Download Inferences about Means of Dependent Samples and Statistical

Inferences about Means of
Dependent Samples
Chapter 12
Homework: 1-4, 7
Problems 3, 4, & 7: skip parts i and l,
do not calculate U in part n
Exam 3: Wednesday, May 3
Dependent Samples

Subjects are statistically related
 2 measurements of same individual
 individuals that are related
IQ,
GPA, married, etc
Order of data in each sample important
 Not independent
 must modify hypothesis testing ~

Dependent Samples: Examples

Pretest-posttest design
also
called repeated measures
measure each individual twice
 pretest ---> treatment ---> posttest
 compare scores
 Matched pairs
 match individuals on important
characteristic
 assign to different levels of IV ~

Difference Score
Di = Xi 1 - Xi 2
 subject’s score in group 1 minus
related score in group 2
 Requires same number of scores
in each group
 Mean difference score is sample
statistic


D
Evaluating Hypotheses:
Dependent Samples
Treat difference scores as if a single
sample
 same test just substitute difference
score
 Null hypothesis
 text: H0: m D = 0
(nondirectional)
 H0: m D < 0 or H0: m D > 0 (directional) ~

Test Statistic

t test for 2 dependent samples
D
t
sD


[df = n - 1]
n = number of pairs of scores
sD
sD 
n
standard
error of the mean of differences ~
Test Statistic

Standard deviation of differences
 same as for single sample
2 dependent samples
 D  D
Single sample
2
sD 
i
n 1
s
 X
i
X
n 1

2
Example
Does drinking 3 oz of alcohol affect
performance on an object
recognition task?
 n1 = 6, n1 = 6
 pretest-posttest
 count number of errors
1. State Hypotheses
 H 0: m D = 0
 H 1: m D  0 ~

Example
2. Set criterion for rejecting H0,
 a = .05
 directionality?
 df =
 tCV =
Example
i
Xi1
Xi2
1
1
5
2
0
7
3
2
7
4
2
6
5
3
6
6
1
8
Di
D  D  D  D
2
i
i
Example

compute sD
sD 

 D  D
2
compute sD
sD
sD 
n
i
n 1
Example

compute test statistic
tobs
D

sD
[df = n - 1]
Example
4. Interpret results
 Is tobs beyond tCV?
 decision:
 practical significance
effect
size index
d
D obs
sD