Learn Before
Evaluating Methods for Counting Pairwise Differences
An analyst is tasked with calculating all the unique income differences between every pair of individuals in a town of 50 people. They consider two approaches:
- Method 1: For each of the 50 individuals, compare their income to the other 49 individuals.
- Method 2: Compare the 1st individual to the other 49. Then, compare the 2nd individual to the remaining 48. Continue this pattern, reducing the number of comparisons by one for each subsequent individual.
Evaluate these two methods. In your response, identify which method is correct for finding only the unique differences and explain the fundamental problem with the other method.
0
1
Tags
Sociology
Social Science
Empirical Science
Science
Economics
Economy
CORE Econ
Introduction to Microeconomics Course
Evaluation in Bloom's Taxonomy
Cognitive Psychology
Psychology
Related
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:
- Compare Household A to households B, C, D, and E.
- Compare Household B to households A, C, D, and E.
- 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