1. Analysis of Covariance vs. Analysis of Difference Scores
Lord’s Paradox
Analysis of Covariance vs. Analysis of Difference Scores
Lord, F. M. (1967). A paradox in the interpretation of group comparisons. Psychological
Bulletin, 68 (5)

2. Inconsistency in significance testing
In analyzing how subjects change, analysis of covariance, and analysis of difference scores yield different results
The same data sets, analyzed for the same effects, using different techniques yielded qualitatively different results

3. Lord’s example A test of sex differences in the “Freshman 15”
Analysis of difference scores for males and females shows no difference
Analysis of covariance shows a significant difference
So, what is going on?

4. -Distributions on top = initial weight distributions -Distributions on side = final weight distributions -Ovals = scatter plots of male and female weights

5. “with the data usually available for such studies, there simply is no logical or statistical procedure that can be counted on to make proper allowances for uncontrolled pre-existing conditions between groups”
-Frederic Lord

6. Different questions = Different answers
ANCOVA “asks” how can one variable predict variation in another (in our example how can weight at the beginning be used to predict weight at the end)
Analysis of difference scores “asks” how do initial scores differ from final scores
Pike, G. R. (2004). Lord’s paradox and the assessment of change during college. Journal
of College Student Development, 45 (3)

7. Take Home Message
When evaluating differences within individuals, there may not be a consistently best way
Think of the question that you want to ask
Think of what question the statistical tools can ask
Be careful in interpreting your results

8. Thanks!