Relationships between Variables

Abstract

In previous chapters, we have looked at ways in which statistical methods are used to collect, summarize, and draw conclusions from data on a single variable at a time. Now we analyze the data on two or more variables at the same time; that is, we study relationships between variables. Most sciences have as a goal establishing relationships between variables, and statistics plays in important role in this task. In this chapter we suggest the scope of concerns for statistical analysis. A good deal of the rest of the book expands on the study of relationships between variables.

The ecology club of the university plans to put increased funding into refreshments and entertainment at meetings in hopes of attracting dues-paying members. As a club member, you are in charge of determining whether an increase in entertainment and refreshment expenditures actually does increase income from dues. Is there a relationship between these two variables: expenditures and dues?

A local store is asked to purchase advertising in the school yearbook. They want to know if advertising in the yearbook increases business with students. As business manager, you are asked to respond to this query.

The football team has been asked whether they would like to play on Astroturf or keep the grass. Their response hinges on the injury rates for grass versus Astroturf surfaces. If you were to advise the team, how would you answer this question?

Turning to more global issues, has there been any change in the percentage of women in the labor force over the last decades? Do people of different races smoke different brands of cigarettes? Do fewer or more pregnant women with AIDs who take AZT pass on the virus to their babies? Do places with different mean annual temperatures have different rates of breast cancer? Does the number of executions affect the homicide rate?