Systematic Variance
I.Dividing Variance
Back to the stare/glance example:
- What amount of variabilty realtes to stare/glance?
- We do not care if people are different in things we are not interested in
- TOTAL VARIANCE = SYSTEMATIC VARIANCE + ERROR VARIANCE
- Systematic Variance is systematically related to the independent variable
- Error Variance is associated with all other variables; individual differences
- Hypothetical demonstration of error variance; subjects 1, 2, 3 are stare; 4, 5, and 6 are glance
| Subject | Time
|
|---|
| 1 | 1.0
|
| 2 | 1.0
|
| 3 | 1.0
|
| 4 | 3.0
|
| 5 | 3.0
|
| 6 | 3.0
|
- Within each group there is no variance
- No error variance
- Subjects are the same except in terms of the independent variable
II. An Example
- First we compute the total variance, then error variance. Then we can get systematic variance = total - error
| Subject | Time | x-mean | (x-mean)2
|
|---|
| 1 | 1.0 | -.75 | .56
|
| 2 | 1.25 | -.5 | .25
|
| 3 | 0.85 | -.9 | .81
|
| 4 | 3.0 | 1.25 | 1.56
|
| 5 | 2.6 | .85 | .72
|
| 6 | 1.8 | .05 | .003
|
- Total variance = (3.91/5) = .78 minutes squared
- Stare Variance = 0.04
- Glance Variance = 0.37
- Error Variance is the average of the conditions
- Error Variance = (stare variance + glance variance)/2 = (.04+.37)/2 = 0.21
- Systematic Variance = Total - Error = .78 - .21 = .57
- You actually want to report the proportion/% of systematic variance so you can compare studies
- R2 = Systematic Variance/Total Variance = .57/.78 = .73 x 100 = 73%
- The more systematic variance, the more behavior is explained by the independent variable(s)
If there are different numbers of subjects in each group, you cannot take the average, but have to compute a pooled variance.
Cohen Criteria: how to interpret R2
- R2 = 0.01 then a small effect
- R2 = 0.06 then a medium effect
- R2 = 0.15 then a large effect