NESTED DESIGNS
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This document discusses nested designs in experiments. It defines nested designs as those where levels of one factor (B) are nested within or occur only with levels of another factor (A). An example is given of a forest genetics study measuring tree seedling height where seeds come from trees nested within different forests. The document outlines the linear model, effects, null hypotheses, partitioning variation, nested ANOVA table, testing hypotheses, and computations for a nested design.
![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
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](https://image.slidesharecdn.com/finalpresentation-150427092058-conversion-gate02/85/NESTED-DESIGNS-15-320.jpg)
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 15.8 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
- 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 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
- 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