isn't this just a nice example of median != mean ?
A couple of super failing school, e.g., could lower the D.C. average level so far that it'd be easy to surpass.
Sebastian:
Sure, lots of numbers are possible. The point is that "more than half" of students being worse than average is not any kind of scandal in itself. There are enough scandalous things happening in the DC schools without using this innocuous statistic as evidence of anything.
"At least once since 2008" is a bit funny, since (if we're talking about complete school years) that means either the 2008-2009 school year or the 2009-2010 school year, so it's really just two possibilities.
But still, Sebastian (and Andrew, if you didn't think of this) there's more than one way that more than half the schools could be above average. One way, as noted, is that the median could be greater than the average. The other is that some of the schools were above average in the 2008-2009 school year, the other half in the 2009-2010 school year. In principle, it could happen that every single school was above average at least once since 2008. (This is true, of course, whether the statistic is innocuous or not).
It wasn't scores that they were describing, it was a higher than expected number of erasures that were changed to correct answers on standardized tests. So your comment devolves to "a few really honest schools could make the distribution sufficiently asymmetric so as to allow more than half of the schools to appear to be cheating more than the average." But what the fear is, is that there were a few really dishonest schools. If that were the case we would find more schools than half with fewer suspicious erasures. That wasn't the problem.
I think the issue of mean vs. median is a red herring in this instance.
Isn't rather worrying that although in
"the past three school years most of Noyes’ classrooms had extraordinarily high numbers of erasures on standardized tests" that they only "have had erasure rates that surpassed D.C. averages at least once since 2008".
If Noyes is bad in some way than what does it say about the other schools that are like them or worse?
(If you were expecting cheaing would you expect the median
"Noyes is one of 103 public schools here that have had erasure rates that surpassed D.C. averages at least once since 2008. That’s more than half of D.C. schools."
So ? Each school has been tested more than once(since they specifically state at least once). If erasure rates are anything near random you would expect more than half of the schools would surpass the average over a span of > 1 trials, right ? If I 100 kids flip each flip a coin 10 times today, they will roughly average 5 heads, and roughly half will exceed the average. If they do it again tomorrow, same thing, but the kids who exceed the average won't be the same both days, which means that overall, over the two days, a lot more than 50% of the kids would have exceeded the average.
Tbwhite:
Exactly. It's unexceptional. This is why it was silly for the comparison to be presented as if it were telling us something.
oh OK – that I agree with. I got thrown off by the Wobegon reference – I thought you were implying this couldn't be the case (like all children being above average)
isn't this just a nice example of median != mean ?
A couple of super failing school, e.g., could lower the D.C. average level so far that it'd be easy to surpass.
Sebastian:
Sure, lots of numbers are possible. The point is that "more than half" of students being worse than average is not any kind of scandal in itself. There are enough scandalous things happening in the DC schools without using this innocuous statistic as evidence of anything.
"At least once since 2008" is a bit funny, since (if we're talking about complete school years) that means either the 2008-2009 school year or the 2009-2010 school year, so it's really just two possibilities.
But still, Sebastian (and Andrew, if you didn't think of this) there's more than one way that more than half the schools could be above average. One way, as noted, is that the median could be greater than the average. The other is that some of the schools were above average in the 2008-2009 school year, the other half in the 2009-2010 school year. In principle, it could happen that every single school was above average at least once since 2008. (This is true, of course, whether the statistic is innocuous or not).
It wasn't scores that they were describing, it was a higher than expected number of erasures that were changed to correct answers on standardized tests. So your comment devolves to "a few really honest schools could make the distribution sufficiently asymmetric so as to allow more than half of the schools to appear to be cheating more than the average." But what the fear is, is that there were a few really dishonest schools. If that were the case we would find more schools than half with fewer suspicious erasures. That wasn't the problem.
I think the issue of mean vs. median is a red herring in this instance.
Also the missing web address for the article is:
http://www.usatoday.com/news/education/2011-03-28… ?sms_ss=email&at_xt=4d90a3b0c658d1b2%2C2
Isn't rather worrying that although in
"the past three school years most of Noyes’ classrooms had extraordinarily high numbers of erasures on standardized tests" that they only "have had erasure rates that surpassed D.C. averages at least once since 2008".
If Noyes is bad in some way than what does it say about the other schools that are like them or worse?
(If you were expecting cheaing would you expect the median
"Noyes is one of 103 public schools here that have had erasure rates that surpassed D.C. averages at least once since 2008. That’s more than half of D.C. schools."
So ? Each school has been tested more than once(since they specifically state at least once). If erasure rates are anything near random you would expect more than half of the schools would surpass the average over a span of > 1 trials, right ? If I 100 kids flip each flip a coin 10 times today, they will roughly average 5 heads, and roughly half will exceed the average. If they do it again tomorrow, same thing, but the kids who exceed the average won't be the same both days, which means that overall, over the two days, a lot more than 50% of the kids would have exceeded the average.
Tbwhite:
Exactly. It's unexceptional. This is why it was silly for the comparison to be presented as if it were telling us something.
oh OK – that I agree with. I got thrown off by the Wobegon reference – I thought you were implying this couldn't be the case (like all children being above average)