Transcript Part I In the Beginning

Part IV
Significantly Different
Using Inferential Statistics
Chapter 16    
What to Do When You’re Not Normal:
Chi-Square and Some Other
Nonparametric Tests
What you will learn in Chapter 16
 A brief survey of nonparametric
statistics
 When they should be used
 How they should be used
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”
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
Computing Chi-Square
 What do those symbols mean?
More Hypotheses
 Null hypothesis
 Research hypothesis
Computing Chi Square
Category
O
E
D
(O-E)2
(O-E)2/E
For
23
30
7
49
1.63
Maybe
17
30
13
169
5.63
Against
50
30
20
400
13.33
Total
90
90
C2 = 20.6
Computing Chi Square: You
Try!! Critical Value pg. 364;
Category
O
Republican
800
Democrat
700
Independent
900
Total
2400
E
D
(O-E)2
C2 =
(O-E)2/E
Computing Chi Square: You
Try!!
Category
O
E
D
(O-E)2
(O-E)2/E
Republican
800
800
0
0
0
Democrat
700
800
100
10000
12.5
Independent
900
800
100
10000
12.5
Total
2400
C2 = 25
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
Using the Computer
 One-Sample Chi Square using SPSS
SPSS Output
 What does it all mean?
Other
Nonparametric
Tests
Glossary Terms to Know
 Parametric
 Nonparametric
 One-sample Chi Square