## Learning Math: Data Analysis, Statistics, and Probability

# Designing Experiments

## Examine how to collect and compare data from observational and experimental studies, and learn how to set up your own experimental studies.

**In This Session**

**Part A:**Comparative Studies

**Part B:**Comparative Observational Studies

**Part C:**Comparative Experimental Studies

**Homework**

The statistics problems in previous sessions primarily seek to answer questions about a single group. For example, our analysis and interpretation of “How many raisins are in a box of raisins?” was typically focused on describing the number of raisins for one brand of raisins. Until now, our primary focus has been on describing characteristics of a single distribution by organizing data in graphs and tables and by determining numerical summary measures for data.

In this session, we will investigate the idea of comparative studies — studies that focus on comparing several different distributions. The analysis and interpretation of data from comparative studies depend on the method of data collection, which can be either experimental or observational. See Note 1 below.

The goal of this session is to understand the concepts involved in comparing two or more groups. In this session, you will do the following:

• Investigate comparative studies, which can be experimental or observational

• Learn how to analyze and interpret results from comparative studies

• Learn how to design a comparative experiment

• Explore paired and unpaired comparative studies

### Notes

**Note 1**

In this session, we are analyzing experimental results informally. More standard statistical methods use formal inference procedures to make generalizations from the results of experiments.

### Key Terms

**Previously Introduced:**

bias

box plot

distribution

Five-Number Summary

interquartile range

mean

median

**New in This Session:**

comparative experimental study

comparative observational study

comparative study

design of a comparative study

random assignment

treatment