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Understanding Equity Statistics

Understanding Equity Statistics. Lawrence O. Picus. 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 . Measures of Horizontal Equity.

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Understanding Equity Statistics

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  1. Understanding Equity Statistics Lawrence O. Picus

  2. 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

  3. 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

  4. 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

  5. Coefficient of Variation • CV = STD / Mean • Describes the amount of variation around the mean • Often expressed as a percent • For Example 0.1 = 10%

  6. Coefficient of Variation

  7. 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

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

  9. Gini Coefficient

  10. Gini Coefficient

  11. Gini Coefficient • Value of Gini: A / (A+B) • 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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