1. Part IV Significantly Different Using Inferential Statistics
Chapter 16    
What to Do When You’re Not Normal:
Chi-Square and Some Other Nonparametric Tests

2. What you will learn in Chapter 16
A brief survey of nonparametric statistics
When they should be used
How they should be used

3. 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”

4. 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

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

6. More Hypotheses Null hypothesis Research hypothesis
Categories do not differ significantly from each other;

7. 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/E
For 23 30 7 49
1.63
Maybe 17 13
169
5.63
Against 50 20
400
13.33
Total 90
C2 = 20.6

8. Computing Chi Square: You Try!! Critical Value pg. 364;
Category O E D
(O-E)2
(O-E)2/E
Republican
800
Democrat
700
Independent
900
Total
2400
C2 =

9. Computing Chi Square: You Try!!
Category O E D
(O-E)2
(O-E)2/E
Republican
800
Democrat
700
100
10000
12.5
Independent
900
Total
2400
C2 = 25
Pg. 364; Critical value= dfs=2; critical value=5.99;

10. 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

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

12. SPSS Output
What does it all mean?

13. Other Nonparametric Tests

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