ANOVA
Presentation
•
Mathematics
•
University
•
Practice Problem
•
Easy
Keith Mitchell
Used 8+ times
FREE Resource
13 Slides • 21 Questions
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Want to compare MANY (i.e ≥ 2) groups/populations to see if there are differences between them...
Need some way of determining if centres of populations/groups are either:
⊳close (so no difference between groups) or
⊳far apart (so difference between groups)
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4
Compare between-group variance to within-group variance using F-ratio:
5
The F-ratio is calculated using an ANOVA Table:
6
where...
7
A decision (about whether there is at least one group/population that is different to the others) is made by comparing the F-ratio to a critical/threshold value Fc .
Fc is found from statistical tables using
k - 1 numerator degrees-of-freedom, and
n - k denominator degrees-of-freedom
Decision: if F-ratio > Fc then reject H0 (i.e. at least one group/population different).
8
EXAMPLE: Below is a partially completed ANOVA Table. For this table, answer the questions that follow.
9
Fill in the Blanks
How many treatments/groups are there?
Type answer...
10
Fill in the Blanks
What is the total sample size?
Type answer...
11
Fill in the Blanks
What is the within-group d.f.?
Type answer...
12
Fill in the Blanks
What is the within-group sum-of-squares?
Type answer...
13
Fill in the Blanks
What is the between-group sum-of-squares?
Type answer...
14
Fill in the Blanks
What is the between-group variance (i.e. between-group mean sum-of-squares)?
Type answer...
15
Fill in the Blanks
What is the F-ratio?
Type answer...
16
Multiple Choice
What are the hypotheses corresponding to this table?
H0: μ1=μ2=μ3 H1: at least two means are different
H0: F = 0
H1: F =0
H0: μ1+μ2+μ3 = 0 H1: μ1+μ2+μ3=0
17
Fill in the Blanks
What is the critical/threshold F-value?
Type answer...
18
Multiple Choice
What is the decision regarding the hypotheses?
Reject H0 (i.e. there is a difference between the groups)
Fail to reject H0 (i.e. there is no difference between the groups)
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EXAMPLE:
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Fill in the Blanks
What is the within-group sum-of-squares?
Type answer...
22
Fill in the Blanks
What is the Total d.f.?
Type answer...
23
Fill in the Blanks
What is the within-group d.f.?
Type answer...
24
Fill in the Blanks
What is the between-group d.f.?
Type answer...
25
Fill in the Blanks
What is the between-group mean sum-of-squares?
Type answer...
26
Fill in the Blanks
What is the F-ratio (to 3 d.p.)?
Type answer...
27
Fill in the Blanks
What is the critical/threshold value for F ( to 2 d.p.)?
Type answer...
28
Multiple Choice
What is the decision about the hypotheses?
Reject H0 i.e. the groups are not different.
Reject H0 i.e. at least two groups are different.
Fail to reject H0 i.e. the groups are not different.
Fail to reject H0 i.e. at least two groups are different.
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Multiple Choice
Does this confirm that none of the groups are different from one another?
No, all the confidence intervals are different.
Yes, all confidence intervals overlap.
No, the confidence intervals have a clear order.
Yes, all the confidence intervals exclude 0.
33
Fill in the Blanks
What was the standard error used to calculate these confidence intervals (to 3 d.p.)?
Type answer...
34
Fill in the Blanks
What is the critical/threshold t value used to calculate these confidence intervals (to 3 d.p.)?
Type answer...
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