Wikipedia:Reference desk/Archives/Mathematics/2007 April 9

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April 9

y = x^2

What's the curve called if y = x²? Thanks very much. 208.72.125.179 02:20, 9 April 2007 (UTC)

It's a parabola. -- JackofOz 02:24, 9 April 2007 (UTC)

Perhaps I am setting a terrible precedent, but I just made a redirect: y=x^2 − Twas Now ( talk • contribs • e-mail ) 07:12, 9 April 2007 (UTC)

Please don't do this. Do you have any idea how many different ways we could write a parabola? Now an admin will have to delete this. --KSmrq^T 07:33, 9 April 2007 (UTC)

Done. By the way, the answer to the original question could be "It is a function in Cartesian two-dimensional space"... so the redirect wasn't proper to begin with. Titoxd^{(?!? - cool stuff)} 08:02, 9 April 2007 (UTC)

We have an article E=mc², which is also the equation of a parabolic curve for varying speeds of light :)  --Lambiam^Talk 11:06, 9 April 2007 (UTC)

...Thank God that the speed of light is constant >_> --Ķĩřβȳ♥♥♥ŤįɱéØ 17:32, 10 April 2007 (UTC)

It's what now? Capuchin 07:35, 12 April 2007 (UTC)

Is there are a statistical method like this?

(Disclaimer, this is not homework!). I have data from two treatments that I'd like to compare (treatment 1 and 2), n=5 for each. I have performed a t-test, but p=~0.09 (unpaired, one-tailed). However, 80% of the values in treatment 1 are higher than 12, wheras 20% of the values in treatment 2 are higher than 12. Is there any statistical method like this using cut off values?

These are my results:

treatment 1	treatment 2
8.67	3.88
21.74	31.39
43.23	7.22
17.94	11.86
24.17	7.12

Thanks for any help! —The preceding unsigned comment was added by 140.251.33.179 (talk) 16:15, 9 April 2007 (UTC).

If the assumptions behind the t-test are true, then you really cannot do better than it. But by looking at your data, I would suspect that the assumptions are not all true (the data seem right-skewed, and I suspect that values less than zero are impossible). It would be possible to do a cutoff type test (e.g., Fisher's exact test), but please note the issues on pages such as testing hypotheses suggested by the data, data snooping bias, and data dredging.

A more appropriate test which is somewhat in the spirit of what you are getting at by looking at the ordering of the values is the Wilcoxon rank sum test (this was mentioned in the See Also section of the t-test article, BTW). But again, pay attention to what the test means, and the assumptions it makes (albeit less than those of the t-test). However, note that you still are deciding what to do after seeing the data, so your type I and II errors will not be exactly as you say they are. See Regression Modeling Strategies (F. Harrell, 2001) for a great discussion of this issue in many different contexts. Baccyak4H (Yak!) 02:33, 10 April 2007 (UTC)

I seem to remember that the Kolmorogov-Smirnov test Kolmogorov-Smirnov test is good when the population distribution of the values is unknown. Plot the cumulative distributions and refer the greatest vertical distance to tables of critical values. No article seems to exist, but the test is described in Sidney Siegel, Nonparametric Statistics for the Behavioural Sciences.==81.159.76.0 17:56, 10 April 2007 (UTC)

Here is the page on that test. It makes *no* restrictions on the distributions, but by being more general it is also less sensitive than either the t or the rank sum (so long as the respective assumptions are met). Baccyak4H (Yak!) 18:10, 10 April 2007 (UTC)

In this case it might actually give a better result, and unlike the t-test, KS does not use any unwarranted assumptions that I can think of.  --Lambiam^Talk 20:30, 10 April 2007 (UTC)

Thank you all for your help! There is a lot of information for me to read up on. Thanks again!