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 Categories do not differ significantly from each other;

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

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 =

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= .05 3-1 dfs=2; critical value=5.99;

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