# The Evolution of Pearson’s Correlation Coefficient/Exploring Relationships between Two Quantitative Variables

This material is replicated on a number of sites
as part of the
SERC Pedagogic Service Project

Initial Publication Date: January 10, 2008

## Summary

Using interactive lecture, this activity explores a collection of nine scatterplots to develop the notion of association between two quantitative variables. The activity is designed to help students better understand how statistical measures are "invented," and why certain measures are preferred. Specifically, this activity proposes a non-standard "intuitive" measure of association and, by examining properties of this measure, develops the more standard measure, Pearson's Correlation Coefficient.

## Learning Goals

Students will come to understand the notion of association between two quantitative variables and Pearson's Correlation Coefficient as a measure of the direction and strength of the linear relationship between two quantitative variables.

## Context for Use

This activity is usually done as an introduction to the study of relationships between two quantitative variables. The lesson takes approximately two class periods (100 minutes) and works best as an interactive lecture. The activity is designed for introductory statistics at the high school or college level.

## Description and Teaching Materials

The activity explores a collection of scatterplots. With the exception of the first two scatterplots, the data were constructed to control for characteristics that students might attend to when judging the direction, form and strength of the relationship between the two variables. A detailed description of the activity, including the scatterplots and discussions, will be available in NCTM's Mathematics Teacher Focus Issue on Data Analysis and Probability, November 2008.

## Teaching Notes and Tips

**Introduction to Bivariate Data and Association**

The first part of this activity is an interactive lecture using whole group discussion of a scatterplot to understand association. Below is an example of this discussion including scatterplots, questions and prompts.

**The Quadrant Count Ratio: A First Measure for Strength of Association**

**Pearson's Correlation Coefficient**

**Summary of Activity**

This activity provides a developmental sequence for understanding Pearson's correlation coefficient. Pearson's correlation coefficient is a measure of the direction and strength of the linear relationship between two quantitative variables.