Understanding Equity Statistics

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Understanding Equity Statistics

• Lawrence O. Picus

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Measures of Horizontal Equity

• Range
• Difference Highest minus Lowest
• Pros
• Includes all observations
• Cons
• Only measures two observations
• Outliers not accounted for
• Sensitive to Inflation

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Measures of Horizontal Equity

• Restricted Range
• Difference Between Observation at 95th Percentile
  and 5th Percentile
• Pros
• Generally avoids problems of Outliers
• Cons
• Still only two observations
• Sensitive to Inflation
• Preferred to Range, but Still not Great

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Measures of Horizontal Equity

• Federal Range Ratio
• 95th - 5th
• 5th
• Indicates how much larger the observation at the
  95th percentile is than the observation at the
  5th percentile

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Coefficient of Variation

• CV STD / Mean
• Describes the amount of variation around the mean
• Often expressed as a percent
• For Example 0.1 10

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Coefficient of Variation
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Coefficient of Variation

• Pros
• Includes all values in the data set
• Does not change with inflation
• Easy to understand
• Cons
• What is the value that determines a fair or
  equitable distribution?
• Use a relative or absolute standard?
• We suggest a target goal of 0.1

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Gini Coefficient

• Lorenz Curve
• Used in Income Equity Analyses
• Measures the proportional share of total revenue
  in the state for a proportion of students

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Gini Coefficient
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Gini Coefficient
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Gini Coefficient

• Value of Gini
• A / (AB)
• Value ranges from 0 to 1
• Smaller Values Represent Greater Equity
• If expenditures are completely equal, A 0 and
  the Gini Coefficient becomes 0

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