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      NJ PARCC Algebra 1 Scores Changes Over A Year

      Eugen G Tarnow  January 4 2017 06:49:41 PM
      By Eugen Tarnow, Ph.D.
      Avalon Business Systems, Inc.
      http://AvalonAnalytics.com

      The 2016 PARCC scores are out and they are quite interesting.  The zero score is 650 and the highest possible is 850, a 200 point spread. Below I show you the 2016 scores versus the 2015 scores in Algebra 1 for all schools.  There is a spread - the scores of those two years are not quite the same.

      Image:NJ PARCC Algebra 1 Scores Changes Over A Year

      If I plot the difference between the two years as a function of the 2015 score we end up with the plot below.  Overall the average scores have improved by 5, the standard deviation is 9, and the improvement is highest for the lowest performing schools.  Some schools improved by as much as 50 points but some schools declined by 40 points.  

      Image:NJ PARCC Algebra 1 Scores Changes Over A Year

      Some of these changes are statistical noise as can be seen in the corresponding plots of schools with at least 100 valid scores.  Again the improvement is on average 5 points but the standard deviation is a smaller 7.6.  The improvement is highest for the lowest performing schools.  Some schools improved by 35 points and some declined by 20 points.

      Image:NJ PARCC Algebra 1 Scores Changes Over A Year

      What could account for the large differences?  The students or the teachers?  Let's increase the number of valid scores to 200 to lower the noise from the student population further.  The corresponding plots are below. The improvement is on average 5 points and the standard deviation is 7.3 and the improvement is highest for the lowest performing schools.  Again some schools improved by as much as 20-30 points and some declined by 10-20 points.

      Image:NJ PARCC Algebra 1 Scores Changes Over A Year

      Since we varied the number of students and got similar results, it would seem that the difference in test scores are due to the teachers. In other words, variability between Algebra 1 teachers within the same school account for about 7 PARCC points (but can vary between -20 to 35 according to the plot just above).

      Finally, the extra 5 points are somewhat dependent on socioeconomic characteristics, see the plot below.  "A", "B" etc. refer to "District Factor Groups" and the order is low to high socioeconomic characteristics.

      Image:NJ PARCC Algebra 1 Scores Changes Over A Year

      The score differences as a function of socioeconomic characteristics are shown below:
      Image:NJ PARCC Algebra 1 Scores Changes Over A Year

      There is no strong relationship of large declines or improvements with socioeconomic characteristics, see below:

      Image:NJ PARCC Algebra 1 Scores Changes Over A Year

      As always, I reserve the right to be wrong.
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