1. Power in Measuring Change in Two-Wave Studies
David A. Kenny

2. Terms X: the causal variable Y1 and Y2: the outcome at two times
gap: If X is a dichotomy, the mean difference on Y1 for the two levels of X.
b: the effect of Y1 on Y2 controlling for X

3. Relative Power for CfB vs. CSA
Power for CfB is usually greater for CSA
Why?: Error variance less for CfB because b is chosen to minimize it.

4. Exception Power for CfB not greater than CSA: Beta very near 1
Large gap

5. The Tradeoff
Power gain as b gets larger which makes the variance in the errors smaller.
Power loss as the “gap” at time 1 increases as this increases multicollinearity.
If the ratio below is less than 1, there is power gain, and if greater than 1, there is power loss.

6. Recommendation
CfB is more powerful than CSA if the gap is not too large.
If there is a gap, then likely the study is a non-randomized study, and one needs to determine which model of selection is appropriate. Power considerations become irrelevant.

7. Latent Variables
Lowers power, especially if the standardized loadings are small.
For CSA might wish to consider a composite over a latent variable to gain power.
For CfB, one needs to use a Y1 latent variable to remove the biasing effect of measurement error in Y1, but power is increased by dropping the Y2 latent variable.