1. Correcting for Regression to the Mean in Behavior and Ecology
Colleen Kelly and Trevor D. Price, 2005
The American Naturalist
Presented by:
Sifat Tasnim
Casey Engstrom

2. What is regression to the mean (RTM)?
Statistical phenomenon
Also known as regression effect
If two successive trait measurements have less than perfect correlation, individuals on average tend to be closer toward the mean on the second measurement
There is a negative correlation between individuals state at time 1 and time 2
Test 1
Test 2

3. Problem in Observational studies - no comparison available
Problem of Regression effect (in Behavior and Ecology)
Problem in Observational studies
- lack of control group
- no comparison available
2. Can draw erroneous conclusions
- statistical artifacts

4. Examples: Illustrate the problem of Regression effect
Example1: Mass Loss depends on initial mass
Example2: Mating success of hybrid drosophila in two different generations

5. Example1: Mass Loss depends on initial mass
Amount of mass lost = Initial mass – final mass
r = 0.55, P = .0096
Need further statistical analysis

6. Example2: Mating success of hybrid drosophila in two different generations
Need further statistical analysis

7. Taking RTM into account
With better experiment/study methods:
Controls (manipulative experiments)
Multiple baseline measurements over several days
Increase N, replicates
In analysis:
Pitman-Morgan test
Can adjust data to “exclude” RTM, make a new linear model, etc

8. Pitman-Morgan test: Is there a change in values beyond that expected by RTM?
Uses variance to measure RTM
T-value is a function of sample size, correlation, and variance
Interpreting the t test

9. 1. Pitman-Morgan underlying concept: Variance1 = Variance2, -> suggests RTM
Data scenario 1: RTM
Day 1
Day 2
mean
mean
frequency a b b a
light
heavy

10. 1. Pitman-Morgan underlying concept: Variance1 = Variance2, -> suggests RTM
Data scenario 1: RTM
Day 1
Day 2
Overall actual population distribution
frequency
No change in overall distribution, our samples experienced RTM a b b a
light
heavy

11. 1. Pitman-Morgan underlying concept: Variance1 = Variance2, -> suggests RTM
Data scenario 1: RTM
Day 1
Day 2
Change in variance
Interpretation
No change
Overall the population stays the same, the extreme values have simply “regressed to the norm”
frequency a b b a
light
heavy
Data scenario 2: real effect
“a” and “b” same as scenario 1, but all data values are converging, variance decreases
heavy birds are getting lighter, light birds getting heavier a b a b

12. 2. Pitman-Morgan equation
sd1
Sample size
sd2
Inputs:
correlation
Output:
T-value: “ratio of signal to noise”

13. 3. Interpreting t-value T=
Generally, greater T values -> worse fit with model (in this case, the null hypothesis)
Source:

14. Taking into account RTM
After Correction
Before Correction

15. When doing your own study…
Conclusions
When reading…
Assume RTM, unless proven otherwise!
When in doubt, run Pitman-Morgan yourself on the data
When doing your own study…
Control or multiple baseline measurements (if experiment or clinical trial possible)
Placate skeptics with Pitman-Morgan t test or similar