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    NJ School Districts: SAT Scores, PARCC Scores, Suspension Rates & Family Income

    Eugen G Tarnow  August 26 2016 10:44:50 PM
    By Eugen Tarnow, Ph.D.
    Avalon Business Systems, Inc.
    http://AvalonAnalytics.com

    Many families live in particular New Jersey towns for the school districts and at least some select the school district based on the SAT scores. However, a higher SAT school district carries with it financial hardship.  One can make a more optimal financial decision if one could tease out what part of the SAT scores are based on school performance and what is based on individual family spending on SAT coaching – since the coaching can take place in any school district.
    For this purpose, I am able to exploit a new standardized test in NJ public schools, the PARCC test, which is relatively opaque to parents.  It was designed with a lowest possible score of 650, presumably to avoid parental shock, is accompanied by frequent assurances to students that the PARCC test scores are “confidential”, the student reports are almost unreadable (including a demographically matched set of school districts that do not match the local area) and the schools do not discuss their performance reports.  This suggests that the PARCC results reflect the combination of the quality of the school education and the quality of the students and less so parent involvement.  The SAT score, on the other hand, alerts parents and worries students as it carries great importance in college admission, suggesting that the SAT score reflects, in addition to the quality of the school education and the quality of the students, more student effort and parental input.

    One important part of the student effort and parental involvement to increase the SAT score is paid coaching.  It would seem reasonable that the access to paid coaching is income based.  The lowest incomes should correspond to little paid coaching while the highest incomes should correspond to the best paid coaching available. Thus if one removes the effects of the school environment via the PARCC scores, the remainder should reflect the effect of best paid coaching available (this reasoning is similar to that of Zwick & Green, 2007).

    Fig. 1 displays the effect of family income on PARCC and SAT scores as well as the student teacher ratio and the student suspension rate.  The student teacher ratio has a very small effect and will be neglected.  Income differences affect some subject scores more than others.  Note the trend for English – as high school progresses the correlation with income decreases.  The correlation with income is also low for Algebra 1. The strongest PARCC test correlation with income is the overall average.  The student suspension rate is also strongly correlated with income.
    Image:NJ School Districts: SAT Scores, PARCC Scores, Suspension Rates & Family Income
    Fig. 1 PARCC and SAT test score correlations with median family income.  


    In Fig. 2 is displayed the correlation with income of the SAT score with the PARCC average and the student suspension rates removed separately and together via a linear regression.  In Table 1. is displayed the SAT score difference for incomes between $50,000 and $170,000. The unaltered difference is 187 and the difference with the effects of the PARCC average score and student suspension rates is 74.

    Image:NJ School Districts: SAT Scores, PARCC Scores, Suspension Rates & Family Income
    Figure 2.  Correlation of SAT score with family income removing effects from suspensions and PARCC averages.


    Removing suspensions Removing PARCC Average Removing both PARCC Average and suspensions
    SAT score difference 50,000-220,000 income 187 (out of 800) 119 (out of 800) 91 (out of 800) 74 (out of 800)



    Table 1.  The difference in SAT scores for school districts with mean family incomes of $220,000 and $50,000.

    In Fig. 3 is displayed the student suspension rate as a function of income.  The functional form is close to exponential which means that an extra $30,000 in income results in the halving of the suspension rate.
    Image:NJ School Districts: SAT Scores, PARCC Scores, Suspension Rates & Family Income
    Figure 3.  The effect of family income on suspension rate is exponential; an extra $30,000 in family income lowers the suspension rate by 50%.


    In Table 2 is displayed the financial correlations of an SAT point.

    Increase in tuition per year Increase in earnings per year
    1 point increase in SAT score $36 $61



    Table 2.  The consequence of one SAT point.




    Discussion

    Many people live in particular New Jersey towns for the school districts and at least some select the school district based on the SAT scores.  I find that each SAT point correlates with an increase in the mean family income of about $1,000.  On the other hand, 74 points out of 800 are presumably attributable the cost of SAT coaching.  If the most expensive SAT coaching is $7,400 this is a lot cheaper alternative at a one-time cost of $100 per SAT point.  

    I find that college average SAT scores correlate with $61 additional yearly income per SAT point, partially offset by a tuition increase of $147 for a four year stay per SAT point, suggesting that SAT coaching is worthwhile (breakeven point occurs after four years) but a better neighborhood may not be worthwhile (Tarnow, 2015).

    Interestingly, the tuition increase for an SAT point is suboptimal for the colleges: for every point increase in the SAT score, a college can expect an increase in the median family income of $3,000 (in NJ, it may be different in other states).  However, they only tap $147.

    Colleges could use an “effective” SAT score with the role of family income removed but if they did, they would correspondingly compromise their financial needs.

    Within the PARCC test I find large variations in how much the median family income influences the subject scores (Fig. 1).  The influence is the lowest for Algebra 1 and 11th grade English. The reason is unclear though I venture to guess that it has to do with a lack of parental involvement: Algebra 1 is taught both in middle school and high school and may be harder to keep track of and 11th grade English may be a topic hard to understand and/or control.  I note that New Jersey is not a state in which parents are particularly involved with the schools other than comparing school districts.

    The suspension rate declines exponentially with median family income.  $30,000 halves the suspension rate.  The cost of moving from a “bad” neighborhood to a better one is extremely expensive.  Interestingly, teachers in the NJ school system can do this for free even though others can only do this at a substantial cost.  The freedom of teachers to move districts may also be a reason for low performing school districts staying low performing.  I suggest a solution to the problem: tax the contract benefit of moving to a richer school district at the difference in median family income between the two districts.
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