Download Chapter 9: Introduction to the t statistic OVERVIEW 1. A sample

Chapter 10
The t Test for Two
Independent Samples
PSY295 Spring 2003
Summerfelt
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. nondistraction)
 No
knowledge of the parameters of the
populations (μ and σ2)
Vocabulary lesson
 Independent
 Design
that uses separate sample for each condition
 Repeated
 Design
 Pooled
measures/Between-subjects design
measures/Within-subjects design
that uses the same sample in each condition
variance (weighted mean of two sample
variances)
 Homogeneity of variance assumption
Discuss hypothesis testing procedure
1.
State hypotheses and select a value for α

2.
Locate a critical region (sketch it out)

3.
Add the df from each sample and use the t
distribution table
Compute the test statistic

4.
Null hypothesis always state a specific value for μ
Same structure as single sample but now we have
two of everything
Make a decision

Reject or “fail to reject” null hypothesis
The t Test formula

Difference in the means over the standard error
One Sample
Two Samples
X 
t
sX
( X 1  X 2 )  ( 1  2 )
t
sX 1 X 2
Formula for the degrees of freedom in a t
test for two independent samples
df  (n1 1)  (n2 1)  n1  n2  2
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

SS1  SS 2
s 
df1  df 2
2
p
Calculating the Standard Error
for the t statistic

Using the pooled variance estimate in the original
formula for standard error
old   s X 
s2
n
new   sx1  x 2 
s 2p
n1

s 2p
n2
Magnitude of difference by
computing effect size

Two methods for
computing effect size

Cohen’s d
d
X1  X 2
s
 r2
2
t
r2  2
t  df
2
p
Example
 Researcher
wants to assess the difference in
memory ability between alcoholics and nondrinkers
 Sample of n=10 alcoholics, sample of n=10 nondrinkers
 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?