1. Part IV Significantly Different: Using Inferential Statistics
Chapter 13 
Two Groups Too Many?
Try Analysis of Variance (ANOVA)

2. What you will learn in Chapter 13
What Analysis of Variance (ANOVA) is and when it is appropriate to use
How to compute the F statistic
How to interpret the F statistic
How to use SPSS to conduct an ANOVA
single factor design

3. Analysis of Variance (ANOVA)
Used when more than two group means are being tested simultaneously
Group means differ from one another on a particular score / variable
Example: DV = GRE Scores & IV = Ethnicity
Test statistic = F test
R.A. Fisher, creator

4. Path to Wisdom & Knowledge
How do I know if ANOVA is the right test?

5. Different Flavors of ANOVA
ANOVA examines the variance between groups and the variances within groups
These variances are then compared against each other
Similar to the t Test…only in this case you have more than two groups
One-way ANOVA
Simple ANOVA
Single factor (grouping variable)

6. More Complicated ANOVA
Factorial Design
More than one treatment/factor examined
Multiple Independent Variables
One Dependent Variable
Example – 3x2 factorial design
Number of Hours in Preschool G e n d r
Male
5 hours
per week
10 hours
20 hours
Female

7. Computing the F Statistic
Rationale…want the within group variance to be small and the between group variance to be large in order to find significance.

8. Hypotheses
Null hypothesis
Research hypothesis

9. Source Table Source SS df MS F Between 1,133.07 27 566.54 8.799 Within
1,738.40 29
64.39
Note: F value for two group is the same as t2

10. Degrees of Freedom (df)
Numerator
Number of groups minus one
k-1
3 groups – 1 = 2
Denominator
Total number of observations minus the number of groups
N-1
100 participants – 3 = 97
Represented: F (2, 27)

11. How to Interpret F (2,27) = 8.80, p < .05 F = test statistic
2,27 = df between groups & df within groups
{Ah ha…3 groups and 30 total scores examined}
8.80 = obtained value
Which we compared to the critical value
p < .05 = probability less than 5% that the null hypothesis is true
Meaning the obtained value is GREATER than the critical value

12. Omnibus Test
The F test is an “omnibus test” and only tells you that a difference exists
Must conduct follow-up t tests to find out where the difference is…
BUT…Type I error increases with every follow-up test / possible comparison made
1 – (1 – alpha)k
Where k = number of possible comparisons

13. Using the Computer
SPSS and the One-Way ANOVA

14. SPSS Output
What does it all mean?

15. Post Hoc Comparison

16. Glossary Terms to Know Analysis of variance Omnibus test
Simple ANOVA
One-way ANOVA
Factorial design
Omnibus test
Post Hoc comparisons
Source table

17. Part IV Significantly Different: Using Inferential Statistics
Chapter 17    
What to Do When You’re Not Normal:
Chi-Square and Some Other Nonparametric Tests

18. What you will learn in Chapter 17
A brief survey of nonparametric statistics
When they should be used
How they should be used

19. Introduction Parametric statistics have certain assumptions
Variances of each group are similar
Sample is large enough to represent the population
Nonparametric statistics don’t require the same assumptions
Allow data that comes in frequencies to be analyzed…they are “distribution free”

20. One-Sample Chi-Square
Chi-square allows you to determine if what you observe in a distribution of frequencies is what you would expect to occur by chance.
One-sample chi-square (goodness of fit test) only has one dimension
Two-sample chi-square has two dimensions

21. Computing Chi-Square
What do those symbols mean?

22. More Hypotheses H0: P1 = P2 = P3 H1: P1 P2 P3 Null hypothesis
Research hypothesis
H1: P1 P2 P3

23. Computing Chi Square C2 = 20.6 For 23 30 7 49 1.63 Maybe 17 13 169
Category O E D
(O-E)2
(O-E)2/2
For 23 30 7 49
1.63
Maybe 17 13
169
5.63
Against 50 20
400
13.33
Total 90
C2 = 20.6

24. So How Do I Interpret… x2(2) = 20.6, p < .05
x2 represents the test statistic
2 is the number of degrees of freedom
20.6 is the obtained value
p < .05 is the probability

25. Using the Computer
One-Sample Chi Square using SPSS

26. SPSS Output
What does it all mean?

27. Other Nonparametric Tests

28. Glossary Terms to Know
Parametric
Nonparametric
One-sample Chi Square