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academic achievement levels achievement process achievement tests argued assess assumed Atlanta public schools Atlanta sample attending summer school black children books read causal child classical test theory cognitive growth cohorts consistently correlations differences differential effects of schooling enrolled equal equality of outcomes estimates exposure to schooling factors fall achievement family background family income Father's education grade equivalent scores household impact income level increase influence interaction interviews irrespective Kerckhoff less level of measurement measures ment metrics observed outcomes parental status patterns pretest prior achievement racial rates raw scores Regression relationship relative reliability Seventh grade sixth grade social class socioeconomic background socioeconomic status specific spring achievement standard errors standard scores structured programs substantially suggest summer activities summer learning summer programs summer school programs survey Table tend test scores tion vacation variables variance weighted least squares white children white students Word Knowledge