Archive for March, 2013
The paper “The Problem With “Proficiency”: Limitations of Statistics and Policy Under No Child Left Behind” by Andrew Dean Ho published in Educational Researcher, Vol. 37, No. 6, pp. 351–360 (August/September 2008), makes the salient point that interpretation and use of cut scores, in particular the percentage Proficiency scores (PPS), gives inherently misleading accounts of progress and comparisons among groups.
The problem is not caused by intentional bias on the part of psychometricians or those determining the cut scores, though Ho does imply it could be used, and perhaps has been used, by those knowledgeable of this problem to give biased results.
In the following I summarize the problem he describes and later reference a Mathematica CDF file I will design and make available that simulates, dynamically, the effects of cut score placement and test score distribution changes to illustrate the principles discussed.
Assume Cut1 is at -1.5, and Cut2 is at 0.5. Then imagine two different scenarios. In the first scenario, assume the student 4th grade math WKCE scores fall at Cut1 for first year 1, and in year 2 the 4th grade class scores are 0.5 stdev higher. Visually, the cut score holds its position on the horizontal line while the whole bell curve shifts to the right by 0.5 stdev. A comparison between year 1 and year 2 would show a 4.4% improvement as this group would move into the next category. Cut1 would now strike at the -2.0 stdev point. Note also that no improvements will be recognized for about 95% of the students, yet all improved by the same amount.
In the second scenario, the students scores fall instead at Cut2, the first year, and in the second year, Cut2 falls at the 0.0 stdev point due to the 0.5 stdev improvement. In this case the year 1 and year 2 comparison would show a 19.1% improvement, 81% showing no improvement.
These scenarios show that for the identical improvement, that is all kids improved by 0.5 stdev in both scenarios, the perceived improvements show mediocre in scenario 1 and spectacular in scenario 2. Neither interpretation is wrong, but the results are grossly misleading. If one makes teacher evaluations, or AYP decisions based on either scenario, then the resulting consequences will be wrong in both scenarios.
The key understanding one needs to take away from these scenarios is for any cut score like Cut2 sitting right of the bell curve peak (the mean, median and mode), as the bell curve shifts smoothly right comparisons will make it seem that the schooling is getting better by the year, that the schools and teachers have found the magic solution. This will be a false conclusion. Once the bell curve moves to the point where the cut score is to the left of the peak, the rate of improvements will decrease, rapidly at first, decreasing less rapidly as the bell curve shifts further right. Any conclusion that the teachers are losing their edge, the curriculum needs to be changed or some heads must roll would be wrong. All such effects seen are an artifact of cut scores’ interaction with a bell curve, and nothing more.
The above logic applies to every cut score and every demographic subpopulation. Basic, minimum, proficient and advanced will be different as will rates for different ethnicities as will rates for different schools and school districts. Without more, interpretations are guaranteed to be wrong.
There is a rule here that must be exercised. No statistic can be understood unless and until it is related back to the original data. That is, in order to make sense of any statistic, and in particular, test outcomes, it is necessary to have either the full distributional information (the original scores) or the basic distribution statistics such as counts, mean, median, variance, skewness and kurtosis for each category and subgroup that would allow each of the distributions to be simulated.
TO BE CONTINUED
TJ Mertz Facebook linked to a Diane Ravitch post accusing the President and Arne Duncan of aligning themselves with right wing conservatives in their goal of destroying the public school system. See DianeRavitchWhoseSide. I disagree with Ravitch’s and Mertz’s suggestions.
I do assume Obama wants and expects Blacks and other minorities to get a good education. If one isn’t assuming that and considers oneself liberal or progressive, then you’re missing the important issue. When the President backs positions of the reform movement, even the right-wing allies, I have no doubt that he is not doing so because his strings are being pulled by his puppet masters. I certainly do feel that way about Republicans or other corporate types who take the same positions, but that is a different question — I assume evil intent and I think there is far more evidence than needed to support that position. However, the President’s positions are a different matter entirely.
The President does send his kids to private schools; he knows that schools can teach and kids can learn at a high level. He knows what it took for him to get an education. His mother homeschooled him when they were living in Thailand and his mother and especially his grandparents sent him to elite schools in Hawaii, and sacrificed to do it. He is also assuming that if he could get a good education, so can other Blacks.
Let’s put Obama, the man, into some context. We start by admitting to the obvious. Obama is self-assured, and has a healthy ego; no one has the temerity to run for President without an incredible ego, especially a Black man with a Kenyan name. Unlike a Romney, born into a extreme wealth and a warped ego who believes this raises him above the common folk, Obama believes others can rise to similar heights as he if given the opportunity. What is lacking is opportunity, Obama believes. If you do not agree with Obama’s sentiments on this issue, I think you have a lot of explaining to do as a liberal or progressive. Obama’s passion and belief does not come through as President but his writing, his biographers and those who know him as the man, have said as much. He also knows that most minorities do not have the options for a good education that he and his kids had (and Michelle). He knows that it can be done, he experienced it, and he knows that most public schools are not getting it done.
However, I have no doubt that the private school movement, charter schools, and vouchers will not work either; there is no question that the corporations want to milk the system for profit. There also no question that no one who is or has been involved in making education decisions knows what they are doing. That should be obvious, otherwise the failure to educate Blacks and other minorities would be rare, not typical.
We have had at least 45 years of consistent failure, at least nine 5-year plans that had promised to turn it around have passed without success. Why should we believe the tenth 5-year plan will succeed, whether charter, private, public, or vouchered.
I take it for granted that the President doesn’t know what the solution is; he is relying on Duncan, and Duncan doesn’t know. But the President does know, as we all must, that what is being done is not working. Public schools are simply not getting it done, and history shows they never have. Yes, the attacks on the public schools are making it less likely that they can turn it around, but where is the evidence that but for the attacks, they would be doing a good job? There is none. Should we then send our hard-earned tax dollars to private or charter or vouchers? No, and for the same reasons. There has been no evidence that the educational establishment or any implementation has made a difference, at least any that can be replicated at the scale necessary to raise the level of educational attainment that is expected and needed.
So let me answer the question which Mertz and Ravitch raised as to whose side the President and Duncan is on. Pubic Education. That is “Education of the Public”, which I suggest Thomas Jefferson espoused. And no, support for “Public Schools” is not the same as support for “Public Education”.
Sadly, however, the President will be disappointed because there are no viable institutions that will successfully support public education for all. Those who spend their time in political and financial posturing, like Ravitch especially, are not creating institutions that will succeed. Politics is the game that is being played, not education.