Advice

1
Advice

• It is difficult without lots of experience to
  know when to use categorical explanatory
  variables as fixed effects and when as random
  effects

2
Fixed or random effects?
Some suggestions fixed random
Am I interested in the effect sizes? ?
It is reasonable to suppose that the factors come form a population of levels? ?
Are the factor levels informative? ?
Are the factor levels just numeric labels? ?
Am I mostly interested in making inference about the distribution of effects, based on a random sample of effects? ?
Is it a hierarchical experiment, where the factor levels are experimentally manipulated? ?
Is it a hierarchical observational study? ?
3
Split-Plot ANOVA
http//stephenyears.com/wordpress/wp-content/uploa
ds/2007/11/crops_wheat.jpg
4
Partly nested analysis of variance

• In this design, treatments of one factor are
  applied to plots of different sizes. Each
  different plot size is associated with its own
  error variance, so instead of having one error
  variance, we have as many error terms as there
  are different plot sizes.

5
Crop yield

• This example is an design field experiment on
  crop yield with three treatments
• Irrigation (yes or not)
• Sowing density (with three levels)
• Fertilizer (N, P, or both)

6
Block
Irrigation
Density
Fertilizer
7
Split plot design (first two levels)
Irrigation Irrigation Irrigation
Yes No
Block 1
Block 2
Block 3
Block 4
8
Split-plot analysis of variance
9
(No Transcript)