Daily puzzles/problems.

[Tallon]

maybe cats are more popular than dogs, so cats were finding homes more often and having to drop of out of class. or maybe there is less dogs in the shelter and so they are more likely to be admitted when they apply but there were less applications.

[billl]

maybe cats are more popular than dogs, so cats were finding homes more often and having to drop of out of class. or maybe there is less dogs in the shelter and so they are more likely to be admitted when they apply but there were less applications.

Actually, no animals are dropping out of classes. The number of puppies vs. kittens in the shelter isn't a factor, and they are all trying to get into classes.

And, for simplicity's sake (although it doesn't really matter, I guess), let's say that each animal is applying to just one class.

[billl]

OK, to sum up (I can't tell if people are having a tough time, or just haven't been online, or if my description sucks--so just in case):

• Significantly more kittens are being accepted into classes at the Academy. (Controversy!!!)
• For each class, the dogs that apply for the class are AT LEAST AS LIKELY to be accepted as a kitten applying for the class.

What was the real explanation behind the controversy?
What sort of solution would the teachers most likely come up with?

[kasie]

'Positive' discrimination?

[billl]

I don't think so, kasie, but I'm not sure exactly what that might mean. It is certainly the case that the teachers judging the applications are not discriminating, one way or the other, for or against any of the submitted applications.

[prendrelemick]

Like Tallon said, the intake reflected the pool it was drawn from. There are more kittens than pups making applications.

[billl]

OK, one more thing: There are an equal number of kittens and puppies applying, and an equal number of applications from each of them (kittens and puppies).

Ex.

100 kittens (each applying once), 100 puppies (each applying once)
58 kittens accepted to classes at the academy this session.
42 puppies accepted to classes at the academy this session.

5 classes, 20 students each.

for each class, puppies and kittens were rejected at the same rate.

(Note: I'll let this example override the example statistics I gave earlier--not because the previous example in which puppies were accepted more often wouldn't work just as well, but because the math would be more difficult, and I've just crafted a solution based on the simpler example featured here.)

I hope this makes it easier to think about the problem--sorry I didn't mention that the number of applicants from each group (kittens and puppies) could be equivalent.

Like Tallon said, the intake reflected the pool it was drawn from. There are more kittens than pups making applications.

I am just going to say that Tallon didn't have it right. ;-)
No snark here, either... Just a last bit of caginess.

[billl]

Please note, at 6:37 I made a FINAL ALTERATION to the above quote, which is now accurate and (I hope) clear!

[MarkBastable]

How are the applications made? By post? In person? I mean, if the assessors are human and allergies to dogs are more prevalent than allergies to cats, that might do it. Or, however inclusive the authoritative creatures involved, it could be that the proportional entry of kittens and puppies reflects the relative numbers of cats and dogs on the panel.

[billl]

Mark, the teachers doing the deciding are elders among the cats and dogs in the shelter. An even mix, let's say. There could still be some inadvertent bias in some form, of course--but they make no distinction among candidates and judge fairly among the applicants to the classes that they are teaching. In each class, the kitten has as good of a chance as the puppy applying in the next application folder--and the rejection and acceptance rates reflect this.

EDIT: I now realize that, with 5 classes, there can't be an "even mix" of cat and dog teachers admitting students into their classes. (EDIT: actually there COULD be, if each class had an even number of assessors, as Mark was probably imagining--whereas I had imagined a sole instructor doing that duty.) This is not a relevant point in the 'puzzle', however, and could be corrected by doubling the number of classes and teachers and students (which I should have done, in retrospect, sorry for the improvised and ramshackle nature of this thing.)

The applications are judged without unfairness and without favorability towards kitten or puppy, in the case of any particular class.

[MarkBastable]

Given that this is based on a real issue that came up at your college, would the problem work just as well if you'd chosen, say, elephants and giraffes? In other words, we're not looking for something cute about dogs and cats, right?

[billl]

Right, this puzzle is based on an interesting aspect of statistical evaluation. Nothing about cuteness, or animals being particularly quirky. (The 'real world' issue involved human males and females, apparently.)

Btw, it didn't happen at the school I went to, I just read about it this past week, happening on some other U.S. university at some point.

[MarkBastable]

Right - so we have very few elements to consider.


1. some inherent attribute that differs between the two groups of students
2. some inherent aspect of the process of enrolment that favours one of the groups of students (possibly but not necessarily because of 1)
3. some flaw in the lens of the data analysis that skews the perception of what's going on in 1 and 2.


In fact, as you hinted strongly in your last post, it has to be the last one, doesn't it because...

100 kittens (each applying once), 100 puppies (each applying once).....
for each class, puppies and kittens were rejected at the same rate.

but, if the rejection rate was the same then how can it betrue that

58 kittens accepted to classes at the academy this session.
42 puppies accepted to classes at the academy this session.



I shall think about this on the train to work.... Were the applicant kittens lying about their species? Or - here's a longshot - does the input form for the stats default to 'kitten' and when the inputters come up against a name of ambiguous species, do they leave it as the default?

[billl]

Number 2, more than anything.

With number 3 being a repetition of 2 perhaps, or maybe the "What will they do about it?" part of the question... Actually, Number 3 is maybe just US STRUGGLING with the problem.

Or, shoot--you could blame it all on number 1, maybe.

[billl]

clarifying presentation:

Imagine you are of group A (man, dog, etc.) and there is another group B (woman, cat, etc.) that is also applying to study at some university that is offering some selection of classes. The university has an equal number of applicants from A and B (and, for argument's sake, each student applies just once, choosing only one class). All of that is equal. ALSO, if you (an 'A') are in line to submit your application to a professor, you can be absolutely assured that your chances of acceptance into the class are exactly the same as the A in front of you and the B behind you--everyone has an equal chance.

The puzzle is: Why is the university accepting significantly more members of one group?

(58% of those accepted are of type 'B', for example)