From the article: "Seventy percent of the study participants, all college undergraduates, said they thought they were better than average at multitasking. Of course, that's statistically impossible" [my emphasis]
It's time this misconception ended. I can't remember the amount of times I've read something like "but only 50% of people can be above average!" To put it another way, I imagine most of you reading this comment have an above average number of legs.
When people say "better than average", their intuition tends to be "better than half" (the concept here is the median), as opposed to "better than a particular number that happens to be the average value of that hing" (the concept here is the average or arithmetic mean). And in this context indeed only 50% can be above median.
People's intuition of stats is not that bad actually, but most invariably fuck up when it comes to mapping their fuzzy intuitive concepts to mathematical concepts: they make the mistake of mapping their "intuitive average" with the "mathematical average" when instead it should map to the "median". And yes, for people that understand the word "average" as "arithmetic mean" (as Excel does and most technically literate people do), there is no such "intuitive average" and its wrong mapping to math. But for "lesser minded" people it works like described above, and in their understanding of the words (incorrect... but real, as this how their minds work), the phrase "but only 50% of people can be above average!" is actually valid.
You make a fair point. I'm happy to accept that colloquially when someone says "better than average" they mean "better than the median" but it's when an article, such as this, uses strong language like "[it's a] statistical impossibility" that it irks me, because that's a definitive factual statement that's not true (or, at best, not well defined enough to be meaningful).
Statistics are so often abused that rigour is more than just a matter of pedantry. Perhaps if journalists stopped having such a loose relationship with statistics we'd all be better off.
Well, it would be correct if they were using "average" to mean "median".
It's also correct if you know that the data fits a normal distribution, or something similar.
So yes, it's not, in general, statistically impossible for most people to be above the mean on some metric. But there are several interpretations of that statement in which it is correct.
Even if the person meant "median", the author's sentence is still ambiguous: It is definitely possible that 70% of _college students_ are "above median" at multitasking than the _general population_.
If I recall correctly, this was the first lesson in Darrell Huff's "How to Lie With Statistics". Exploit the ambiguity in the word "average", which can mean median, mode, or mean at different times.
Not that I think you or the article is lying. But I think you are confused by the article's use of the word "average". To you, it means "mean". To the article, it means "median". If you had both used the word you meant, there wouldn't be an issue.
IMO, survey results like that are often indicative of a bad survey question, or a survey question hunting for a desired outcome.
Often you'll see a question like: "Are you better, worse, or about average at doing multiple tasks at the same time?"
Writing the question that way is letting the person answering the question set the scope. Average of what? The general population? Quantum physicists? Secretaries? Nursing home residents? Peers?
In surveys like that, it's also good to give examples, so the respondent can gauge their own experiences against the survey scale; otherwise you are measuring their self-ranking on their own value scale, which hasn't been registered with the survey's scale.
It's time this misconception ended. I can't remember the amount of times I've read something like "but only 50% of people can be above average!" To put it another way, I imagine most of you reading this comment have an above average number of legs.