4 ms·

I sometimes can't tell if people are joking or stupid. The following quote, for example, has to be a joke: "The reported mean of 7.7 is misleading because it a

by laumars 11y ago

I sometimes can't tell if people are joking or stupid. The following quote, for example, has to be a joke: "The reported mean of 7.7 is misleading because it appears that close to half of your participants are scoring below that mean"

illivah 11y ago
It would be weird if it was exactly half. Mean isn't median after all.
- kaeluka 11y ago
  but it's "close to half"
jerf 11y ago
I can easily imagine that coming up in the social sciences.
chengiz 11y ago
I dont get why this is a joke. My guess is the paper probably reported the mean as having some significance in the context of how participants scored, and the professor is pointing out that this is misleading. In other words, they should have not reported the mean but the median.
- kazinator 11y ago
  It's funny because it's stating the obvious. Yes, arithmetic means are inherently misleading and everyone knows that. They summarize a quantity of information and conceal its important attributes like variance and skew. The 7.7 figure was probably not being used to deliberately mislead. The complainer hadn't in fact fact mislead; they had access to other data from the paper on which to base the complaint. Basically it boils down to "you shouldn't have summarized such and such data using an arithmetic mean because I don't like means; whenever someone uses a mean, they are trying to deceive".
- mikeash 11y ago
  If "close to half" scored below the mean, then the mean and median are probably very close together. I think the charitable interpretation would be that some conclusion in the paper hinges on the value of the mean, but that conclusion is not valid when you consider that values are more widely distributed, and the reviewer just stated it poorly.
cuckcuckspruce 11y ago
This would be expected in a very Normal distribution, but there are some skewed statistical distributions where you would not expect that to be the case. For example, if you're doing an analysis of the following data: 1, 2, 3, 4, ..., 98, 1000000, 1000000 then the mean would be 2,004,851 / 100 = 20048.51. In that case, 98% of your sample points fall below the mean.
- mikeash 11y ago
  Right, but apparently this distribution is not particularly skewed, since close to half of the values are below the median. And since distributions where the mean and median line up are common and expected, it's really weird to say that the mean is misleading because of that. I suspect/hope the reviewer meant to say that the use of the mean is misleading because the lower values somehow don't support whatever conclusion was reached.
  - cuckcuckspruce 11y ago
    That's most likely, and I agree that it's likely in the case mentioned that the data is not skewed. However, the main reason I posted is because the post I was responding to appeared to make the assumption that nearly half of the data points will always be below the mean, and I was pointing out that there are some distributions where you should not expect that to be the case because they are skewed.
    - laumars 11y ago
      I made no such assumption. Why would you even assume that I expect this to always be the case? As already pointed out, it's pretty easy to make an assumption about this specific example since we're told that close to half of the values are below the median.
FireBeyond 11y ago
It did remind me of this Dilbert cartoon: http://dilbert.com/strip/1996-04-18 http://dilbert.com/strip/1996-04-18 "It has come to my attention that 40% of your sick days are on Fridays and Mondays. This is unacceptable." "Ha ha ha! That's a good one. ... Please tell me he was kidding?" "Welcome to hell, kid."

by laumars 11y ago

illivah 11y ago

It would be weird if it was exactly half. Mean isn't median after all.

kaeluka 11y ago
but it's "close to half"

jerf 11y ago

I can easily imagine that coming up in the social sciences.

chengiz 11y ago

I dont get why this is a joke. My guess is the paper probably reported the mean as having some significance in the context of how participants scored, and the professor is pointing out that this is misleading. In other words, they should have not reported the mean but the median.

kazinator 11y ago
It's funny because it's stating the obvious. Yes, arithmetic means are inherently misleading and everyone knows that. They summarize a quantity of information and conceal its important attributes like variance and skew. The 7.7 figure was probably not being used to deliberately mislead. The complainer hadn't in fact fact mislead; they had access to other data from the paper on which to base the complaint. Basically it boils down to "you shouldn't have summarized such and such data using an arithmetic mean because I don't like means; whenever someone uses a mean, they are trying to deceive".
mikeash 11y ago
If "close to half" scored below the mean, then the mean and median are probably very close together. I think the charitable interpretation would be that some conclusion in the paper hinges on the value of the mean, but that conclusion is not valid when you consider that values are more widely distributed, and the reviewer just stated it poorly.

cuckcuckspruce 11y ago

This would be expected in a very Normal distribution, but there are some skewed statistical distributions where you would not expect that to be the case. For example, if you're doing an analysis of the following data: 1, 2, 3, 4, ..., 98, 1000000, 1000000 then the mean would be 2,004,851 / 100 = 20048.51. In that case, 98% of your sample points fall below the mean.

mikeash 11y ago
Right, but apparently this distribution is not particularly skewed, since close to half of the values are below the median. And since distributions where the mean and median line up are common and expected, it's really weird to say that the mean is misleading because of that. I suspect/hope the reviewer meant to say that the use of the mean is misleading because the lower values somehow don't support whatever conclusion was reached.
- cuckcuckspruce 11y ago
  That's most likely, and I agree that it's likely in the case mentioned that the data is not skewed. However, the main reason I posted is because the post I was responding to appeared to make the assumption that nearly half of the data points will always be below the mean, and I was pointing out that there are some distributions where you should not expect that to be the case because they are skewed.
  - laumars 11y ago
    I made no such assumption. Why would you even assume that I expect this to always be the case? As already pointed out, it's pretty easy to make an assumption about this specific example since we're told that close to half of the values are below the median.

FireBeyond 11y ago

It did remind me of this Dilbert cartoon: http://dilbert.com/strip/1996-04-18 http://dilbert.com/strip/1996-04-18 "It has come to my attention that 40% of your sick days are on Fridays and Mondays. This is unacceptable." "Ha ha ha! That's a good one. ... Please tell me he was kidding?" "Welcome to hell, kid."