No one thinks they are stupid, even when they are

Yesterday I mentioned the commenter at another blog who said “people like to believe they are smarter than they have any justification for.”

The truth of this statement can be proven by looking at the data from Monitoring the Future: A Continuing Study of American Youth (12th-Grade Survey), 2006. High school seniors were asked the following question:

How intelligent do you think you are compared with others your age?

And here are the answers:

Frequency Distribution
Cells contain: -Column percent -N of cases		Distribution
V174	1: FAR BLOW:(1)	1.1 150
	2: BELOW AV:(2)	1.5 216
	3: SL BELOW:(3)	4.3 597
	4: AVERAGE:(4)	31.4 4,389
	5: SL ABOVE:(5)	24.9 3,476
	6: ABOVE AV:(6)	28.6 3,993
	7: FAR ABOV:(7)	8.3 1,158
	COL TOTAL	100.0 13,979

Quite humorously, we see that only 6.9% of respondents assessed their intelligence as being below average, but 61.7% said they were above average.

Comments

[Days of Broken Arrows]

Should we blame this on Mr. Rogers for telling all kids they're special, as the WSJ reently asserted?
http://online.wsj.com/public/article/SB118358476840657463.html

I'd like to see a breakdown of this data by intelligence, ethnic groups and gender, explaining which kids they're so smart.

[JewishAtheist]

English doesn't translate well to statistics. It's reasonable, for example, for someone to call anybody in the 90-110 IQ range "average." Removing all the people from the left half of the curve who have dropped out before senior year, a substantial majority of respondents would in fact fall into the "average" bucket or better.

[Shnugi]

I wonder what the distribution would look like for commenters on this website. *wink* *wink* *nudge* *nudge*

[Jason Malloy]

It's worse: A substantial fraction of the 6.9% were probably just depressive, self-loathing smart people.

[Cameron]

Half Sigma, high schoolers estimation of their intelligence seems fairly accurate. As JewishAtheist said, the dumb ones tend to drop out. I would imagine there being less leftward skewness in the true bellcurve since no one wants to admit to being below average.

[DF]

I believe DoBA is on to something.

[fullerene]

Consider also that students more likely than not have only their classmates to compare themselves against. Their classmates are rarely going to be representative of the country as a whole, and the realization of this is probably less common at low performing schools. Otherwise, it seems like most people still estimate that their abilities are average or slightly above average.

[NP]

The U.S. high school dropout rate is about 10%.

[miles]

"Hardly anyone is ever satisfied with their wealth, while nearly EVERYONE is satisfied with their intelligence"----------------

Don't remember who said that (Franklin?), but I still remember reading it 20 years later..........

[SFG]

For the record, it actually is possible for almost any fraction of the population to be below or above average. (If Bill Gates walks into a bar, every other person has a below average income.)

Below the median, on the other hand...

[Yafawi]

Speak for yourself Mr. Sigma!

How intelligent do you think YOU are compared with others your age?

[Yafawi]

For the record, it actually is possible for almost any fraction of the population to be below or above average.

Below, not above (you can't get less than zero, in this case). And IQ is not distributed like wealth. (Or income, but income isn't that bad...)

[SFG]

Below, not above (you can't get less than zero, in this case). And IQ is not distributed like wealth.
No, you're right, IQ is normally (Gaussian) distributed. The median actually does equal the mean, more or less. In a perfect normal distribution, the mean equals the median equals the mode, but there's a bit of a long tail to the left (negative skewness) due to brain damage and the like for IQ.

I think they did actually try to use probability distributions for income at least and found it was lognormal with a power-law tail, but I forget where I read that...

[Kirk]

I'll confess to having trouble figuring out what a "standard deviation" is. Everyone else seems to understand the term, so maybe I'm a little left of the curve around here.

Also, I've never been able to understand those friggin' colored charts H.S. keeps posting. Now, when I see one, I just pass on the post entirely. bleah...

[mgl]

I'll confess to having trouble figuring out what a "standard deviation" is.

Kirk, it's a measure of the spread of a set of values around their mean. For a normally distributed set like IQ scores (normal distributions have the "bell curve" shape), 68% of the values lie within one standard deviation from the mean (either above or below), 95% lie within two standard deviations, and 99.7% lie within three standard deviations.

In IQ, one standard deviation is about 15 points, and the mean is 100, so 68% of the population have IQs between 85 and 115, 95% have between 70 and 130, and 99.7% between 55 and 145. The controversial thing around here is that Asians have slightly higher IQs than whites, and whites have IQs about one standard deviation higher than blacks. This despite many decades of attempts to explain away or otherwise narrow the gap.

[mgl]

Oh, and I'd say I'm distinctly average in my peer group (engineers and other professionals, mainly), and know several people who are clearly smarter than I am.

So there.

[Half Sigma]

I'll confess to having trouble figuring out what a "standard deviation" is.

Where I went to college, a class in statistics was required for anyone getting a BS degree.

[Kirk]

Where I went to college, a class in statistics was required for anyone getting a BS degree.

To paraphrase a Far Side cartoon:

"Late one night, the middle-aged Half Sigma realizes that no one gives a damn what his GPA was."

[lukelea]

That puts me in the majority!