Presented by: Hossein AhmadiBehzad HosseinzadehSupervisor: Dr.Riahi

DESIGN OF EXPERIMENTSNESTED DESIGNS

Spring 2015 numbers of slides: 19

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

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

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

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

6

Example

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

7

Linear Model

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

8

Null Hypotheses

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

9

Null Hypotheses

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

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

Nested ANOVA Table

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

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

Computation

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

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

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

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