1. Understanding Statistics in Research

2. Reminders
Final drafts of the APA Style Paper are due in lecture next Wednesday (Nov 19)

3. Statistics Descriptive Statistics Inferential Statistics
Describe the data you collected from the sample
Inferential Statistics
Making inferences about the population from the data collected from the sample
Generalize results from study to the population

4. Inferential Statistics
Example Experiment:
Group A - gets treatment to improve memory
Group B - gets no treatment (control)
After treatment period test both groups for memory
Results:
Group A’s average memory score is 80%
Group B’s average memory score is 76%
Is the 4% difference a “real” difference (statistically significant) or is it just sampling error?
Would this difference be found in the population? This is what inferential statistics tests.

5. Inferential Statistics
This type of statistics is based on making hypotheses and testing them
Five main steps to test hypotheses

6. Testing hypotheses Step 1: State your hypotheses
Step 2: Set your criteria
Step 3: Collect your data from your sample
Step 4: Compute your test statistics
Step 5: Make a decision about your hypotheses
Reject your null hypothesis
Fail to reject your null hypothesis

7. Testing hypotheses Step 1: State your hypotheses Null hypothesis (H0):
“There are no differences between the groups”
This is the hypothesis that you are testing!
Alternative hypothesis (Ha):
“There are effects/differences between the groups”
This is what you expect to find!

8. State your hypotheses
The Null hypothesis is always opposite the alternative hypothesis
Example:
Ha: The training group will be different from the control group
H0: The training group will not be different from the control group
Ha: The training group will perform better than the control group
H0: The training group will not perform better than the control group (equal or worse)

9. State your hypotheses
You are not attempting to prove your alternative hypotheses
You are testing the null hypothesis
If you reject the null hypothesis, then you are left with support for the alternative(s)

10. State your hypotheses In memory example experiment
Alternative- Ha: mean of Group A ≠ mean of Group B
(Or: Group A > Group B)

11. State your hypotheses In memory example experiment
Alternative- Ha: mean of Group A ≠ mean of Group B
(Or: Group A > Group B)
Null- H0: mean of Group A = mean of Group B
(Or: Group A  Group B)

12. State your hypotheses In memory example experiment
Alternative- Ha: mean of Group A ≠ mean of Group B
(Or: Group A > Group B)
Null- H0: mean of Group A = mean of Group B
(Or: Group A  Group B)
Which hypothesis do we test?

13. Testing hypotheses Step 1: State your hypotheses
Step 2: Set your decision criteria
Your alpha level will tell you what to decide
Reject the null hypothesis
Fail to reject the null hypothesis

14. Set your decision criteria
Because you set the criteria it is possible that you could make the wrong decision
Type I error: saying there is a difference when there really isn’t one
Reject null when you should fail to reject
alpha level = probably of making this type of error
Type II error: saying there is not a difference when there really is one
Fail to reject when you should have reject

15. Types of Errors Real world (truth) Type I error Type II error
H0 is correct (really are no differences)
H0 is wrong (really are differences)
Type I error
Reject H0 (there are differences)
Type II error
Experimenter’s conclusions
Type II error
Fail to reject H0 (there are no differences)

16. Types of Errors Real world example: Courtroom Analogy
Real world (truth)
Defendant really is innocent
Defendant really is guilty
Type I error
Found guilty
Jury’s decision
Type II error
Found not guilty

17. Types of Errors
Type I error: concluding that there is an effect (a difference between groups) when there really isn’t
Alpha level (a)
Sometimes called “significance level”
Pick a low level of alpha
Psychology: 0.05 and 0.01 most common
Type II error: concluding that there isn’t an effect, when there really is.
Beta (b)
Related to the Statistical Power of a test (1- b)
How likely are you able to detect a difference if it is there

18. Testing hypotheses Step 1: State your hypotheses
Step 2: Set your decision criteria
Step 3: Collect your data from your sample(s)
Step 4: Compute your test statistics
Descriptive statistics (means, standard deviations, etc)
Inferential statistics (t-tests, ANOVA, etc)

19. Testing hypotheses Step 1: State your hypotheses
Step 2: Set your decision criteria
Step 3: Collect your data from your sample(s)
Step 4: Compute your test statistics
Step 5: Make a decision about your hypotheses
Reject H0: Statistically significant differences
Fail to reject H0: Not statistically significantly differences

20. Decision about your hypotheses
What does statistically significant differences mean?
Reject the null hypothesis
Support the alternative hypothesis
The differences/effects you found are above what you’d expect by “chance”

21. Decision about your hypotheses
Level of chance is determined by how much sampling error there is
More sampling error less likely to have a significant finding
Sampling error is the difference between the sample and the population
Influenced by:
Sample Size
Population variability

22. (Pop mean - sample mean)
Sampling Error
Population mean
Population
Distribution x
n = 1
Sampling error
(Pop mean - sample mean)

23. (Pop mean - sample mean)
Sampling Error
Population mean
Population
Distribution
Sample mean x x
Sampling error
(Pop mean - sample mean)
n = 2

24. (Pop mean - sample mean)
Sampling Error
Population mean
Population
Distribution
Sample mean x
n = 10
As the sample size increases, the sampling error decreases
Sampling error
(Pop mean - sample mean)

25. Sampling Error
Due to a smaller range of possible sample means, the sampling error decreases
Large population variability
Small population variability

26. Sampling Error Influenced by: Sample size Population variability
As sample size increases, the sampling error decreases
Population variability
As the population variability decreases, the sampling error decreases

27. Distribution of sample means
These two factors (pop variability and sample size) combine to impact the distribution of sample means.
A distribution of all possible sample means of a particular sample size that can be drawn from the population
Population
Distribution of sample means XC
Samples of size = n XA XD
Avg. Sampling error XB
“chance”

28. What is Significance? Rejecting the null hypothesis
A statistically significant difference means:
The researcher is concluding that there is a difference above and beyond chance
With the probability of making a type I error at 5% (assuming an alpha level = 0.05)
Not the same thing as theoretical significance
Only a statistical difference
Doesn’t mean that it is an important difference

29. What is Non-significance?
Failing to reject the null hypothesis
Can’t accept because can’t prove anything
Usually not as interesting as rejecting the null
Typically, check to see if you made a Type II error (failed to detect a difference that is really there)
Check the statistical power (probability of finding an effect if there is one) of your test
Sample size is too small
Effects that you’re looking for are really small
Check your method, may be too much variability

30. Testing hypotheses: Next lecture
Tests that calculate significance
Generic statistical test
T-test: 2 group means
Analysis of Variance (ANOVA): more than 2 group means