1. Reasoning in Psychology Using Statistics
2018

2. Exam 3 review: Inferential Statistics
Distribution of sample means
Standard error
Central limit theorem
Hypothesis testing
5 step program
Hypotheses
Null and Alternative
1 or 2 tailed
Error types
p(Type I error) = α alpha
p(Type II error) = β beta
Reaching a conclusion
Reject the H0
Fail to reject H0
Test statistics
1-sample z
1-sample t
Related sample t
Independent sample t
Exam 3 review: Inferential Statistics

3. Inferential statistics
Hypothesis testing
Testing claims about populations (and the effect of variables) based on data collected from samples
Using estimates of the sampling error (expected difference between the sample statistics and the population parameters)
Population
Sample
Inferential statistics used to generalize back
Sampling to make data collection manageable
Inferential statistics

4. Testing Hypotheses Hypothesis testing A five step program
Testing claims about populations (and the effect of variables) based on data collected from samples
Using estimates of the sampling error (expected difference between the sample statistics and the population parameters)
A five step program
Step 1: State your hypotheses
Step 2: Set your decision criteria
Step 3: Collect your data from your sample
Step 4: Compute your test statistics
Step 5: Make a decision about your null hypothesis
Testing Hypotheses

5. Concluding that there isn’t an effect, when there really is
Real world (‘truth’)
Concluding that there is a difference between groups (“an effect”) when there really isn’t
H0 is correct
H0 is wrong
Type I error
Reject H0
Experimenter’s conclusions
Fail to Reject H0
Type II error
Concluding that there isn’t an effect, when there really is
Error types

6. Properties of the distribution of sample means
Central Limit Theorem
For any population with mean μ and standard deviation σ, the distribution of sample means for sample size n will approach a normal distribution with a mean of μ and a standard deviation of as n approaches infinity
(good approximation if n > 30).
Population σ μ
Distribution of sample means
Sample s X
Properties of the distribution of sample means

7. Properties of the distribution of sample means
Central Limit Theorem
For any population with mean μ and standard deviation σ, the distribution of sample means for sample size n will approach a normal distribution with a mean of μ and a standard deviation of as n approaches infinity
(good approximation if n > 30).
Distribution of sample means
the average amount a sample mean (of a particular sample size) will differ from the population mean.
Standard error:
Used as our difference expected by chance in our test statistics.
Properties of the distribution of sample means

8. Properties of the distribution of sample means
Could be difference between a sample and a population, or between different samples
“Generic” test statistic
the average amount a sample mean (of a particular sample size) will differ from the population mean.
Standard error:
Used as our difference expected by chance in our test statistics.
Properties of the distribution of sample means

9. Performing your inferential statistics
Analyze the question/problem.
The design of the research: how many groups, how many scores per person, is the population σ known, etc.
Use the decision tree
Will you use z’s or t’s?
If two samples, are they independent or related?
Write out what information is given
Means, standard deviations, number of subjects, α-level, etc.
Is it asking you to test a difference or make an estimate?
If hypothesis test:
What are the H0 and HA?
1-tailed or 2-tailed hypotheses?
What is your critical value of your test statistic (z or t from table, you will need your α-level, and df, and 1-or-2 tailed)
|z|
.00
.01 :
1.0
2.0
3.0
0.5000
0.1587
0.0228
0.0013
0.4960
0.1562
0.0222
Performing your inferential statistics

10. Performing your inferential statistics
Analyze the question/problem.
Now you are ready to do some computations
Write out all of the formulas that you will need
Test statistic, (estimated) standard error, standard deviation, SS, mean, degrees of freedom
Then fill in the numbers as you know them
Performing your inferential statistics

11. Performing your inferential statistics
Analyze the question/problem.
Now you are ready to do some computations
Draw a Conclusion and Interpret your final answer
Reject or fail to reject the null hypothesis?
Distribution of the t-statistic or z-statistic
The α-level defines the critical regions
Performing your inferential statistics

12. Performing your inferential statistics
Analyze the question/problem.
Now you are ready to do some computations
Draw a Conclusion and Interpret your final answer
Reject or fail to reject the null hypothesis?
Distribution of the t-statistic or z-statistic
“Evidence suggests that the treatment has an effect”
If the observed test statistic is here Reject H0
If the observed test statistic is here Fail to reject H0
“Evidence suggests that the treatment has no effect”
Performing your inferential statistics

13. The t-distribution Drawing your conclusions: Using the t-table
Suppose that you conduct a one sample t-test and get a computed t = (with a df = 8). Using a 2-tailed test with an α-level of 0.05, what would you conclude?
α = 0.05
2-tailed
df = n - 1 = 8
“Reject H0”
t =
tcrit = +1.86
The t-distribution

14. The t-distribution Drawing your conclusions: Using the SPSS output
Suppose that you conduct a one sample t-test and get a computed t = (with a df = 8). Using a 2-tailed test with an α-level of 0.05, what would you conclude?
α = 0.05
2-tailed
df = n - 1 = 8
“Reject H0”
t =
0.001 area in the tail
tcrit = +1.86
, which is within the .05 defined by α
Can compare the p-value and the alpha level
t-value large enough, p < α (e.g., .05)
Reject H0
t-value too small, p > α (e.g., .05)
Fail to reject H0
The t-distribution

15. 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

16. How do I study for this test?
The usual:
Review lecture notes and labs
Re-read the Reading packet
Do practice problems
Remember to ask yourself “conceptual questions”
e.g., “What would happen to my standard error if I increased my sample size?”
Make Flash Cards of problems
How do I study for this test?

17. Make your flash cards Side 1: Write out the problem
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 (A) the new treatment but not the other (B) and then tests both groups with a memory test. Use α = 0.05.
Side 1: Write out the problem
Independent samples t-test
Two tailed “any impact”
H0: μA = μB
HA: μA ≠ μB
α-level =0.05
Side 2: Write out the solution
Fail to Reject H0
Evidence suggests that the treatment has no effect
Make your flash cards

18. Make your flash cards Related samples t-test
Dr. Ruthie asked each member of 10 married couples with children to rate the importance of “nights out” (1=not important, 5= very important). Dr. Ruthie hypothesized that wives would consider the nights out more important than the husbands. Test her hypothesis with a probability of making a type I error = 0.05.
Husbands: 5, 3, 4, 2, 3, 4, 5, 1, 1, 4
Wives: , 4, 5, 3, 2, 4, 5, 2, 3, 4
Related samples t-test
Reject H0
One tailed “more important”
H0: μD > 0
HA: μD < 0
α-level =0.05
Evidence suggests that wives do care more
Make your flash cards

19. Make your flash cards One sample t-test
Dr. Psychic examined the performance of 28 students who answered multiple-choice items on the SAT test without having read the passages to which the items referred. The mean score was 46.6 (out of 100), with a standard deviation of Test whether these students performed different than chance (chance performance would result in 20 correct scores) with an α-level = 0.01.
One sample t-test
Reject H0
Two tailed “different than”
H0: μ = 20
HA: μ ≠ 20
α-level =0.01
Evidence suggests that performed differently from chance
Make your flash cards

20. 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

21. 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

22. 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 difference scores in related samples t-test reduce difference expected by chance (taking out variability from individual differences)
Comparing statistical tests

23. Practice determining which statistical test is appropriate for a number of different situations, and carrying out that test (practice by hand and using SPSS).
In labs