Formula for Calculating the Number of Pairwise Differences in a Population

An economist is studying income differences in a small community of 5 households, labeled A, B, C, D, and E. To find the total number of unique income differences, the economist devises the following plan:

1. Compare Household A to households B, C, D, and E.
2. Compare Household B to households A, C, D, and E.
3. Continue this process for all five households.

What is the primary flaw in this methodology for counting the unique differences?

An economist needs to calculate all unique income differences between four individuals (Person 1, Person 2, Person 3, and Person 4) to avoid counting any pair more than once. Arrange the following sets of comparisons into the correct logical sequence for a systematic count.

Evaluating Methods for Counting Pairwise Differences

Applying the Systematic Comparison Method

Continuing a Systematic Comparison

To systematically count all unique pairwise income differences in a population of 20 households, the number of comparisons made for the 10th household in the sequence will be the same as the number of comparisons made for the 11th household.

An analyst is systematically calculating all unique income differences among 15 households. The first household is compared with the 14 other households. The second household is then compared with the remaining 13 un-paired households. Following this method, the fifth household will be compared with ____ other households.

An economist is systematically calculating all unique pairwise income differences for a group of 6 individuals (labeled 1 through 6). The process starts by comparing Individual 1 to all others, then Individual 2 to all remaining individuals, and so on. Match each individual (after the first) to the number of new comparisons they will be part of.

Auditing a Pairwise Comparison Log

Auditing a Pairwise Comparison Log