nolanessentials3e

Chapter 9 Introduction

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CHAPTER 9

The Single-Sample t Test and the Paired-Samples t Test

The t Distributions

Estimating Population Standard Deviation from a Sample

Calculating Standard Error for the t Statistic

Using Standard Error to Calculate the t Statistic

The Single-Sample t Test

The t Table and Degrees of Freedom

The Six Steps of the Single-Sample t Test

Calculating a Confidence Interval for a Single-Sample t Test

Calculating Effect Size for a Single-Sample t Test

The Paired-Samples t Test

Distributions of Mean Differences

The Six Steps of the Paired-Samples t Test

Calculating a Confidence Interval for a Paired-Samples t Test

Calculating Effect Size for a Paired-Samples t Test

BEFORE YOU GO ON

You should know the six steps of hypothesis testing (Chapter 7).
You should know how to determine a confidence interval for a z statistic (Chapter 8).
You should understand the concept of effect size and know how to calculate Cohen’s d for a z test (Chapter 8).

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Holiday Weight Gain and Two-Group Studies Two-group studies indicate that the average holiday weight gain by college students is less than many people believe—only about 1 pound.

MASTERING THE CONCEPT

9-1: There are three types of t tests: (1) We use a single-sample t test when comparing a sample mean to a population mean but do not know the population standard deviation. (2) We use a paired-samples t test when comparing two samples and every participant is in both samples—a within-groups design. (3) We use an independent-samples t test, discussed in Chapter 10, when comparing two samples and every participant is in only one sample—a between-groups design.

In many parts of the world, the winter holiday season is a time when family food traditions take center stage. Popular wisdom suggests that during this season, many Americans put on 5 to 7 pounds. But before-and-after studies suggest a weight gain of just over 1 pound (Hull, Radley, Dinger, & Fields, 2006; Roberts & Mayer, 2000; Yanovski et al., 2000). A 1-pound weight gain over the holidays might not seem so bad, but weight gained over the holidays tends to stay (Yanovski et al., 2000).

The fact that researchers used two groups in their study—students before the holidays and students after the holidays—is important for this chapter. With a t distribution, we can compare one sample to a population when we don’t know all the details about the parameters, and we can compare two samples to each other. There are two ways to compare two samples: by using a within-groups design (as when the same people are weighed before and after the holidays) or by using a between-groups design (as when different people are in the preholiday sample than those in the postholiday sample). For a within-groups design, we use a paired-samples t test. The steps for a paired-samples t test are similar to those for a single-sample t test, which is why we learn about both of these hypothesis tests in this chapter. (For a between-groups design, we use an independent-samples t test, which we will learn about in Chapter 10.)