-SD 12 Comparing Means - One & Paired-sample t-test.ppt

t test

1. Comparing Two Means:
One-sample &
Paired-sample
t-tests
Lesson 12

2. Inferential Statistics
Hypothesis testing
Drawing conclusions about differences
between groups
Are differences likely due to chance?
Comparing means
t-test: 2 means
Analysis of variance: 2 or more means ~

3. Comparing 2 means: t-tests
One-sample t-test
Is sample likely from particular
population?
Paired-Sample t-test
2 dependent (related) samples
Independent-samples t-test
2 unrelated samples ~

4. The One-sample t-test
Evaluating hypothesis about population
taking a single sample
Does it likely come from population?
Test statistics
z test if sknown
ttest if sunknown ~

5. t statisticX
s
X
t

 1ndf

6. Example: One-sample t-test
Survey: college students study 21 hr/wk
Do Coe students study 21 hrs/week?
Select sample (n = 16)
sunknown
Nondirectional hypothesis:
H
0: = 21; H
1: 21
reject H
0if increase ordecrease
PASW/SPSS: Test value = 21
Assumed from H
0~

7. PASW One Sample T Test
Menu
Analyze
Compare Means
One-Sample T Test
Dialog box
Test Variable(s) (DV)
Test Value (value of testing against)
Options(to change confidence intervals) ~

8. PASW Output
*1-tailed probability: divide Sig. 2-tailed by 2

9. Paired-Samples t-tests
2 samples are statistically related
Less affected by individual differences
reduces variance due to error
Repeated-measures
2 measurements on same individual
Matched-subjects
Match pairs on some variable(s)
Split pairs into 2 groups ~

10. Difference Scores
Find difference between each score
D = X
2-X
1
Requires n
1scores equal n
2scores
Calculate mean D

And standard deviation of D
 ~N
D
D

  
1
2



n
DD
s
D

11. Repeated-measures
2 measurements of same individual
Pretest-posttest design
measure each individual twice
pretest treatment posttest
compare scores ~

12. Matched-subjects
Match individuals on important
characteristic
individuals that are related
IQ, GPA, married, etc
Assign to different treatment groups
each group receives different
levels of independent variable ~

13. Assumptions: Related Samples
Population of difference scores
is normal
Observations withineach
treatment independent
scores for each subject in a
group is independent of other
subjects scores ~

14. Related-samples Hypotheses
Nondirectional
H
0: 
D= 0
H
1: 
D0
Directional
H
0: 
D>0
H
1: 
D< 0
Remember: it depends on the
directionof the prediction ~

15. Sample Statistics
Mean difference
Mean for single sampleN
X
X

 D N
D


16. Standard Deviation:
Related-samples Single sample 
1
2



N
DD
s
D  
1
2



N
XX
s 1Ndf
D 1Ndf

17. Estimated Standard Error
Calculate same as single sample
use standard deviation of
difference scoresD
s N
s
D


18. Test Statistic
Related-samplest test
Since 
D= 0D
D
obs
s
D
t

 D
obs
s
D
t

19. Example
Does exercising longer have greater
health benefits?
Participants
7 pairs of people matched on age,
sex, & weight
Manipulation (IV)
1 of each pair exercised 2 hrs/week
1 of each pair exercised 5 hrs/week
Outcome (DV): Health rating ~

20. PASW Paired-Sample T Test
Data entry
1 column each DV
Menu
Analyze
Compare Means
Paired-Sample T Test
Dialog box
Paired Variable(s) (DV)
Options(to change confidence intervals) ~

21. PASW Output