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Part IV
Significantly Different:
Using Inferential Statistics
Chapter 13 
Two Groups Too Many?
Try Analysis of Variance (ANOVA)
Analysis of Variance (ANOVA)
 Used to test for differences between two or
more group means.
 Group means differ from one another on a
particular score / variable
 Example: Do GRE Scores differ by major?
 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 (Variance Between / Variance
Within)
 Same function as the t Test…only in this case
you have more than two groups
 One-way ANOVA
 Simple ANOVA
 Single factor (grouping variable)
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 groups ANOVA 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
 10 participants per group x 3 groups = 30 – 3 = 27
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
 There are significant differences in the means.
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
 Cumulative Type 1 Error = 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

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