Transcript Part IV Significantly Different: Using Inferential Statistics

Part IV
Significantly Different:
Using Inferential Statistics
Chapter 13 
Two Groups Too Many?
Try Analysis of Variance (ANOVA)
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
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
Path to Wisdom & Knowledge
 How do I know if ANOVA is the right test?
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)
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
e
r
Male
Female
5 hours
per week
10 hours
per week
20 hours
per week
5 hours
per week
10 hours
per week
20 hours
per week
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.
Hypotheses
 Null hypothesis
 Research hypothesis
Source Table
Source
Between
SS
1,133.07
df
27
MS
566.54
Within
1,738.40
29
64.39
F
8.799
Note: F value for two group is the same as t2
Degrees of Freedom (df)
 Numerator
 Number of groups minus one
 k-1
 3 groups --- 3 – 1 = 2
 Denominator
 Total number of observations minus the number of
groups
 N-1
 100 participants --- 30 – 3 = 97
Represented: F (2, 27)
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
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
Using the Computer
 SPSS and the One-Way ANOVA
SPSS Output
 What does it all mean?
Post Hoc Comparison
Glossary Terms to Know
 Analysis of variance
 Simple ANOVA
 One-way ANOVA
 Factorial design
 Omnibus test
 Post Hoc comparisons
 Source table
Part IV
Significantly Different:
Using Inferential Statistics
Chapter 17    
What to Do When You’re Not Normal:
Chi-Square and Some Other
Nonparametric Tests
What you will learn in Chapter 17
 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
(O  E)
x 
E
2
 What do those symbols mean?
2
More Hypotheses
 Null hypothesis
H0: P1 = P2 = P3
 Research hypothesis
H1: P1 P2 P3
Computing Chi Square
Category
O
E
D
(O-E)2
(O-E)2/2
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
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