School Finance Equity Statistics
Two principles of school finance equity are addressed here: 1) fiscal neutrality; and 2) horizontal equity. Fiscal neutrality refers to the degree to which the resources available to schools vary with local fiscal capacity, such as property wealth or household income. Two commonly used statistics for measuring fiscal neutrality are the correlation coefficient and wealth elasticity.
The correlation coefficient measures the strength of the linear relationship between two variables, for example, property wealth and expenditures per pupil. The value of the correlation coefficient ranges between -1.0 and +1.0, with a value of +1.0 representing a perfect positive relationship and a value of -1.0 a perfect negative relationship. A value of zero indicates no linear relationship between the two variables. A positive correlation indicates that the values of two variables will change in the same direction. For example, a positive correlation between property wealth and per pupil spending means that as property wealth increases, so does per pupil spending. A negative correlation indicates that two variables will change in opposite directions. Generally, as property wealth per pupil decreases, per pupil state aids increase, signifying a negative correlation.
Wealth elasticity measures the magnitude, or policy significance, of the relationship between two school finance variables. For example, while property wealth and per pupil expenditures may be positively correlated, if a large increase in property wealth per pupil results in only a small increase in per pupil expenditures, then the magnitude of the relationship may have little policy significance. The elasticity statistic measures the percent change in one variable relative to a one percent change in another variable. The statistic usually ranges from zero to any positive number, though it can also be negative. For example, an elasticity statistic of 1.0 between per pupil spending and property wealth indicates that spending increases, in percentage terms, at the same rate as property wealth.
The principle of horizontal equity states that similarly situated students should be treated similarly for school finance purposes. In other words, students in two school districts with comparable characteristics, such as property wealth and student demographics, should receive comparable levels of state and local resources and instructional quality. Horizontal equity statistics measure the degree of inequality that exits in a school finance variable, such as per pupil expenditures. Two common measures of horizontal equity are the coefficient of variation and the McLoone Index.
The coefficient of variation shows the percent of variation of a variable around its mean (i.e. the average). It is computed by dividing the variable's standard deviation by its mean. The value of the coefficient of variation ranges from zero to 1.0, or from zero to 100 if shown in percentage terms. The higher the value of the coefficient of variation, the greater the variation, or level of inequality, that exists in a school finance variable. A coefficient of variation of 10 or less is generally considered to indicate an acceptable level of equity.
The McLoone Index was created to measure the bottom half of a distribution to indicate the degree of equality for those schools or school districts below the 50th percentile. The McLoone Index is computed by finding the ratio of the sum of all values below the 50th percentile (or median) to the sum of all observations if they all had the median value. The McLoone Index ranges from zero to 1.0, with 1.0 representing perfect equality. An index of 0.95 is considered desirable.