After reviewing the changes in math and reading scores at all DC public schools for 2006 through 2009, I have come to the conclusion that the year-to-year school-wide changes in those scores are essentially random. That is to say, any growth (or slippage) from one year to the next is not very likely to be repeated the next year.

Actually, it’s even worse than that.The record shows that any change from year 1 to year 2 is somewhat NEGATIVELY correlated to the changes between year 2 and year 3. That is, if there is growth from year 1 to year 2, then, it is a bit more likely than not that there will be a shrinkage between year 2 and year 3. Or, if the scores got worse from year 1 to year 2, they there is a slightly better-than-even chance that the scores will improve the following year.

And it doesn’t seem to matter whether the same principal is kept during all three years, or whether the principals are replaced one or more times over the three-year period.

In other words, all this shuffling of principals (and teachers) and turning the entire school year into preparation for the DC-CAS seems to be futile. EVEN IF YOU BELIEVE THAT THE SOLE PURPOSE OF EDUCATION IS TO PRODUCE HIGH STANDARDIZED TEST SCORES. (Which I don’t.)

Don’t believe me? I have prepared some scatterplots, below, and you can see the raw data here as a Google Doc.

My first graph is a scatterplot relating the changes in percentages of students scoring ‘proficient’ or better on the reading tests from Spring 2006 to Spring 2007 on the x-axis, with changes in percentages of students scoring ‘proficient’ or better in reading from ’07 to ’08 on the y-axis, at DC Public Schools that kept the same principals for 2005 through 2008.

If there were a positive correlation between the two time intervals in question, then the scores would cluster mostly in the first and third quadrants. And that would mean that if scores grew from ’06 to ’07 then they also grew from ’07 to ’08; or if they went down from ’06 to ’07, then they also declined from ’07 to ’08.

But that’s not what happened. In fact, in the 3rd quadrant, I only see one school – apparently M.C.Terrell – where the scores went down during both intervals. However, there are about as many schools in the second quadrant as in the first quadrant. Being in the second quadrant means that the scores declined from ’06 to ’07 but then rose from ’07 to ’08. And there appear to be about 7 schools in the fourth quadrant. Those are schools where the scores rose from ’06 to ’07 but then declined from ’07 to ’08.

I asked Excel to calculate a regression line of best fit between the two sets of data, and it produced the line that you see, slanted downwards to the right. Notice that R-squared is 0.1998, which is rather weak. If we look at R, the square root of R-squared, that’s the regression constant, my calculator gives me -0.447, which means again that the correlation between the growth (or decline) from ’06 to ’07 is negatively correlated to the growth (or decline) from ’07 to ’08 – but not in a strong manner.

OK. Well, how about during years ’07-’08-’09? Maybe Michelle Rhee was better at picking winners and losers than former Superintendent Janey? Let’s take a look at schools where she allowed the same principal to stay in place for ’07, ’08, and ’09:

Actually, this graph looks worse! There are nearly twice as many schools in quadrant four as in quadrant one! That means that there are lots of schools where reading scores went up between ’07 and ’08, but DECLINED from ’08 to ’09; but many fewer schools where the scores went up both years. In the second quadrant, I see about four schools where the scores declined from ’07 to ’08 but then went up between ’08 and ’09. Excel again provided a linear regression line of best fit, and again, the line slants down and to the right. R-squared is 0.1575, which is low. R itself is about -0.397, which is, again, rather low.

OK, what about schools where a principal got replaced? If you believe that all veteran administrators are bad and need to be replaced with new ones with limited or no experience, you might expect to see negative correlations, but with positive overall outcomes; in other words, the scores should cluster in the second quadrant. Let’s see if that’s true. First, reading changes over the period 2006-’07-’08:

Although there are schools in the second quadrant, there are also a lot in the first quadrant, and I also see more schools in quadrants 3 and 4 than we’ve seen in the first two graphs. According to Excel, R-squared is extremely low: 0.0504, which means that R is about -0.224, which means, essentially, that it is almost impossible to predict what the changes would be from one year to the next.

Well, how about the period ’07-’08-’09? Maybe Rhee did a better job of changing principals then? Let’s see:

Nope. Once again, it looks like there are as many schools in quadrant 4 as in quadrant 1, and considerably fewer in quadrant 2. (To refresh your memory: if a school is in quadrant 2, then the scores went down from ’07 to ’08, but increased from ’08 to ’09. That would represent a successful ‘bet’ by the superintendent or chancellor. However, if a school is in quadrant 4, that means that reading scores went up from ’07 to ’08, but went DOWN from ’08 to ’09; that would represent a losing ‘bet’ by the person in charge.) Once again, the line of regression slants down and to the right. The value of R-squared, 0.3115, is higher than in any previous scatterplot (I get R = -0.558) which is not a good sign if you believe that superintendents and chancellors can read the future.

Perhaps things are more predictable with mathematics scores? Let’s take a look. First, changes in math scores during ’06-’07-’08 at schools that kept the same principal all 3 years:

Doesn’t look all that different from our first Reading graph, does it? Now, math score changes during ’07-’08-’09, schools with the same principal all 3 years:

Again, a weak negative correlation. OK, what about schools where the principals changed at least once? First look at ’06-’07-‘-8:

And how about ’07-’08-’09 for schools with at least one principal change?

Again, a very weak negative correlation, with plenty of ‘losing bets’.

Notice that every single one of these graphs presented a weak negative correlation, with plenty of what I am calling “losing bets” – by which I mean cases where the scores went up from the first year to the second, but then went down from the second year to the third.

OK. Perhaps it’s not enough to change principals once every 3 or 4 years. Perhaps it’s best to do it every year or two? (Anybody who has actually been in a school knows that when the principal gets replaced frequently, then it’s generally a very bad sign. But let’s leave common sense aside for a moment.) Here we have scatterplots showing what the situation was, in reading and math, from ’07 through ’09, at schools that had 2 or more principal changes from ’06 to ’09:

This conclusion is not going to win me lots of friends among those who want to use “data-based” methods of deciding whether teachers or administrators keep their jobs, or how much they get paid. But facts are facts.

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A little bit of mathematical background on statistics:

Statisticians say that two quantities (let’s call them A and B) are positively correlated when an increase in one quantity (A) is linked to an increase in the other quantity (B). An example might be a person’s height(for quantity A) and length of a person’s foot (for quantity B). Generally, the taller you are, the longer your feet are. Yes, there are exceptions, so these two things don’t have a perfect correlation, but the connection is pretty strong.

If two things are negatively correlated, that means that when one quantity (A) increases, then the other quantity (B) decreases. An example would be the speed of a runner versus the time it takes to run a given distance. The higher the speed at which the athlete runs, the less time it takes to finish the race. And if you run at a lower speed, then it takes you more time to finish.

And, of course, there are things that have no correlation to speak of.

I’m surprised that you are drawing so many conclusions using linear best fit lines with R squared values that are extremely low. R squared tells us how well the model (in this case, a linear best fit line) fits the data. When you have 0.05 as an R-squared, that essentially means your line doesn’t fit the data at all–that there is no linear relationship; you could draw another random line with a random slope and that would be just as good of a fit.

Even your highest R-squared value of .31 is not high enough to be making such firm conclusions.

You’re also wrongly interpreting the meaning of R squared. It’s not about what percentage you can predict the next year’s value; it’s about whether the best fit line which you (in this case, Excel) constructed can “account for” the actual data.

That you are making all these bold claims using your supposed “statistical analysis” is misleading. There is not nearly enough evidence behind anything that you’ve said in this post. I suggest you be more careful before drawing what appear to be unsupported conclusions. Indeed, “facts are facts”, but what you are showing are not.

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Actually, wookster12/iron bulldog, my conclusion was that there was next-to-no connection whatsoever between the scores one year and the scores during the next year, no matter what happens (replacing a principal or not), which I think is essentially what you are saying as well. Any correlation is extremely weak, but tends to be in a slightly negative direction. What other conclusions did I appear to draw, that you object to?

Notice that your conclusion (and mine) is quite different from the claims of Rhee and her acolytes, which are that her replacement principals have marvelously outscored their veteran counterparts.

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