1. S519: Evaluation of Information Systems
Social Statistics
Inferential Statistics
Chapter 11: ANOVA

3. This week When to use F statstic How to compute and interpret
Using FTEST and FDIST functions
How to use the ANOVA

4. The problem with t-tests…
We could compare three groups with multiple ttests: M1 vs. M2, M1 vs. M3, M2 vs. M3

5. What is ANOVA? “Analysis of Variance”
A hypothesis-testing procedure used to evaluate mean differences between two or more treatments (or populations).
Related to: t-tests using independent-measures or repeated- measures design.
Advantages:
1) Can work with more than two samples.
2) Can work with more than one independent variable

6. What is ANOVA?
In ANOVA an independent or quasi-independent variable is called a factor.
Factor = independent (or quasi-independent) variable.
Levels = number of values used for the independent variable.
One factor → “single-factor design”
More than one factor → “factorial design”

7. What is ANOVA? An example of a single-factor design
A example of a two-factor design

8. F value Variance between treatments can have two interpretations:
Variance is due to differences between treatments.
Variance is due to chance alone. This may be due to individual differences or experimental error.

9. Three Types of ANOVA
Independent measures design: Groups are samples of independent measurements (different people)
Dependent measures design: Groups are samples of dependent measurements (usually same people at different times; also matched samples) “Repeated measures”
Factorial ANOVA (more than one factor)

10. Excel: ANOVA Three different ANOVA: Anova: single factor - independent
Anova: two factors with replication - factorial
Anova: two factors without replication - dependent

11. Example (independent)
Three groups of preschoolers and their language scores, whether they are overall different?
Group 1 Scores
Group 2 Scores
Group 3 Scores 87 89 86 85 91 76 99 96 56 78 79 98 81 90 77 82 66 75 67 93

12. F test steps Step1: a statement of the null and research hypothesis
One-tailed or two-tailed (there is no such thing in ANOVA)

13. F test steps
Step2: Setting the level of risk (or the level of significance or Type I error) associated with the null hypothesis
0.05

14. F test steps Step3: Selection of the appropriate test statistics
See Figure 11.1 (S-p227)
Simple ANOVA (independent)

15. F test steps Between-group degree of freedom=k-1
k: number of groups
Within-group degree of freedom=N-k
N: total sample size

16. F test steps
Step4: determination of the value needed for rejection of the null hypothesis using the appropriate table of critical values for the particular statistic
Table B3 (S-p363)
df for the denominator = n-k=30-3=27
df for the numerator = k-1=3-1=2

17. F test steps
Step5: comparison of the obtained value and the critical value
If obtained value > the critical value, reject the null hypothesis
If obtained value < the critical value, accept the null hypothesis
8.80 and 3.36

18. F test steps Step6 and 7: decision time What is your conclusion? Why?
How do you interpret F(2, 27)=8.80, p<0.05

19. Example (dependent)
Five participants took a series of test on a new drug T1 T2 T3 T4 P1 3 4 6 7 P2 P3 2 1 5 P4 P5

20. F test steps Step1: a statement of the null and research hypothesis
One-tailed or two-tailed (there is no such thing in ANOVA)

21. F test steps
Step2: Setting the level of risk (or the level of significance or Type I error) associated with the null hypothesis
0.05

22. F test steps Step3: Selection of the appropriate test statistics
See Figure 11.1 (S-p227)
Simple ANOVA (independent)

23. F test steps Between-group degree of freedom=k-1
k: number of groups
Within-group degree of freedom=N-k
N: total sample size
Between-subject degree of freedom=n-1
n: number of subjects
Error degree of freedom=(N-k)-(n-1)

24. F test steps
Step4: determination of the value needed for rejection of the null hypothesis using the appropriate table of critical values for the particular statistic
Table B3 (S-p363)
df for the denominator = (N-k)-(n-1)=16-4=12
df for the numerator = k-1=4-1=3

25. F test steps
Step5: comparison of the obtained value and the critical value
If obtained value > the critical value, reject the null hypothesis
If obtained value < the critical value, accept the null hypothesis
24.88 and 3.49

26. F test steps Step6 and 7: decision time What is your conclusion? Why?
How do you interpret F(3, 12)=24.88, p<0.05

27. Factorial ANOAVA
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