SAME AVERAGE
Same averages. Different groups.
An overall lead can agree with, disappear within, or reverse inside the groups. Keep the records and their outcomes. Change only how they are grouped.
A is 20 percentage points ahead.
These two averages never move.
Success / total · every bar uses the same 0–100% scale
The weights do the work.
Each overall rate is a weighted average of its two group rates. A and B can use different weights. That is how the overall lead survives a reversal inside both groups.
Group share × group rate
Follow the same 400 records
Each mark keeps its category, position, and outcome. Only its group changes. Square = Group 1; circle = Group 2. Filled = success; outline = failure. A stays violet and B stays teal in UV.
| Category / group | Success | Failure | Total | Rate |
|---|
Read the study
What stays the same
There are 200 records in A, with 120 successes, and 200 in B, with 80 successes. A success is 1 and a failure is 0, so these success rates are averages of binary outcomes. Every record retains its ID, category, and outcome in all three constructions.
What changes
The assignment of records to Group 1 or Group 2. This is a constructed comparison of possible groupings, not three analyses of an observed covariate.
Read the denominators
In Reverse, A has 160 records in Group 1 and 40 in Group 2; B has 40 and 160. B’s rates are 80% and 30%, above A’s 70% and 20%. But A puts 80% of its weight on Group 1, while B puts only 20% there.
Agree has a 20-point A lead within each group. Disappear has equal within-group rates of 75% and 25%. Reverse has a 10-point B lead within each group. Every numerator and denominator is an integer.
What this does not decide
A pooled comparison and a within-group comparison answer different questions. Neither automatically establishes a causal effect, and a more detailed grouping is not automatically a better analysis. In an application, group meaning and the question being asked must justify the comparison.
Construction
Within each category, IDs are fixed in success-first order. Each grouping assigns the specified count of successes and failures to Group 1, and the remainder to Group 2. The 400-record view makes this assignment visible. These labels are deliberately constructed using outcomes; they are not evidence that an appropriate real-world grouping could be selected this way.
Switching groupings replaces one complete assignment with another. There are no fractional records or interpolated rates.