1. Reasoning in Psychology Using Statistics
2017

2. Announcements Quiz 7 Due Friday at midnight.
It has a section on independent-t, and another the has the rest to help with reviewing for exam
Exam 3 is 1 week from today (both in-class and in-lab exams)
Distribution of Sample Means (including Central Limit Theorem)
Hypothesis testing
1 sample z
1 sample t
related sample t
independent sample t
Announcements

3. Independent-samples t-test
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples (4 in each group). He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use α = 0.05.
2 samples
The groups are independent
People in one group are not related to those in the other group
Samples are independent
No Memory
treatment
Random
Assignment
Memory
patients
Memory
treatment
Independent-samples t-test

4. Independent-samples t-test
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples (4 in each group). He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use α = 0.05.
2 samples
Samples are independent
Memory
Test X
One score per subject
No Memory
treatment
Compare these
two means
Memory
patients
Random
Assignment
Memory
treatment
Memory
treatment
patients
No Memory
Test
scores
related
Compare pair-wise differences D
Compare: Related-samples t-test (from last lecture)
Independent-samples t-test

5. Independent-samples t-test
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples (4 in each group). He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use α = 0.05.
2 samples
Samples are independent
One score per subject
Independent sample t-test
Independent-samples t-test

6. Independent-samples t-test
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples (4 in each group). He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use α = 0.05.
Memory
Test X
No Memory
treatment
Compare these
two means
Memory
patients
Random
Assignment
Memory
treatment
Hypotheses:
H0:
Memory performance by the treatment group is equal to memory performance by the no treatment group, that is, μA = μB.
Memory performance by the treatment group is NOT equal to memory performance by the no treatment group, that is, μA ≠ μB.
HA:
Independent-samples t-test

7. Testing Hypotheses Hypothesis testing: a five step program
Step 1: State your hypotheses
Step 2: Set your decision criteria
Step 3: Collect your data
Step 4: Compute your test statistics
Compute your estimated standard error
Compute your t-statistic
Compute your degrees of freedom
Step 5: Make a decision about your null hypothesis
Independent-samples t
Related-samples t
These are computed differently than last time
Testing Hypotheses

8. Independent-samples t-test
Related-samples t
Sample means
Test statistic
Independent-samples t-test

9. Independent-samples t-test
Related-samples t
Population means
from the hypotheses
Test statistic
Note that population mean is 0 (difference between group means), just as in related-samples design (average difference)
H0:
Memory performance by the treatment group is equal to memory performance by the no treatment group, that is, μA = μB.
Independent-samples t-test

10. Independent-samples t-test
Related-samples t
Test statistic
Population means
from the hypotheses
H0: Memory performance by treatment group is equal to that by no treatment group or
Difference in memory performance is 0.
HA: Memory performance by treatment group is not equal to to that by no-treatment group or Difference in memory is not 0.
Independent-samples t-test

11. Independent-samples t-test
Related-samples t
Test statistic
Estimated standard error
(difference expected by chance)
estimate is based on one sample
We have two samples, so the estimate is based on two samples
Independent-samples t-test

12. Independent-samples t-test
We combine the variance from the two samples
“pooled variance”
Number of subjects in group A
Number of subjects in group B
Independent-samples t-test

13. Independent-samples t-test
Recall “weighted means,”
need to use
“weighted variances” here
We combine the variance from the two samples
“pooled variance”
Variance (s2) * degrees of freedom (df)
Independent-samples t-test

14. Independent-samples t-test
We combine the variance from the two samples
Recall “weighted means,”
need to use
“weighted variances” here
“pooled variance”
Variance (s2) * degrees of freedom (df)
variance
Independent-samples t-test

15. Performing your statistical test
Independent-samples t
Compute your estimated standard error
Pick whichever one
is easier given what
you know
Compute your t-statistic
Compute your degrees of freedom
This is the one you use to look up your tcrit
Performing your statistical test

16. Independent-samples t-test
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples (4 in each group). He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use α = 0.05.
Need to compute the mean and SS for each sample
Exp.
group
Control group 45 55 40 60 43 49 35 51
Independent-samples t-test

17. Independent-samples t-test
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples (4 in each group). He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use α = 0.05.
Need to compute the mean and SS for each sample
Exp.
group
Control group 45 55 40 60 43 49 35 51
Control group
= 50
(45-50)2 + (55-50)2 + (40-50)2 + (60-50)2
= 250
SS = A
Independent-samples t-test

18. Independent-samples t-test
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples (4 in each group). He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use α = 0.05.
Need to compute the mean and SS for each sample
Exp.
group
Control group 45 55 40 60 43 49 35 51
Exp. group
= 44.5
( )2 + ( )2 + ( )2 + ( )2
= 155
SS = B
Independent-samples t-test

19. Independent-samples t-test
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples (4 in each group). He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use α = 0.05.
Exp.
group
Control group 45 55 40 60 43 49 35 51
= 0.95
Independent-samples t-test

20. Independent-samples t-test
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples (4 in each group). He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use α = 0.05.
Exp.
group
Control group 45 55 40 60 43 49 35 51
= 0.95
tobs= 0.95
tcrit= ±2.447
α = 0.05
2-tailed
Independent-samples t-test

21. Independent-samples t-test
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples (4 in each group). He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use α = 0.05.
Exp.
group
Control group 45 55 40 60 43 49 35 51
= 0.95
tobs= 0.95
tcrit= ±2.447
α = 0.05
2-tailed
Fail to Reject H0
+2.45 = tcrit
tobs=0.95
Independent-samples t-test

22. Independent-samples t-test
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples (4 in each group). He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use α = 0.05.
Exp.
group
Control group 45 55 40 60 43 49 35 51
= 0.95
tobs= 0.95
tcrit= ±2.447
α = 0.05
2-tailed
Fail to Reject H0
“The evidence suggests that there is no difference between those who got the treatment and those who did not.”
Independent-samples t-test

23. Comparing statistical tests
Independent-samples t
Related-samples t
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples (4 in each group). He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use α = 0.05.
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he collects a sample of 4 patients and gives them his new treatment. Before the treatment he gives them a pre-treatment memory test and after the treatment a post-treatment memory test. The data are presented below. Use α = 0.05.
Similar numerators: both involve differences
Between sample means or mean of pair-wise difference scores
Null population mean of no difference = =
Differences between sample means, mean of pair-wise differences
Comparing statistical tests

24. Comparing statistical tests
Independent-samples t
Related-samples t
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples (4 in each group). He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use α = 0.05.
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he collects a sample of 4 patients and gives them his new treatment. Before the treatment he gives them a pre-treatment memory test and after the treatment a post-treatment memory test. The data are presented below. Use α = 0.05.
Dissimilar denominators (standard or sampling error):
Based on pooling 2 samples (n’s can differ) vs. 1 sample of differences
Comparing statistical tests

25. Comparing statistical tests
Independent-samples t
Related-samples t
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use  = 0.05.
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he collects a sample of 4 patients and gives them his new treatment. Before the treatment he gives them a pre-treatment memory test and after the treatment a post-treatment memory test. The data are presented below. Use  = 0.05.
Exp.
group
Control group 45 55 40 60 43 49 35 51
Difference
scores 2 6 5 9
Pair
Group A
Group B 1 3 4
What happens if data are the same?
Comparing statistical tests

26. Comparing statistical tests
Independent-samples t
Related-samples t
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 8 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. The data are presented below. Use  = 0.05.
Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he collects a sample of 4 patients and gives them his new treatment. Before the treatment he gives them a pre-treatment memory test and after the treatment a post-treatment memory test. His sample averaged 60 errors before the treatment and 55 errors after the treatment.
Exp.
group
Control group 45 55 40 60 43 49 35 51
Difference
scores 2 6 5 9
Pair
Group A
Group B 1 3 4
Although data are exactly the same, designs are different, so use different statistical tests, which may produce different conclusions
= 0.95
Fail to Reject H0
Reject H0
Note: that pair-wise differences in related samples t-test reduce difference expected by chance (taking out variability from individual differences)
Comparing statistical tests

27. Hypothesis testing formulas summary
(Estimated)
Standard error df
Design
Test statistic
One sample, σ known
One sample, σ unknown
Two related samples, σ unknown
Two independent samples, σ unknown
Hypothesis testing formulas summary

28. In lab: Practice using independent-sample t-tests, by hand and using SPSS
Questions?
Wrap up

29. Assumptions of t-tests
All t-tests:
Independence: No influence of some scores on other scores (e.g., participants are not from the same family).
Normality: Population is normally distributed. Only extreme violations of this assumption influence t-tests.
Independent-samples t-test:
Homogeneity of Variance: Samples have equal variances. If Levene’s Test of Equality of Variance finds significant difference, SPSS provides corrected values of observed t and degrees of freedom.
Independence: It is impossible to detect violations of this assumption statistically. It is avoided by good research design.
Assumptions of t-tests

30. Independent-Samples T Test in SPSS
Dependent Variable
Independent Variable
Note: First design requiring data column for independent variable
Type in whatever numbers used to code 2 groups
Independent-Samples T Test in SPSS

31. Independent-Samples T Test in SPSS
If Levene’s Test is not significant (small F, p > .05), use upper row to find t-test p-value.
p-value testing Homogeneity of Variance.
If Levene’s Test is significant (large F, p <.05), use lower row to find t-test p-value.
Independent-Samples T Test in SPSS

32. Independent-Samples T Test in SPSS
Fail to reject H0
t-value too small, p > .05
Independent-Samples T Test in SPSS

33. Graphing Independent-Samples T Tests

34. Graphing Independent-Samples T Tests