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Tim Myers: The curious case of the test-result aggregate

Myers' Musings

Posted: September 11, 2010 3:25 p.m.
Updated: September 12, 2010 4:30 a.m.

Two weeks ago I shared an analysis of how the various school districts in the Santa Clarita Valley, when combining their mean STAR scores into a unified district, compared well in STAR-testing league tables to more comparable peer suburban communities in Southern California — rather than the common local school administration practice of comparing mean district results with rather low state and county averages.

I found that the SCV compared favorably with suburban districts in Ventura and Orange counties, and wondered why the local school districts did not trumpet this fact.

As stated above, this comparative analysis used the mean or average district STAR scores on the English proficiency test to provide an aggregate comparison.  However, I got curious about the variability of the various school locations in each district around the district mean. I analyzed this using the basic statistical tool of standard deviation.

A short statistics lesson: The tool of standard deviation calculates the variability of a population of numbers around their mean, or average, value.  Statistical methods provide that 95 percent of the numbers in a sample will fall within two standard deviations on either side of the mean. (The so-called “Bell curve.”)

Therefore, the higher the standard deviation, the wider the variability of the various members of the population around their mean. A higher standard deviation implies the mean gets less predictive of the result of any particular member of the population on the metric analyzed.

Parents should find this variability important because it would verify their belief that if they moved anywhere into the district, they could hope their children’s school would perform at least near the mean. A low standard deviation would imply consistent results across the district. With one exception, I found this assumption false.

Take the case of the Newhall School District, which boasted the highest mean, at around 76 percent testing proficient or advanced. Unfortunately, the Newhall district also possesses the highest variability around that mean with a standard deviation of more than 10, so that one could only predict any school within the Newhall district might fall between a score of 56 and 96.

In fact, the high score in the Newhall district came from Stevenson Ranch Elementary at 92, with the lowest from Newhall Elementary at 55.

The second-place Saugus Union School District fared little better in producing consistent results across all its sites, with only a slightly lower standard deviation implying a range of outcome between 50 to 88 and, in fact, an actual spread of 37 between the highest-scoring site (Helmers Elementary at 85) and the lowest-scoring site (Cedar Creek at 48). Sulphur Springs stood slightly less variable than the Saugus district, with an actual spread of 29 between its highest (Golden Oak at 77) and lowest (Canyon Springs at 48).

What about the comprehensive middle and high schools of the William S. Hart Union High School District? Still much variability with a standard deviation of around eight. Middle schools varied from a high of 81 (Rio Norte) to a low of 58 (La Mesa), and comprehensive high schools ranged from a high of 70 (West Ranch and Valencia basically tied) to a low of 55 (Golden Valley).

The Castaic Union School District produce the most consistent results, with a comparatively low standard deviation of five, but still a low of 59 (Live Oak) and a high of 73 (Castaic).

One finds this variability important for two reasons. First, just moving into the district does not assure a good result. It appears that one must also concentrate on moving into the right ZIP code or even the right tract.

The second reason revolves around the greater societal impact of this variability, something called by educational experts and reformers the “achievement gap,” basically between those students whose mothers did not complete their college education and those who did.

Suburbanites may generally feel sanguine about their results, assuming the achievement gap exists between their bubbled enclaves and the frightening urban areas that many fled or never frequent. This variability shows the achievement gap clearly exists within our own community, and not in a small way.

While our family might feel sanguine and smug that our children attended the highest-scoring schools in the Saugus and Hart districts (Helmers, Rio Norte and Valencia), I take cold comfort that schools with much lower outcomes exist a mere eight miles away.

But that is a subject for another column — perhaps several.

    Tim Myers is a Valencia resident. His column reflects his own views and not necessarily those of The Signal. “Myers’ Musings” appears Sundays in The Signal.


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