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

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Student's t-test wikipedia, lookup

Taylor's law wikipedia, lookup

Bootstrapping (statistics) wikipedia, lookup

Resampling (statistics) wikipedia, lookup

Misuse of statistics wikipedia, lookup

Degrees of freedom (statistics) wikipedia, lookup

Psychometrics wikipedia, lookup

Transcript
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?