Manipulative Nested ANOVA

Manipulative experiment- “manipulation”

- laboratories – rigidly controlled- natural system – loosely controlled

Nested Experiments

levels of one factor (A) are NOT the same in each levels of the other factor

The levels of B are different for different levels of A

A

B

• A Nested design is not the same as a two-way ANOVA which is represented by:

Nested ANOVA Models

1. Mixed – fixed main group factor, random subgroup

factor

2. Pure – group and subgroup factors are random

Hypothesis Testing

Ho: µA = µB …. µi (groups have the same means)

Ha: there is a difference in group means

Ho: µA1 = µA2 … µAa (subgroups within each groups have the same means)

Ha: there is a difference in subgroups means

Calculations

ANOVA Table

Fcrit

Example:Two independent measurements (replication level) of

the length of the left wing have been made on 4 female mosquitoes Aedes intrudens (nested factor) reared in each of 3 cages (main factor). The total number of observations is thus 3 x 4 x 2 = 24. The data are the following:

Sokal and Rohlf , 1995

1. Ho: µcage1 = µcage2 = µcage3

Ha: there is a significant difference in the length of left wings of mosquitoes in at least one of the cages

Ho: µmosquito1 = µmsoquito2 = µmosquito3 = µmosquito4

Ha: there is a significant difference in the length of left wings in at least one of the of mosquitoes

Sokal and Rohlf , 1995

Conclusion: Cage factor have no significant effect on the length of left wing in mosquitoes, but there is a variation

Fcrit

4.26

2.80