# Comparing Means and Other Measures of Location between Two Populations by Significance Tests and Effect Size

## Breadcrumb

### Course Topics

**Motivation:** Frequently, comparing samples from two populations is of interest. For example, is the average height in the US different from that in China? If they are different, how different?

**Goal: **In this short course, we will compare averages and other measures of location using significance tests and effect size estimates.

In classical hypothesis testing, significance tests assume the null hypothesis is true. Then the probability that data as extreme as or more extreme than those observed is calculated. If this probability is very low, then we reject the null hypothesis. For the two sample case, we will focus on the following methods and questions:

- Parametric method: two-sample t-test
- What are the null hypothesis and alternative hypothesis of a two-sample t-test?
- What are the assumptions of two-sample t-test?
- How do we check if these assumptions hold?
- Should we use pooled or unpooled estimates for standard deviation?
- How to run two-sample t-test in R?
- What effect size estimate is appropriate in this scenario?

- Nonparametric method: Mann-Whitney U test
- What are the null hypothesis and alternative hypothesis of a Mann-Whitney U test?
- What are the assumptions of Mann-Whitney U test?
- How to check if these assumptions hold or not?
- How to run Mann-Whitney U test in R?
- What effect size estimate is appropriate in this scenario?

We will use the following datasets:

- Data from a lung cancer study at VA (http://biostat.mc.vanderbilt.edu/wiki/pub/Main/DataSets/valung.csv).
- Data from a monkey calls study (link).
- Data from a study on high school students (www.ats.ucla.edu/stat/r/modules/hsb2.csv).

LISA Short Course: Comparing Means and Other Measures of Location between Two Populations by Significance Tests and Effect Size from LISA on Vimeo.