is used in a situation where the data isn’t paired.

Describe what happens if the two sample t-test is used in a situation where the data is paired.

Identify the appropriate test based on a setting and comparison of interest.

Identify which margins in a $$2 \times 2$$ table are fixed by the study design.

Identify the kind of sampling being used (Multinomial, Binomial, Retrospective) in a binary data setting from the study design.

Identify which probabilities may be estimated in a $$2 \times 2$$ table based on the study design.

State the null hypothesis the Wilcoxon Rank Sum tests with the addition of the location-shift hypothesis.

State the null hypothesis the Wilcoxon Rank Sum tests without the addition of the location-shift hypothesis.

Describe how Simpson’s paradox may complicate the analysis of multiple $$2 \times 2$$ tables.

What additional assumption is crucial for the Mantel-Haenszel test?

Describe why the F-test for variances isn’t reccomended.

Describe how to construct a bootstrap confidence interval for a parameter of interest.

Apply the delta method to find an approximate sampling distribution for a function of a statistic and use the result to construct a confidence interval.

## Procedures

You should know how to perform the following test procedures (this includes describing the appropriate setting for the test, the null and alternative hypotheses, the test statistic, the reference distribution, as well as being able to complete the calculations), and be able to write a statistical summary from the results:

• Chi-square goodness of fit
• Two sample Z-test/confidence interval/p-value
• Two sample equal variance t-test/confidence interval/p-value
• Two sample Welch’s t-test/confidence interval/p-value
• Paired t-test/confidence interval/p-value
• Two proportion Z-test/confidence interval/p-value
• Chi-square for homogeniety of proportions/independence test/p-value
• Fisher’s Exact test/p-value
• Log Odds Ratio test/p-value
• McNemar’s paired binary data test/p-value
• Paired binary data t-test/p-value
• Mantel-Haenszel test/common odds ratio estimate
• Mood’s median test/p-value
• Wilcoxon Rank Sum test statistic/p-value
• Levene’s test/p-value
• Two sample Kolmogorov-Smirnov test/p-value