NESTED DESIGNS
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Transcript of NESTED DESIGNS
Presented by: Hossein AhmadiBehzad HosseinzadehSupervisor: Dr.Riahi
DESIGN OF EXPERIMENTSNESTED DESIGNS
Spring 2015 numbers of slides: 19
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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
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Nested Vs. Crossed
Factors A and B are considered crossed ifEvery level of B occurs with every level of AA 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
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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
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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 aremeasured 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
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Example
- Definition- Nested Vs. Crossed- Example- Linear Model- Effects - Null Hypotheses- Partitioning Total Variation- Nested ANOVA Table - Testing Null Hypotheses- Computation
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Linear Model
- Definition- Nested Vs. Crossed- Example- Linear Model- Effects - Null Hypotheses- Partitioning Total Variation- Nested ANOVA Table - Testing Null Hypotheses- Computation
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Null Hypotheses
- Definition- Nested Vs. Crossed- Example- Linear Model- Effects - Null Hypotheses- Partitioning Total Variation- Nested ANOVA Table - Testing Null Hypotheses- Computation
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Null Hypotheses
- Definition- Nested Vs. Crossed- Example- Linear Model- Effects - Null Hypotheses- Partitioning Total Variation- Nested ANOVA Table - Testing Null Hypotheses- Computation
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Partitioning Total Variation
- Definition- Nested Vs. Crossed- Example- Linear Model- Effects - Null Hypotheses- Partitioning Total Variation- Nested ANOVA Table - Testing Null Hypotheses- Computation
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Nested ANOVA Table
- Definition- Nested Vs. Crossed- Example- Linear Model- Effects - Null Hypotheses- Partitioning Total Variation- Nested ANOVA Table - Testing Null Hypotheses- Computation
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Testing Null Hypotheses
- Definition- Nested Vs. Crossed- Example- Linear Model- Effects - Null Hypotheses- Partitioning Total Variation- Nested ANOVA Table - Testing Null Hypotheses- Computation
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Computation
- Definition- Nested Vs. Crossed- Example- Linear Model- Effects - Null Hypotheses- Partitioning Total Variation- Nested ANOVA Table - Testing Null Hypotheses- Computation
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Computation
A B C D E Forest
1 2 3 4 5 6 7 8 9 10 Tree
15.8 13.9 18.5 17.9 12.3 14 19.5 18.7 16 15.8
Rep15.6 14.2 18 18.1 13 13.1 17.5 19 15.7 15.6
16 13.5 18.4 17.4 12.7 13.5 19.1 18.8 16.1 16.3
15.8 13.87 18.3 17.8 12.67 13.54 18.7 18.83 15.93 15.9
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
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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
SSWerror = 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
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Computation
- Definition- Nested Vs. Crossed- Example- Linear Model- Effects - Null Hypotheses- Partitioning Total Variation- Nested ANOVA Table - Testing Null Hypotheses- Computation
17
Computation
- Definition- Nested Vs. Crossed- Example- Linear Model- Effects - Null Hypotheses- Partitioning Total Variation- Nested ANOVA Table - Testing Null Hypotheses- Computation