Chapter 10Chapter 10The t Test for Two The t Test for Two

Independent SamplesIndependent SamplesPSY295 Spring 2003PSY295 Spring 2003

SummerfeltSummerfelt

Overview

Introduce the t test for two independent samples

Discuss hypothesis testing procedure Vocabulary lesson New formulas Examples

Learning Objectives

Know when to use the t test for two independent samples for hypothesis testing with underlying assumptions

Compute t for independent samples to test hypotheses about the mean difference between two populations (or between two treatment conditions)

Evaluate the magnitude of the difference by calculating effect size with Cohen’s d or r2

Introducing the t test for two independent samples

Allows researchers to evaluate the difference between two population means using data from two separate samples

Independent samples Between two distinct populations (men vs. women) Between two treatment conditions (distraction v. non-

distraction) No knowledge of the parameters of the

populations (μ and σ2)

Vocabulary lesson

Independent measures/Between-subjects design Design that uses separate sample for each condition

Repeated measures/Within-subjects design Design that uses the same sample in each condition

Pooled variance (weighted mean of two sample variances)

Homogeneity of variance assumption

Discuss hypothesis testing procedure

1. State hypotheses and select a value for α Null hypothesis always state a specific value for μ

2. Locate a critical region (sketch it out) Add the df from each sample and use the t

distribution table

3. Compute the test statistic Same structure as single sample but now we have

two of everything

4. Make a decision Reject or “fail to reject” null hypothesis

The t Test formula

Difference in the means over the standard error

2

2121

1

)()(

XXs

XXt

Xs

Xt

One Sample

Two Samples

Formula for the degrees of freedom in a t test for two independent samples

2)1()1( 2121 nnnndf

Estimating Population Variance

Need variance estimate to calculate the standard error Since these variances are unknown, we must estimate

them Pooling the sample variances proves to be the best way Add the sums of squares for each sample and divide by

the sum of the df of each sample

21

212

dfdf

SSSSsp

Calculating the Standard Error for the t statistic

Using the pooled variance estimate in the original formula for standard error

n

ssoldX

2

2

2

1

2

21 n

s

n

ssnew pp

xx

Magnitude of difference by computing effect size

Two methods for computing effect size

Cohen’s d

r2

2

21

ps

XXd

dft

tr

2

22

Example

Researcher wants to assess the difference in memory ability between alcoholics and non-drinkers

Sample of n=10 alcoholics, sample of n=10 non-drinkers

Each person given a memory test that provides a score Alcoholics; mean=43, SS=400 Non-Drinkers; mean=57, SS=410

Example, continued

What if the introduction read… A researcher wants to assess the damage to

memory that is caused by chronic alcoholism Would that change the analysis?