## Representing, measuring and interpreting correlations

### Basic ideas this week:

In the last two sections of this course our attention was focussed on answering a question about a single variable. In dealing with simple experiments in week 11, the problem was to determine whether or not a person had the ability to distinguish between two products. We considered the evidene that we could gather to support the conclusion that an ability was indeed present, and we thought about how to interpret that evidence. In Weeks 12 and 13, we thought about the problem of measuring a population parameter, and we considered the meaning and value of the evidence we could acquire from a random sample. The material from weeks 11-13 belongs to the general area of univariate statistics, because we are mainly concerned with drawing conclusions abpout a single variable. In the case of hypothesis testing, the varible was the boolean. In measuring population parameters, the variable was quantitative.

We are now going to look at questions concerning the relationship between two variables. We are entering a new circle of ideas, called bivariate statistics. Typical questions we might encounter here are:

• Are males more violent than females?
• Is race related to the age at which prisoners receive the death penalty?
• Is there any relationship between the weather reports from a certain TV station and what the weather actually does? Which station has the most accurate reports?
• Do bigger dogs have shorter lives, and if so how strong is the effect?
• Do test scores accurately represent the amount of learning that students feel thay have achieved?

In all these cases, there are two variables involved. They may be qualitatiative (male/female, violent/non-violent) or quantitative (weight, life span). Or we have mixed situations (race and age).

### Assignment:

• Read: Chapter 7, section 1 by Wednesday, November 20. Chapter 7, section 2 by Friday, November 22.
• Review questions:
• Problems:
• In-class:
• EXTRA CREDIT:

### Vocabulary:

• Correlation
• Scatter Plot.
• Correlation coefficient

### Concepts:

Correlation between two quantitative variables. The raw data

Assessments: