I was intrigued by a question in the Observer editorial today, which was:
While few public services will ever sink to the nadir of Mid-Staffs, many will be average, unresponsive... just not good enough. What is the government's answer to that?
I am afraid the question makes little sense. Regression to the mean suggests at some time all services will be average. Indeed, at some time all services will be unresponsive just as at others they may be fantastic. Daniel Kahneman pretty much got a Nobel prize for pointing this out. And it's not a fact for government alone: it's what happens in human behaviour whether in the public or private sector. The only myth has been that it does not happen in the latter and only the former. That's as wrong as the question was misplaced.
The question has to be how is the average improved. That's a different issue.
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The question has to be how is the average improved.
Not so. The average can be improved by one entity turning in a freakishly high score. What you are looking for is an improved median – for the score 50% of the way up the distribution to rise requires an improvement across the board.
But you are right, the original question is misplaced.
You can move the median up by improving just the middle value, without altering much or any of those above or below it. To move the median here with more desirable effect requires, as you say, a general improvement, or a change in the skew of the distribution. The best get better, or the worst get better more than do the currently better. Politicians make unfortunate choices for the distribution with consequences for others and not, directly, for themselves.
But, what has “average” to do with “unresponsive”?
Don’t call me Dave,
No James is right. Even in a non-bellcurve distribution, many values will be clustered near the median. The only way to move it appreciably is to move a lot of cases
Michael G
James didn’t say that the 50% score was to move “appreciably”. And, since the median is likely to be an actual member of the population, all that needs to happen for the median of the distribution to improve is for the current occupier of that position to leapfrog the one above it, so that the one above it now occupies the position of median. This can be done by targetting the original median for special treatment so that it improves sufficiently for the leapfrogging to occur. Et voila! The trick is done. The value gap between the occupants of the positions may be small, but sufficient targetting may shift a few up the ladder to make a large change in the median.
If the population has an even number of members then the median will be the mean value of the two members straddling the mid-point of the sequence, so merely swapping the ones above and below won’t work – you need to target the one at the top of the straddle to leapfrog the one above it, so the new median is the mean of one value that has remained the same – the lower one of the straddle, and one value that has risen – the one that was leapfrogged and is now one position below where it was originally.
Special treatment can improve statistical outcomes without having a great deal of impact for real-world situations. The figures are malleable by minimal interventions.
Personally, I think reading beyond the press and hype may be worthwhile:
http://skwalker1964.wordpress.com/2013/02/26/the-real-mid-staffs-story-one-excess-death-if-that/