Wikipedia:Reference desk/Archives/Mathematics/2009 September 9

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September 9

Effect of type I vs Type II error cost difference

What work has been done on how an appropriate p-value for null hypothesis testing changes when type I errors are more or less costly than type II? (What piques my interest about this question is its implications for understanding the evolution of apophenia.) NeonMerlin[1] 05:21, 9 September 2009 (UTC)

To be precise, p-values are not affected by such considerations: those values are merely calculated from statistics taken from the sample; what type I/II error considerations can do, is affect confidence levels: Bear in mind that p-value can be defined as the least significance level under which your null hypothesis is rejected (here significance level is 1-α, where α stands for confidence level).
In regard with type I/II error issues, set any other considerations aside (such as sample size, which has an inverse relation with both error probabilities), the thumb rule is that the more relatively costly type I error is, the less significance level you are willing to set, or in other words, the more probable is that the statistic from a sample will fall into the non-rejection interval (or the more probable is that the p-value is greater than the (prefixed) significance level. Pallida  Mors 18:21, 10 September 2009 (UTC)

Why angle side angle?

http://imgur.com/MpXTh.jpg

It's given that angle 1 is equal to angle 2, angle 3 is equal to angle 4, point D is the midpoint of line BE, and that line BC is equal to segment DE. BC is equal to BD via substitution, thus triangle ABD is congruent to triangle EBC via ASA, but it's bugging the hell out of me. Shouldn't it be AAS, seeing as how BE is outside of B and C? How would BC help me anyway? Ugh. I hope I phrased that in an understandable way. --Glaesisvellir (talk) 22:05, 9 September 2009 (UTC)

Once you have two angles, you can easily calculate the third using the fact that the sum of all the angles in a triangle is 180 degrees. That means it really doesn't make any difference whether you have ASA or AAS. --Tango (talk) 22:34, 9 September 2009 (UTC)

Thank you. The only problem is, what if the measurements of the other two angles are not listed, and measuring them is not an option? --Glaesisvellir (talk) 00:50, 10 September 2009 (UTC)

If you're trying to prove two triangles are congruent, such as the ones in the image you linked, you can argue that since two of the angles of each triangle are equal, then the third angles of each triangle must be equal. Referring to the image, that argument is $m\angle A=180^{\circ }-m\angle 1-m\angle 3=180^{\circ }-m\angle 2-m\angle 4=m\angle E$. Rckrone (talk) 03:53, 10 September 2009 (UTC)