CONTENTS

Table of Contents
Introduction

1. Descriptive Statistics in Evaluation
2. Subgroup Analysis
3. Variable - Are They Related?
4. Correlation
5. The t-Test of Difference Between Means

Supplements
Resources
Glossary

Wading Through the Data Swamp:
Program Evaluation 201

Module Content Objectives Background Comparing Means Attrition Versus Loss to Followup New Information: Change Scores and Participation How To Construct Scatter Plots How To Interpret Scatter Plots Linear Relationship Strength of the Relationship: Pearson's Correlation Coefficient What Do All the Numbers and Plots Mean? Adding Points to a Scatter Plot Lessons Learned: What Jack Should Have Asked His Evaluator What Did Jack Learn About His Program From These Analyses? How Can Jack Use This Statistical Information to Improve His Program? How Can Jack Use This Statistical Information To Better Promote His Program? Module 4 Quiz

Linear Relationship

How can you tell if there is a relationship between two variables? It's not too hard. The pattern is clearest if we draw a straight line that touches every dot or comes as close to each dot as possible. If all the data points were to fall on a straight line, we would have a perfect linear relationship. But in the real world, nothing's perfect. These types of linear relationships happen very rarely.

If you cannot draw a single straight line in your plot that works like the "best" one (it is called a best-fit line for this reason), then two things are possible. Either there is no relationship between the two variables or the relationship is not linear. If the relationship is not linear, then you will need to hire a statistician. Nonlinear relationships require complex and sophisticated analytical techniques.

Fortunately, we actually do find a lot of linear relationships in our field. Or at least that's what it usually means when we say there is a relationship between two things.

Here is how our scatter plot looks when we draw a line to represent the linear relationship between amount of services and change in alcohol use. This line is also known as a regression line.

Now that the best-fit line has been added, you can see the downward slope to the right much clearer. This figure seems to show a negative linear relationship between participating in the program (services received) and change in alcohol use. As participation increases, alcohol use decreases. Change scores get into the negative range for higher levels of attendance.

Now we know that the more time the participants spent in the program, the greater the decrease in alcohol use from pretest to posttest. But we cannot rely on the information in this figure alone. We need to find out how strong the relationship is between attending Jack's program and reducing alcohol use from pretest to posttest. Remember negative (downward) change in alcohol use is what we were hoping for.