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Topic: Easy: Foot Size Implies Spelling Ability (Read 15603 times) |
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richard w
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Re: Easy: Foot Size Implies Spelling Ability
« Reply #25 on: Mar 24th, 2003, 3:02am » |
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Surely the kids with the big feet are the retarded ones that are kept back a couple of years and for whom spelling just isn't all that easy?
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MattyDK23
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Re: Easy: Foot Size Implies Spelling Ability
« Reply #26 on: May 11th, 2003, 2:25am » |
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I finally returned to this site...going through my bookmarks.
Just to clarify what I was saying:
1. In general, foot size is a (rough) indicator of age.
2. In general, older people have better spelling abilities.
Throw out all this garbage about linear relationships, correlations, etc...the hint said to keep it simple!
Where the confusion comes in, I believe, is here:
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...performance in spelling bees / spelling tests. |
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- A spelling bee is a tournament against other people; in most cases, against people of the same age. At the end, only one person remains. Your performance is usually judged by how you performed in relation to your competitors; say, in what round of the tournament you were eliminated.
- A spelling test is an exam taken by oneself. Your performance usually does not rely on the performance of your peers. Your score may be, for example, the percentage of words your spelled correctly.
So:
Assume there is a positive correlation between foot size and age: a one's feet grows, the older one becomes; and vice versa.
Assume there is a positive correlation between age and spelling ability: The older one grows, the better their spelling ability becomes; and vice versa.
Note that, from these and some basic logic, we can conclude a third positive correlation: between foot size and spelling ability.
(Note: I'm horrible with these definitions of correlations...but you should know what I mean just by the phrase 'positive correlation': the same as in the riddle. I wrote the first two in order to come to the conclusion of the third)
Therefore:
In the same spelling test, a person's performance will usually be the same or better as they grow older -- therefore, by the correlations, their performance will usually be the same or better as their feet grow. This affirms one part of the riddle -- no argument here.
But as for the spelling bee? As you age (and your feet grow), your peers age as well (barring any time dilation...). But by the age-spelling-ability correlation, everybody's spelling ability -- yours and your peers' -- has increased. Some more than others, but regardless, it is still a tournament setting. Little has changed: everyone's spelling ability is (roughly) relatively the same. So how can one positively state that your performance in spelling bees over time will increase?
You can't. And therein lies the problem. Where the wording of the question lies the answer in so many of the riddles...in this one, it is it's bane.
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| « Last Edit: May 11th, 2003, 2:31am by MattyDK23 » |
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Heya
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Re: Easy: Foot Size Implies Spelling Ability
« Reply #27 on: Nov 28th, 2004, 3:28am » |
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Nope. Can't say I liked this one, after all the horror of doing quantitative analysis and my own (ahem) <em>scientific</em> study in my I.T. honours year. But it certainly shows how statistics can be misused, and therefore is a valuable example. I may in fact use this example to illustrate the point next time I am discussing statistical error.
I think there were some valid criticisms of the riddle, eg that spelling bees are usually related to age group and that older people get harder words and so their performance should not really be correlated with age. But then the headline of the riddle uses the term spelling "ability". In that case there would obviously be the correlation, and the riddle itself makes no statement about what use the researchers made of this fact.
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Brad711
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Re: Easy: Foot Size Implies Spelling Ability
« Reply #28 on: Dec 17th, 2004, 8:37pm » |
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You don't have to be so complecated. Foot Size=Age. Age=Spelling ability.(Unless your me and then 1-Age= Spelling Ability)
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