Psych 100A - Lecture 17-18
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Transcript of Psych 100A - Lecture 17-18
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Nonparametric Tests
Chapter 15
Revised by Jeffrey B. Henriques, Ph.D.
University of Wisconsin-Madison
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Nonparametric Statistics
• A special class of hypothesis tests
• Used when assumptions for parametric
tests are not met
• Like?!
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
When to Use Nonparametric Tests
• When the dependent variable is
nominal
• Examples?
• When the dependent variable is ordinal
• Examples?
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
When to Use Nonparametric Tests
• When the sample size is small
• Why?
• When underlying population is not
normal
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Limitations of Nonparametric Tests
• Cannot easily use confidence intervals
or effect sizes
• Have less statistical power than
parametric tests
• More likely to commit type II error
• Meaning?
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Chi-Square Test for Goodness of Fit
• When we have one nominal variable
• The six steps of hypothesis testing1. Identify the populations, distribution, and
assumptions
2. State the null and research hypotheses
3. Determine the characteristics of the
comparison distribution
4. Determine the critical value, or cutoff
5. Calculate the test statistic
6. Make a decision
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Formulae
c 2 =(O- E)2
E
é
ëê
ù
ûúå
1 rowrow kdf
1 columncolumn kdf
))((2 columnrowXdfdfdf
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Step 4: Determine the Critical Value
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Step 5: Calculate the Test Statistic
c 2 =(O-E)2
E
é
ëê
ù
ûúå = (20.571+ 20.571= 41.142
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Step 6: Make a Decision
41.14
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
VEGAS BABY!!!
Rolling dice at the Mirage
Lots of Snake Eyes coming up
Are the dice fixed?
Test with goodness of fit
Does our distribution FIT the expected
distribution
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. HeinzenVEGAS BABY!!!
Expected distribution for 120 rolls if fair:
Each die(dice) has 1/6 chance
1/6 X 120 = 20 of each type
Expected Distribution =
[20,20,20,20,20,20]
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. HeinzenVEGAS BABY!!!
Actual distribution for 120 rolls is:
[28,16,23,23,17,13]
Are these dice fair?
Use Goodness of fit χ2
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. HeinzenVEGAS BABY!!!
Determine critical χ2 value:
df = number of categories – 1
= 6-1 = 5
χ2 critical for df=5 is
11.07 from table
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Chi-Square Test for Independence
• The six steps of hypothesis testing1. Identify the populations, distribution, and
assumptions
2. State the null and research hypotheses
3. Determine the characteristics of the
comparison distribution
4. Determine the critical value, or cutoff
5. Calculate the test statistic
6. Make a decision
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
c 2 =(O- E)2
E
é
ëê
ù
ûúå = (2.218+0.837+ 2.197+0.829 = 6.081
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Step 6: Make a Decision
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Cramer’s V (phi)
• The effect size for chi-square test for
independence
))(( /
2
columnrowdfN
X
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Graphing Chi-Square Percentages
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
An Alternative Graph
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Relative Risk
• We can quantify the size of an effect
with chi square through relative risk,
also called relative likelihood
• By making a ratio of two conditional
proportions, we can say, for example,
that one group is three times as likely
to show some outcome or, conversely,
that the other group is one-third as
likely to show that outcome
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
HUH?!?!?
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Other Nonparametric Tests
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Spearman Rank-Order Correlation
Coefficient
• Quantifies the association between two
ordinal variables
• Calculating Spearman’s correlation
rs=1-
6( D2 )åN (N 2 -1)
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
A little example
• Is there a relationship between
• Level of “national competitiveness”
• Level of “national pride”
?
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
Essentials of Statistics for the Behavioral Sciences, 2nd EditionSusan A. Nolan Thomas E. Heinzen
rs=1-
6( D2 )åN (N 2 -1)
=1-6(98.5)
10(102 -1)=1-
591
10(99)=1-
591
990=1-0.597 = 0.403