NESTED DESIGNS

DESIGN OF EXPERIMENTS�
NESTED DESIGNS

1. Presented by:
Hossein Ahmadi
Behzad Hosseinzadeh
Supervisor: Dr.Riahi
DESIGN OF EXPERIMENTS
NESTED DESIGNS
Spring 2015 numbers of slides: 19

2. 2
Definition
Nested design is a research design in which
levels of one factor (say, Factor B ) are
hierarchically subsumed under (or nested
within) levels of another factor (say, Factor A ).
As a result, assessing the complete combination
of A and B levels is not possible in a nested
design.
- Definition
- Nested
Vs. Crossed
- Example
- Linear Model
- Effects
- Null
Hypotheses
- Partitioning
Total Variation
- Nested ANOVA
Table
- Testing Null
Hypotheses
- Computation

3. 3
Nested Vs. Crossed
Factors A and B are considered crossed if
Every level of B occurs with every level of A
A factorial model involves crossed factors
- Definition
- Nested
Vs. Crossed
- Example
- Linear Model
- Effects
- Null
Hypotheses
- Partitioning
Total Variation
- Nested ANOVA
Table
- Testing Null
Hypotheses
- Computation

4. 4
Nested Vs. Crossed
Factors A and B considered nested if:
Levels of B occur with only one level of A
- Definition
- Nested
Vs. Crossed
- Example
- Linear Model
- Effects
- Null
Hypotheses
- Partitioning
Total Variation
- Nested ANOVA
Table
- Testing Null
Hypotheses
- Computation

5. 5
Example
For example, consider a typical
provenance study where a forest
geneticist collects 5 seeds from 5
superior trees in each of 3 forests. The
seeds are germinated in a greenhouse
and the seedlings are
measured for height
growth. Graphically,
the design would look
like this...
- Definition
- Nested
Vs. Crossed
- Example
- Linear Model
- Effects
- Null
Hypotheses
- Partitioning
Total Variation
- Nested ANOVA
Table
- Testing Null
Hypotheses
- Computation

6. 6
Example
- Definition
- Nested
Vs. Crossed
- Example
- Linear Model
- Effects
- Null
Hypotheses
- Partitioning
Total Variation
- Nested ANOVA
Table
- Testing Null
Hypotheses
- Computation

7. 7
Linear Model
- Definition
- Nested
Vs. Crossed
- Example
- Linear Model
- Effects
- Null
Hypotheses
- Partitioning
Total Variation
- Nested ANOVA
Table
- Testing Null
Hypotheses
- Computation

8. 8
Null Hypotheses
- Definition
- Nested
Vs. Crossed
- Example
- Linear Model
- Effects
- Null
Hypotheses
- Partitioning
Total Variation
- Nested ANOVA
Table
- Testing Null
Hypotheses
- Computation

9. 9
Null Hypotheses
- Definition
- Nested
Vs. Crossed
- Example
- Linear Model
- Effects
- Null
Hypotheses
- Partitioning
Total Variation
- Nested ANOVA
Table
- Testing Null
Hypotheses
- Computation

10. 10
Partitioning Total Variation
- Definition
- Nested
Vs. Crossed
- Example
- Linear Model
- Effects
- Null
Hypotheses
- Partitioning
Total Variation
- Nested ANOVA
Table
- Testing Null
Hypotheses
- Computation

11. 11
Nested ANOVA Table
- Definition
- Nested
Vs. Crossed
- Example
- Linear Model
- Effects
- Null
Hypotheses
- Partitioning
Total Variation
- Nested ANOVA
Table
- Testing Null
Hypotheses
- Computation

12. 12
Testing Null Hypotheses
- Definition
- Nested
Vs. Crossed
- Example
- Linear Model
- Effects
- Null
Hypotheses
- Partitioning
Total Variation
- Nested ANOVA
Table
- Testing Null
Hypotheses
- Computation

13. 13
Computation
- Definition
- Nested
Vs. Crossed
- Example
- Linear Model
- Effects
- Null
Hypotheses
- Partitioning
Total Variation
- Nested ANOVA
Table
- Testing Null
Hypotheses
- Computation

14. 14
Computation
A B C D E Forest
1 2 3 4 5 6 7 8 9 10 Tree
15.813.918.517.912.314 19.518.71615.8
Rep15.614.218 18.113 13.117.519 15.715.6
16 13.518.417.412.713.519.118.816.116.3
15.813.8718.317.812.6713.5418.718.8315.9315.9

14.83 18.05 13.1 18.77 15.93
16.13
- Definition
- Nested
Vs. Crossed
- Example
- Linear Model
- Effects
- Null
Hypotheses
- Partitioning
Total Variation
- Nested ANOVA
Table
- Testing Null
Hypotheses
- Computation

15. 15
Computation
SSA = 2 x 3 [(16.13-14.83)
2
+ (16.13-18.05)
2
+ (16.13-13.1)
2
+ (16.13-18.77)
2
+ (16.13-15.93)
2
]

= 129.28
SS
(A)B
= 3 [(15.8-14.83)
2
+ (13.87-14.83)
2
+ (18.3-18.05)
2
+
(17.8-18.05)
2
+ (12.67-13.1)
2
+ (13.54-13.1)
2
+
(18.7-18.77)
2
+ (18.83-18.77)
2
+ (15.93-15.93)
2
+
(15.9-15.93)
2
]
= 7.4
SSW
error
= 4.01
TSS = 140.69
- Definition
- Nested
Vs. Crossed
- Example
- Linear Model
- Effects
- Null
Hypotheses
- Partitioning
Total Variation
- Nested ANOVA
Table
- Testing Null
Hypotheses
- Computation

16. 16
Computation
- Definition
- Nested
Vs. Crossed
- Example
- Linear Model
- Effects
- Null
Hypotheses
- Partitioning
Total Variation
- Nested ANOVA
Table
- Testing Null
Hypotheses
- Computation

17. 17
Computation
- Definition
- Nested
Vs. Crossed
- Example
- Linear Model
- Effects
- Null
Hypotheses
- Partitioning
Total Variation
- Nested ANOVA
Table
- Testing Null
Hypotheses
- Computation