There is a considerable body of literature (Broomhall and Johnson, 1994; Broomhall, 1993; DeYoung, 1985) that concludes that rural students perform less well than urban students on standardized tests of educational achievement. One hypothesis for the existence of this condition is that expenditures on education do matter, and they are smaller in rural areas than in urban areas (Mulkey, 1993; McDowell, et al, 1992; Jansen, 1991; Reeder, 1989; and DeYoung, 1985). A second hypothesis for the existence of the difference in educational achievement between rural and urban areas involves the relationships between the values in use of particular inputs and the level of such achievement (Hanushek, 1991). And a third hypothesis is that differences by location in attitudes of individuals, parents, and peers about education exist and result in the observed differences in educational achievement by location (Broomhall and Johnson, 1994; and Hanson and Ginsburg, 1988).
While previous studies have focused on the rural versus urban areas issue, this demarcation may be misleading. The fundamental issue explaining student educational achievement is not the rural versus urban areas issue, but the determination of variables within which differences explain the significant variation in student achievement in any area. Students would be expected to perform similarly, if the associated values of explanatory variables are similar, irrespective of location. If the distributions of values of explanatory variables differ by location, the demarcation simply substitutes for the difference in the distributions of such variables and is of little help in the development of appropriate policy.
The intent of this article is twofold. First, we intend to determine if students from both highly rural and highly urban areas with similar associated explanatory variables perform similarly, but less well, on student achievement tests than students from other areas. Second, we intend to show that studies that analyze student achievement should include measures of both cognitive skills and educational market competition as explanatory variables.
The state of Kentucky provides a unique setting in which to determine the relationship between educational achievement and population density. There are 120 counties within the state in which population density varies from 21 people per square mile (in the Robertson County district) to 7,774 people per square mile (in the Bellevue district in Campbell County). The average population density for the state is 591 people per square mile. Coal mining dominates the eastern part of the state known as the Appalachia area. As well, several counties in western Kentucky are noted for their coal mining. At the other extreme, highly populated areas surround Covington, Lexington, and Louisville. Thus, Kentucky provides an excellent setting in which to determine the effect of population density.
The low population density areas of Kentucky tend to be the coal-producing areas. Kraybill, et al, (1987) and Duncan and Tickameyer (1983) compared values of quality-of-life measures in coal-producing areas of Virginia and Kentucky and found that quality-of-life measures in the coal-producing areas tend to be lower than the quality-of-life measures found elsewhere in these two states. Their quality-of-life variables included income, employment, education, health care, and housing. Thus, the rural areas of Kentucky tend to be less appealing in terms of living habitat.
At the other extreme are the areas of high population density. The values of inner-city quality-of-life measures are low and have been declining over the past several years, as well. Conditions with respect to crime, gangs, and deteriorating structures are considered to have led to these declining quality-of-life measures within the inner cities. These conditions have resulted in what is commonly referred to as "urban flight. …