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

What Does the t-Test Assume?

The t-test is a very powerful statistical test in terms of rejecting a null hypothesis that is false. This is a good thing! Like all statistical tests, it is based on a model that makes some assumptions about the data.

1. Normality assumption. The data come from a distribution that has one of those nice bell-shaped curves known as a normal distribution. People worry about violating the assumption of normality because drug use data often look skewed.
   
   Fortunately, it has been shown that if the sample size is even moderate for each group, quite severe departures from normality don't seem to affect the conclusions reached. (See Hays' book, Statistics, published in 1963-it's still true today.)
   
   
2. Equality of variance. Some researchers have argued that equality of variance is actually more important than the assumption of normality. In other words, the standard deviations of the two groups are pretty close to equal. (This is why many of the statistical software packages provide a "test of equality of variances" along with the results of the t-test.)

Don't worry too much about these assumptions. As long as you have enough people in each group (typically greater or equal to 30 cases) and the groups are close to equal in size, you can be confident that the test will be a good, strong tool for getting the correct conclusions. Statisticians say it is a "robust" test. (see Champion's book, Basic Statistics for Social Research, published in 1981.)