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Lecture 11 part 2

Comparing Distributions

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Jury Selection in Alameda County

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Jury Panels

Section 197 of California's Code of Civil Procedure says, "All persons selected for jury service shall be selected at random, from a source or sources inclusive of a representative cross section of the population of the area served by the court."

Eligible jurors in a County

Jury

List of eligible residents

Jury panel

(Demo)

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Two Viewpoints

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Model and Alternative

  • Model:
    • The people on the jury panels were selected at random from the eligible population

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  • Alternative viewpoint:
    • No, they weren’t

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A New Statistic

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Distance Between Distributions

  • People on the panels are of multiple ethnicities
  • Distribution of ethnicities is categorical

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  • To see whether the the distribution of ethnicities of the panels is close to that of the eligible jurors, we have to measure the distance between two categorical distributions

(Demo)

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Total Variation Distance

Every distance has a computational recipe

Total Variation Distance (TVD):

  • For each category, compute the difference in proportions between two distributions
  • Take the absolute value of each difference
  • Sum, and then divide the sum by 2

(Demo)

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Summary

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Summary of the Method

To assess whether a sample was drawn randomly from a known categorical distribution:

  • Use TVD as the statistic because it measures the distance between categorical distributions
  • Sample at random from the population and compute the TVD from the random sample; repeat numerous times
  • Compare:
    • Empirical distribution of simulated TVDs
    • Actual TVD from the sample in the study