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Lecture 9:
15
30
45
Anova: TwoFactor Without Replication
Or one
way
with
blocking
25
35
45
0
40
80
summar
y
Count
Sum
Averag
e
Varianc
e
41
45
49
Row 1
3
90
30
225
40
50
60
Row 2
3
105
35
100
39
55
71
Row 3
3
120
40
1600
80
60
40
Row 4
3
135
45
16
55
65
75
Row 5
3
150
50
100
65
70
75
Row 6
3
165
55
256
Row 7
3
180
60
400
Row 8
3
195
65
100
Row 9
3
210
70
25
Col. 1
9
360
40
612.75
col.2
9
450
50
187.5
col. 3
9
540
60
242.75
ANOVA
Source of
Variation
SS
df
MS
F
Pvalue
F crit
Rows
4500
8
562.5
2.341
0.070
2.591
Columns
1800
2
900
3.746
0.046
3.634
Error
3844
16
240.25
Total
10144
26
1 of 10
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View Full DocumentFor sample data:
a=2, n=3
For sample data:
b=3, n=3
MBA 612 – Quantitative Problem solving
Notes from Lecture 9
The above data set is referenced in the following lecture.
This lecture covers three main topics:
•
Topic 1: Apriori test, as
applied to one way with blocking
•
Topic 2: Scheffé Method of Identifying differences (Posthoc test),
as applied to
one way with blocking
•
Topic 3: Twoway ANOVA
1. Apriori test
Apriori test: This is a preconceived hypothesis of interest before seeing results. There are
applicable to all ANOVA procedures including one way with blocking . Apriori is used to find out
where significant differences are at; once it is determined from the ANOVA procedure that a
significant difference does exist.
We usually hunt for significant differences among the treatment
means. We do not usually perform test of hypothesis hunting for significant differences among
blocking means. The only test we perform on the blocked means is to determine whether or not
we have blocked on a significant variable. We do that by looking at the F value associated with
blocks.
General Information Concerning APrior Tests and Post Hoc Tests Reviewed
An apriori test has a specified level of alpha assigned to that specific test. Recall that alpha is the
probability of rejecting a true hypothesis. The benefit of setting alpha at a reasonable level, (other
than zero) is if alpha is set reasonably high, then one has a good probability of identifying
significant differences when they do exist. That is, if alpha is reasonable high, then one has
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 Summer '10
 chandrasekhar
 Statistics, Replication

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