EXD.6:5 - Archetypal Grounding
Compare a complete prose account of the pooled mean with the table expression in EXD.3. Both carry five selected relations:
- count multiplied by group mean reconstructs group sum;
- group sums combine into total sum;
- group counts combine into the total number of individuals;
- total sum divided by total individual count gives the pooled mean;
- averaging group means equally answers a different weighting question.
The subject values and criteria are available: individual weighting gives 6.75; equal group weighting gives 5.5. The proposed table aligns count, mean and sum. Its intended contribution is correspondence under the recipient’s available preparation and budget, not an additional mathematical ground.
A representative response could reveal that the recipient cannot use the mean-to-sum relation. If the explainer then works that step and obtains a correct response, keep the original response and the supplied help separate. That sequence supports a targeted prerequisite or assistance repair. It does not show that the unassisted table outperformed the prose.
Alternatively, the recipient may already recover all five relations from the prose and use the required statistic. Without another worthwhile contribution, retain the prose. If the table is selected for a known reference task, such as locating counts and sums repeatedly, record that use and the design reason; do not report an unobserved reading-time improvement.
Now suppose the recipient changes the report to equal branch influence. Re-establish the target before comparing the explanations: the selected answer becomes 5.5. Failure to give 6.75 under that new question is not an extraction defect. The source account still supports both conditional answers.
These are constructed comparison branches. Their actual observations, if obtained, must be reported at their own conditions.
For advising, a person may recover the recommendation’s decisive premises and choose differently because of a preference. Keep the explanation if it served that understanding use; return the preference to the decision. Persuasion would require a different declared purpose and its own grounds.