Traditional course condensed
2.
Traditional course regular length
3.
Online course condensed
4.
Online course regular length
Chap 11-53
DCOV
A

Excel Analysis Of Collapsed
Data
Chap 11-54
DCOV
A
Group is a significant effect.
p-value of 0.0003 < 0.05
1.
Traditional regular > Traditional condensed
2.
Online condensed > Traditional condensed
3.
Traditional regular > Online regular
4.
Online condensed > Online regular
If the course is take online should use the
condensed version and if the course is taken
by traditional method should use the regular.

The Randomized Block Design
Is Often Useful
The randomized block design is an on-line topic
Chap 11-55

Chap 11-56
Chapter Summary
In this chapter we discussed
The one-way analysis of variance
The logic of ANOVA
ANOVA assumptions
F
test for difference in
c
means
The Tukey-Kramer procedure for multiple comparisons
The Levene test for homogeneity of variance
The two-way analysis of variance
Examined effects of multiple
factors
Examined interaction between factors

RBD - 1
Online Topic
The Randomized Block Design
Statistics for Managers Using
Microsoft Excel
7
th
Edition

RBD - 2
Learning Objective
To learn the basic structure and use of a randomized block design

RBD - 3
The Randomized Block Design
Like One-Way ANOVA, we test for equal
population means (for different factor levels, for
example)...
...but we want to control for possible variation
from a second factor (with two or more levels)
Levels of the secondary factor are called
blocks
DCOV
A

RBD - 4
Partitioning the Variation
Total variation can now be split into three parts:
SST = Total variation
SSA = Among-Group variation
SSBL = Among-Block variation
SSE = Random variation
SST = SSA + SSBL + SSE
DCOV
A

RBD - 5
Sum of Squares for Blocks
Where:
c = number of groups
r = number of blocks
X
i.
= mean of all values in block i
X = grand mean (mean of all data values)
r
1
i
2
i.
)
X
X
(
c
SSBL
SST = SSA + SSBL + SSE
DCOV
A

RBD - 6
Partitioning the Variation
Total variation can now be split into three parts:
SST and SSA are
computed as they were
in One-Way ANOVA
SST = SSA + SSBL + SSE
SSE = SST – (SSA + SSBL)
DCOV
A

RBD - 7
Mean Squares
1
c
SSA
groups
among
square
Mean
MSA
1
r
SSBL
blocking
square
Mean
MSBL
)
1
)(
1
(
c
r
SSE
MSE
error
square
Mean
DCOV
A

RBD - 8
Randomized Block ANOVA Table
Source of
Variation
df
SS
MS
Among
Groups
SSA
MSA
Error
(r–1)(c-1)
SSE
MSE
Total
rc - 1
SST
c - 1
MSA
MSE
F
c = number of populations
rc = total number of observations
r = number of blocks
df = degrees of freedom
Among
Blocks
SSBL
r - 1
MSBL
MSBL
MSE
DCOV
A

RBD - 9
Main Factor test:
df
1
= c – 1
df
2
= (r – 1)(c – 1)
MSA
MSE
c
.
.3
.2
.1
0
μ
μ
μ
μ
:
H
equal
are
means
population
all
Not
:
H
1
F
STAT
=
Reject H
0
if
F
STAT
> F
α
Testing For Factor Effect
DCOV
A

RBD - 10
Test For Block Effect
Blocking test:
df
1
= r – 1
df
2
= (r – 1)(c – 1)
MSBL
MSE
r.
3.
2.
1.
0

#### You've reached the end of your free preview.

Want to read all 67 pages?

- Summer '16
- Sridhar Telidevara
- Statistics, Variance, DCOVA