Selectivity bias and the determinants of SAT scores

Economics

of Education

Review, Vol. 5, No. 4. pp. 363-371,

0’272-7757/86 $3.00 + 0.00

1986.

Pcrgamon Journals Ltd.

Printed in Great Britain.

Selectivity Bias and the Determinants AMY BEIIKENDT, Department

of SAT Scores

JEFFREY EISENACH and WILLIAM R.

JOtINSON

of Economics, Rouss Hall. University of Virginia. Charlottesville,

VA 22901, U.S.A

Abstract-The determinants of state-wide average SAT scores are estimated for 1982 in a regression analysis which corrects for the proportion of students taking the test. The selectivity correction has a large impact on the estimates of the effects of other variables. Little effect of schooling variables (teachers’ salaries. teachers per pupil, other expenditures) is found in the selectivity-adjusted estimates, except that large schools seem to depress SAT scores and private schools enhance scores. State-wide high school graduation standards also do not explain SAT score variation. In contrast, several demographic variables are quite important. including family size. the college-educated fraction of the population, and female-headed households. We can explain some of the SAT score decline in the 1970s with these cross-section estimates, suggesting that the decline over time is not due to changing resources for schooling hut. in part, to changing demographics. In particular, a large part of the recent SAT score decline was caused by the large families of the post-war hahy boom.

1. INTRODUCTION

THE OBJECT of this study is to estimate the determinants of state-wide average SAT scores in 19811982. As units of observation we take the 50 states and employ multiple regression analysis to determine the effects of educational resources and population characteristics on mean SAT scores in each state. These cross-section estimates have two principal uses. First, they indicate what public policy measures, if any, might be used to improve SAT scores. Second, they can be used to interpret the aggregate decline over time in SAT scores. Although SAT scores are an imperfect measure of educational achievement, they are of interest if for no other reason than that they have figured so prominently in the debate about educational quality and its determinants. Average SAT scores differ dramatically across states from a high of 1068 in North Dakota, where only 3% of students take the test, to a low of 790 in South Carolina, where 48% take the test. Since the most capable students in any state are likely to take SAT tests, states where a high proportion of students take the test are, other things equal, likely [Manuscript

received

15 October

1984; revision

accepted

to have lower observed mean SAT scores than other states. We explicitly account for this selection bias in our estimates to obtain unbiased estimates. If a variable both raises SAT scores and increases the likelihood of a student taking the test, failure to account for selection bias will bias downward the estimated effect of this variable on SAT scores.’ Section 2 describes our model and Section 3 discusses the theoretical rationale behind the selection bias correction we use. Section 4 presents the results of our empirical work. In Section 5 we use the cross-section coefficient estimates to analyze the decline of average SAT scores in the U.S. during the past decade. Section 6 concludes the paper. 2. THE

MODEL

Our method conforms closely to that used by previous researchers interested in estimating ‘education production functions’. A measure of student achievement is taken as the output of a production function, while variables measuring the quantity and quality of schooling are taken as inputs. Other factors thought to influence student achievement, namely ‘environmental’ factors, also belong in the for publication

363

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19SS.j

364

Economics of Education Review

production function because student achievement is affected by family and community environment as well as genetic factors. The measure of achievement used in this study is the mean combined (that is, math plus verbal) SAT score for each state. It has been argued that the use of aggregate data is inappropriate in studies such as this. Summers and Wolfe (1977), for instance, claim that their finding that schooling resources matter is a result of using disaggregated data on individual students and they imply that studies with aggregated data are less likely to find resource effects. Although the reasons for this conclusion are not spelled out by Summers and Wolfe, one reason might be aggregation bias. If the true model is non-linear or involves important interaction effects which are ignored in aggregate analysis, then true effects of resources might be obscured. Of course, this argument could equally well lead to the conclusion that the effects of resources are exaggerated by aggregation or that the effects of other variables are biased too. On the other side of the issue, there are some advantages to the use of aggregate data. In studies of educational output, important explanatory variables cannot be observed and, hence, will be included in the random term even though correlated with observed right-hand side variables. If these unobservables vary more across individuals than across states, as we think likely, then the use of aggregate data reduces the bias that results. For example, parental desire for children’s success, which is unobservable, may directly affect SAT scores and also be positively related to expenditures, especially within a state or even within a school district. Estimates of the effect of expenditures will be biased upward. If the variation in this variable is less across states than within states, then aggregation will reduce the bias.’ The same logic applies to the classic errors in variables problem; any bias induced by measurement error in the explanatory variables will be alleviated by aggregation. Determinants of SAT achievement can be divided into two groups: school characteristics which may be directly manipulated by policy-makers and family characteristics, which may be important but are not controlled by policy-makers. A serious problem in estimating the separate effects arises because school characteristics are often determined by and hence correlated with family characteristics. As an example, the schooling level of the community is likely to have direct effects on achievement as well

as indirect effects through the school resources educated parents demand. Relating achievement only to resources will overstate the effect of resources because it neglects the omitted variable, schooling levels in the community. On the other hand, if school resources and parents’ education are strongly related to each other, it may be impossible to separate their effects on SAT achievement. School characteristics which we deem relevant to SAT scores are: teachers per pupil. to capture class size effects; real teachers’ salaries, for teacher quality and morale; non-salary expenditures, to get at non-labor inputs to education; and average school size, to capture possible scale effects. The first three variables should have a positive effect on SAT scores while the scale effects are ambiguous.’ Throughout the paper, all nominal values are deflated by a state price index.’ In unpublished results, we used the ratio of teacher’s salary to household income in a state, which would be the appropriate salary variable were teachers immobile across states. No appreciable differences with the results presented were found. In addition to the resource variables listed above, we included a measure of academic standards, a zero-one dummy variable signifying the presence of state-wide high school graduation standards in 1980.’ It should be noted that the absence of statewide standards does not necessarily mean that local school systems set lower standards. However, such statewide standards have been cited as a way to improve educational quality. Seven variables are used to capture differences in home or community environment. Median income of a family of four in 1979 is hypothesized to be positively correlated with SAT scores since wealthier parents are expected to provide their children more of the tangible inputs to achievement than other parents. The percentage of children in households headed by a female is expected to be negatively correlated with SAT scores since oneparent households are able to devote less attention to each child than two-parent households. For the same reason, the average number of siblings is expected to be negatively correlated with performance.6 The percentage of population in each state having completed four years of college captures three effects which will be positively correlated with SAT scores: greater taste for higher education; a more stimulating learning environment at home; and genetically transmitted academic ability. The

Selectivity Bias and the Determinants of SAT Scores

percentage of the population residing in the state five years or less is intended to capture the effects on children of moving and/or effects on children of living in communities with highly mobile populations. The non~white/non-oriental fraction of population is included to determine if racial composition has an effect on mean SAT scores, and the percentage of population residing in urban areas tests the effect of urban residence. A summary of the variables used in the model is contained in the 4ppendix. Before discussing the effects of selection bias and liur technique for correcting this problem, several gtther potential problems should be noted. First, current SAT scores are presumably influenced by f‘actors working over the entire lifetimes of those raking the test, not just the last few years. However, inclusion of data from each of the past 18 years is obviously impossible and any weighted average of past values would be arbitrary. Our approach can be defended on the grounds that the observations on the independent variables are likely to be highly i.orrelated over time. A second and closely related problem is that many students taking the SAT test in one state will have undergone part of their education elsewhere. Such ‘sample pollution’ could conceivably cause coefficient bias, for instance if ‘movers’ took the SAT in states with different characteristics on average I han the states they were educated in. We tested for I his by including a variable which interacts mobility and school expenditures. If the interstate movement of students is random with respect to expenditures, then in high expenditure states the incoming students would tend to have experienced less expensive previous educations so the effect of high expenditures would be diluted by high mobility. I Ience, a negative coefficient is expected for the interaction term. Since the estimated coefficients were negative but not significantly different from zero and inclusion of this interaction variable did not appreciably change other estimated coefficients, only regressions without the interaction term are presented. A third issue worthy of note is that the effects of different variables could be different for the math and verbal portions of the SAT score. We tested for this possibility by running separate regressions for the math and verbal scores, and found no major differences from the results using the combined score.

365

A fourth issue concerns the treatment of private schools. While we are primarily interested in determinants of public school outputs as far as policy is concerned, private schools cannot simply be ignored, for they can be expected to have an effect on SAT scores. We controlled for the effect of private schools by including the share of private students in total enrollment as a variable. With these caveats, our approach, assuming that all students took the test, would be to estimate a linear equation of the form SAT = C + X@ i e,

(1)

where SAT is as defined above, C is a constant term, X is the vector of variables describing school and background characteristics, B is the vector of coefficients on these variables, and e is an error term assumed to be distributed normally with mean zero and assumed to be independent of the right-handside variables. 3. THE SAMPLE SELECTION PROBLEM Of course, not all students take the test. Moreover, the selection of students taking the test is not likely to be random, but rather we expect that students more likely to do well on the test are more likely to take it. To see the effect of this sefection bias, consider the process behind (1). Suppose that within stage j, individual i’s SAT score is given by a linear function of observable variables X,, some state-specific unobservable factors ej, and a random error term Ui specific to the individual and drawn independently from a normal distribution with mean zero. In other words, suppose individual scores are determined by SATi, = C + X$ + ej + Ui.

(2)

If every student took the test, then the jth state’s average SAT score, SAT,, would be given by SATj = C + XjP + e, + E(ui),

(3)

or, since the last term is zero when the entire population is sampled, SAI; = C + X,f3 + ej,

(4)

where Xi is a vector of observable characteristics averaged for the state and e, is the term accounting

E~onorn~~s of Education Review

366

for unobservable state characteristics. Note that (4) corresponds to a single observation of the system depicted in (1). However, not all students take the test. As a result, the last term in (3) is the conditional expectation E(uilindividua1 i takes the test), which is not necessarily zero. When not all students take the test, we must rewrite (4) as SAT

= C + X1fl + ei (4’)

+ E(u$ndividual

i takes the test),

where SAT is the observed mean SAT score for state j, which may differ from the mean of the true state distribution. We assume in this paper that student i takes the test if and only if his SAT score exceeds some minimum SAT?“. Defining s, = SATi - SAT?“, we can replace the last term in (4’) by E(u& > 0). If we regard the difference between SAT and SAT, [found by subtracting (4) from (471 as measurement error in the left-hand-side variable, then we have a standard measurement error problem. In particular, the general result holds that, if the measurement error is not correlated with the right-hand-side variables (the Xj vector), then its only effect is to increase the variance of the regression, while leaving the coefficient estimates unbiased. On the other hand, if the last term in (4’) is correlated with the right-hand-side variables, the effect is to produce biased coefficient estimates. Moreover, the direction of the bias cannot generally be predicted. The question, then, is whether the measurement error in this case is likely to be correlated with the X vector, and the clear answer is that it is. First, the model itself predicts that the X vector influences the ‘true’ SAT score, SAT;. Second, we may expect that at least some elements of the X vector also influence SAT?‘“. For instance, we might expect that students from wealthier families are more likely to take the test than other students, regardless of their test scores. Thus, both terms in the expression for Si are influenced by the X vector. Naive estimation of (4), ignoring the measurement error problem, would thus result in biased coefficient estimates. Here we turn to the literature on sample selection bias.7 Following Gronau (1974) most closely, we assume that SATi and SAT?‘” are distributed bivariate normally within each state, so that their difference, Si, is distributed N(l.+(r*) in each state.

Gronau shows that the measurement error term in (4’) can be expressed, for state j, as E(Ui(Si .b 0) = (1 - y) +’ “S

(9

dG-‘(1 - @A Bj

.

In (5), y is the regression coefficient of SAT; on SAT?“, which by assumption, along with usAT and us, is identical across states. The third term in (5) is the inverse of Mills’ ratio (IMR) which differs across states depending on the fraction, ej, of the high school seniors taking the SAT exam in state j. If we define a standard normal variable Zi = (si l-+J,> then Si > 0 implies Zi < -n.Ju,.The third term in (5) is E(Z;[Zi > -p.$r,) or g( -~s/o.~)/[l G( -p.,,/u.J], where g is the standard normal p.d.f. and G is the associated distribution function. But, @j,which is observed, is just equal to 1 - Gf-p+J, and therefore g(-l.QrJ can be written as g[G-‘(1 - 0,)]. Hence the third term in (5), IMR,, is a known function of an observable variable, Bi. Now, substituting (5) into (4’) yields SAT

=: C + X,P + XIMRj + ei,

(6)

where A represents the first two terms in (5). Estimation of (6) by OLS yields consistent estimates of B, and if the ejs are assumed to be normally distributed across states, the standard significance tests apply. One further complication arises in our treatment of the selectivity problem. In many states in the midwest and south, large numbers of students take a competing college entrance exam, the ACT (American College Testing program). In those states, our formulation of the sample selection process will be incorrect if the top students do not take the test. For example if there is no overlap between the ACT-takers and the SAT-takers and if SAT-takers are randomly distributed among all tcsttakers then the appropriate selectivity correction variable is the inverse Mill’s ratio applied to the sum of SAT and ACT fractions. At the other extreme, if the top students always take the SAT, our IMR measure is still appropriate even if they also take the ACT. We tested for the first hypothesis but found that it did not make an appreciable difference in the

Selectivity Bias and the Determinants of SAT Scores results; for presented.’

simplicity

those

regressions

are

not

4. RESULTS The results of our regression analysis, applying OLS to equation (6), are shown in Table 1. Column 1 shows the results with all independent variables Included, while columns 2 and 3 include only schooling and background variables, respectively. Column 4 is identical to 1 except that the selectivity correction is omitted. Column 5 is identical to 1 except that total expenditures per pupil replaces salaries, teachers per pupil, and other expenditures. When the results in column 1 are compared with regression omitting IMR in column 4, the correction

for sample selection is seen to have important consequences for both the estimated coefficients and the standard errors. The omission of the selection term biases the effect of schooling resources downward,’ and also has a large impact on the estimate of demographic factors. As expected, the coefficient on IMR is positive which implies, since 8 is inversely related to IMR, that SAT scores fall as participation rises. Columns 1 and 5 show that when schooling and background variables are both included, the only schooling variables that are significant are ‘scale’ and ‘private’ whose signs argue that larger schools produce lower scores and private schools induce higher scores. lo However, several of the background variables are statistically significant, and act

Table 1. Determinants 1

Salary

0.405 (“0::;;)

Uon-salary expenses (0.041) 61.7 (0.077) -0.109 (1.78) -1.55 (0.192) 2.48* (2.85)

‘reachers per pupil Scale Standards Private Expenditures Black

I lrban Siblings Female head Mobility (Iollege

1ncome IMR ( ‘onstant Standard error -.

0.112 (0.419) -0.206 (0.536) -80.1* (3.21) -3.03 (1.80) -57.6 (0.965) 7.51* (4.11) -0.174 (0.076) 123.0* (13.9) 913.9* (9.60) 18.8

Nores: Absolute t-statistics in parentheses. * = 95% confidence

(two-tailed

test).

of SAT scores

2

3

0.108 (0.043) 16.9 (1.41) -239.3 (0.244) -0.156* (2.86) -18.64

-

(;:;;!

-

(2.26) -

-

-

102.8” (11.9) 842.1* (8.35) 24.9

367

-

-

-0.007 (0.024) -0.177 (0.337) -77.9* (3.03) -5.5s* (3.62) - 104.4 (1.64) 9.00* (4.88) -2.90 (1.26) 120.5* (15.9) 972.8* (12.9) 22.0

4

-14.9* (2.98) 0.148 (0.005) -4355.0* (2.36) -0.517* (3.81) -26.7 _ $p”) (0.693) -0.032 (0.047) 2.68* (3.26) 115.7* (2.22) -2.14 (0.509) 54.6 (0.365) -3.05 (0.726) -2.35 (0.408) 1359.1* (5.99) 47.7

5

-

-0.111* (2.31) -1.79 (0.245) 2.44* (3.11) 1.04 (0.118) 0.113 (0.437) -0.186 (0.529) -78.7* (3.47) -3.01 (1.88) -56.1 (0.981) 7.48* (4.26) -0.152 (0.069) 122.4* (16.4) 919.7* (14.2) 18.3

in the expected direction. Large families, femaleheaded families and a less educated populace reduce SAT scores. Family income, racial composition, mobility, and urban living do not seem to be related to SAT scores. Collinearity between schooling and background variables will inflate the computed standard errors, so that schooling variables might still be significant even though they appear not to be. Column 2, however, reveais that even when background variables are omitted, schooling resource variables are still insignificant, while background variables remain significant when schooling variables are dropped in column 3. Apparently collinearity with background variables is not the cause of the schooling variables’ insignificance. The possibility that the schooling resource variables are collinear with each other is tested in column 5 in which expenditure per pupil is substituted for the separate salary, teacher per pupil and other expenditure variables and is still found to be insignificant. Questions of statistical significance aside, the estimated magnitudes of the effects of the schooling resource variables are quite small. Though collinearity may inflate the standard errors, the estimated coefficients in columns 1 and 5 are still unbiased estimates if the model is correct. Consider the effect of expenditures per pupil in column 5; a $1000 more spent per pupil would raise SAT scores by only 1 point (or a 40% increase in spending would yield a 0.1% increase in SATs). In contrast, the effects of the background variables are quite large. For example, reducing the number of siblings by one person (which is much less than the drop in fertility from the peak of the baby boom to the present would imply) would increase SAT scores by almost 80 points. Increasing the college-educated share of the population by 10 percentage points would exert a similar effect on SAT scores. Although our finding that school resources are ineffective conflicts with some earlier results,” our results do conform with Hanushek’s conclusion from a survey of the literature that: within the range of current school operations, expenditures . . . bear no in variations systematic relationship to variations in the performance of students. Hanushek (1981, p. 37). We also found no convincing evidence of an effect of state-wide graduation standards. It should be noted

that we have only examined a small set of possible educational policies; other policies which affect SAT scores may well exist and some of these may require more resources. Furthermore, the schooling resources we have examined may affect other educational outputs or groups of students besides those who take SAT exams. Another point to emphasize is that these estimates reflect the variation in resources which now occurs across the states; .they certainly do not imply that SAT scores would not suffer if school spending were dropped to zero. Instead, the implication should be that the marginal effect of changes in resources at current levels is small. We were surprised that neither income nor race affected SAT scores in contrast to some previous studies.12 However, income should have its biggest effect through schooling resources which are controlled for explicitly, and while race has a strong univariate effect on SAT scores, it is apparently only a proxy for some demographic conditions of black families (larger families, fewer college-educated parents, and more female-headed families).

5. EXPLAINING THE DROP IN SAT SCORES IN THE 1970s In this section we apply our coefficient estimates to national data from 1971-1972 and 1979-1980 to see if the fact&s that explain cross-sectional differences in scores also explain the 47 point drop in the national average score over this period. The predicted change in the mean SAT score due to changes in each of the variables in our model during this eight-year period is estimated by multiplying the coefficient in column 1 of Table 1 by the change in the independent variable from 1971-1972 to 1979-1980. Overall, the model predicts a 13 point decline in the mean score, while the actual decline was 47 points. The three major contributors to the predicted change in SAT scores in the 1970s are the rise in the number of siblings, which yields a 40 point decline, the rise in female-headed families, for a 9 point decrease, and the rise in the college educated fraction of the population for a 22 point increase in SAT scores. Thus, the predicted decline is due mostly to demographic changes rather than to changes in schooling resources. The importance of family size bodes well for the future since the test-

Selectivity

Bias and the ~e~errn~nan&.~of SAT Scores

takers of the late 1980s will have many fewer siblings than their baby boom predecessors.‘”

6. CONCLUSIONS

Three major conclusions can be drawn from this study. First, correcting for the fraction taking the test is very important in interpreting the effect of various variables on SAT scores. In particular, effects of resources are biased downward by the omission of selectivity. Second, environmental influences, such as family size, parents’ education, and female-headed households, appear to exercise an important influence on

369

SAT scores. Whether these variables work directly (e.g. through parents’ direct influence on their children), or indirectly (e.g. through their effect OR the quality of schools, community lifestyle. etc.) cannot be determined from our regressions. Finally, we can explain some (but not all) of the national decline in SAT scores in the 1970s with the variables we have used. Most of the decline in the 1970s is attributable to demographic changes and, for that reason, a reversal of the decline is in the offing for the 1980s. Acknowledgement: Helpful

suggestions of Victor Fuchs. Charles Holt, and Richard Murnane and the assistance of James Gillespie and Charles Hammes are gratefully acknowledged.

NOTES 1, Powell and Steelman (1984) also correct for the percent taking the test in their analysis of cross-state SAT differences and show that the ranking of states changes radically when selection is introduced. However, they have no explicit model of selection and do not consider as wide a range of explanatory variables as we do. 2. See Cain and Dooley (1976, p. Slgl). 3. Summers and Wolfe (1977) find some diseconomies of scale. 4. We relied on a state price index developed by Fuchs, Michael and Scott (1979). 5. A second measure of standards, the number of years of English and Maths required by state-wide regulation was also tried with no difference in results. 6. These last two variables were computed for children in 1970. In other words, the tvpical child in ,. 1970 is assumed to be the typical tesi-taker in 1981. 7. See, in particular, Barnow et al. (19HO). Gronau (1974) and Heckman (1980). 8. Specifically, we computed the IMR using the sum of the SAT and ACT test-takers, included it in addition to the standard SAT-only IMR, but found that it was not significant. 9. Powell and Steelman (1984) argue this point indirectly. The downward bias makes sense since resources are likely to increase potential SAT scores more than SAT”‘“, thereby increasing the fraction of persons taking the test. IO. The simple correlations between either private or scale and any of the salary or expenditure variables are all less than 11.2. 11. Boardman ef al. (1977) and Dugan f I979) found teachers per pupil to be positively correlated with achievement; Armor (1972) found teachers’ salaries to positively affect achievement; and Dugan (1976) and Sebold and Date (1981) find positive effects of expenditures. 12. Both Dugan (1976) and Pcri (1973) find a positive effect of income. Armor (1976), Brown and Saks (1975), Cohen ez al. (1972), Dugan (1976), Sehold and Data (1981), and Winkler (1977) find race important. 13. Zajonc (1976) has predicted a similar rise on the basis of lower family size.

REFERENCES ARMOR, D.J. (1972) School and family effects on black and white acilievemcnt: a reexamination of the USOE data. lo On E~uatit~ of ~du~u~io~~~~Opportunity (Edited by MUSTELLER, F. and MC)YNIHAN, D.P.). New York: Random House. BARNOW, B.S., CAIN, G.G. and GOLDBER~XK, A.S. (1980) Issues in the analysis of selectivity bias. In Eva~~ufion S&dies Review Annual, Vol. 5 (Edited by STORMSDORER, E. and FARKAS, G.), pp. 43-59. Beverly Hills, CA: Sage. BOARDMAN, A.E., DAVIS, G.A. and SANDAY, P.R. (1977) A simultaneous equations model of the educational process. J. pub. Econ. 7, 23-49. BROWN,B.W. and SAKS, D.H. (1975) The production and distribution of cognitive skills within schools. 1. p&it. Ecorz. 83. 571-593.

370

Economics

of Education

Review

CAIN, G. and Dooley, M. (1976) Estimation of a model of labor supply, fertility and wages of married women. J. polif. &on. 84, 4, part 2. COHEN, D.K., PEITIGKEW, T.F. and RILEY, R.T. (1972) Race and the outcomes of schooling. In On Equality of Educational Opportunity (Edited by MOS.TELI.~K, F. and MOYNIHAN, D.P.). New York: Random House. DUGAN, D.J. (1976) Scholastic achievement: its determinants and effects in the education industry. In Education as an Industry (Edited by FKOOMKIN, J.T., JAMEON. D.T. and RADNEK, R.). Cambridge, MA: Ballingcr. FUCHS, V., MICHAEL, R.T. and Scorr, S.R. (1979) A state price index. Working Paper No. 320. Cambridge. MA: National Bureau of Economic Research. GRONAU, R. (1974) Wage comparisons - a selectivity bias. .I. polil. Econ. 82, 1119-l 143. HANUSHEK, E.A. (1979) Conceptual and empirical issues in the estimation of educational production functions. .I. hum. Resources 14, 351-388. HANUSHEK, E.A. (1981) Throwing money at schools. /. Policy Analysis Management 1, 19-41. HECKMAN, .I. (1980) Sample selection bias as a specification error. In Female Labor Supply (Edited by SMITH, J.P.). Princeton: Princeton University Press. PERL, L.J. (1973) Family background, secondary school expenditure, and student ability. 1. hum. Resources 8, 156-180. P~WEL.L. B. and STEELMAN, L. (1984) Variations in state SAT performance: meaningful or misleading? Harvard Educatl Rev. 54, 389-412. &BOLD,

ZAJONC, R.B.

(1976) Family

configuration

APPENDIX:

Variable

name

and intelligence.

Science (April)

DESCRIPTION

OF DATA

Description

SAT

mean combined

Salary

average salary of teaching staff, 1979-1980 (deflated by state price index) (in 1000s)

Non-salary expenses

current expenditures for public schools less teacher salaries per public school pupil, 1979-1980, deflated (in 1000s)

Teachers pupil

per

SAT score

number of public and private school teachers divided by number of public and private school students, fall 1980

Scale

number of public and private elementary and secondary schools divided by number of public and private students, 1980.

Standards

dummy variable = 1 if state has state-wide high school graduation requirements, 1980

227-236.

Mean value (Standard deviation)

Source

947.92 (70.12)

(1)

16.88 (19.77)

(3)

1.602 (0.383)

0.055

(3), (7)

(3)

(0.006)

395.5 (115.0)

0.8000 (0.404)

(3)

(2)

Selectivity

Bias and the Determinants of SAT Scores

371

Description

Mean value (Standard deviation)

Private

private school enrollment as a percent of total enrollment

9.43 (4.70)

(3)

Expenditures

current expenditures 1981 (1000s)

2.53 (0.468)

(7)

Black

percent of population nonwhite, non-oriental. 1980

14.66 (10.76)

(6)

Urban

percent of population urban areas, 1980

66.9 (14.4)

(6)

Siblings

average number of siblings of children with parents, 30-34, in 1970

2.175 (O.lS7)

(4)

percent of children in households with female head, 1970

12.9 (2.X4)

(4)

Mobility

percent of population residing in state for less than five years

12.6 (6.23)

(5)

College

percent of population years of college

13.83 (2.53)

(6)

Income

Median income of family of four, deflated by state price index (in 1000s)

19.45 (0.218)

(6)

IMR

inverse of Mill’s ratio (see text)

1.43 (0.60)

(1)

Variable

Female

name

head

per pupil,

living in

with four

Source

Sources: (1) Chronicle of Higher Education, October, 1982. (2) National Association of Secondary School Principals, State-Mandated Graduation Requirements 1980. (3) National Center for Educational Statistics, Digest of Educational Statistics, annual editions, 1979-1982. (4) U.S. Census Bureau, Census of Population, 1970. (5) U.S. Census Bureau, Census of Population, 1980. (6) U.S. Census Bureau, Statistical Abstract, annual editions, 1979-1982. (7) U.S. Department of Education, State Performance Outcomes, Resource Inputs and Population Characteristics, 1972 and 1982.