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Comments on: Spurious Sources http://hea-www.harvard.edu/AstroStat/slog/2007/spurious-sources/ Weaving together Astronomy+Statistics+Computer Science+Engineering+Intrumentation, far beyond the growing borders Fri, 01 Jun 2012 18:47:52 +0000 hourly 1 http://wordpress.org/?v=3.4 By: hlee http://hea-www.harvard.edu/AstroStat/slog/2007/spurious-sources/comment-page-1/#comment-94 hlee Fri, 21 Sep 2007 17:03:11 +0000 http://hea-www.harvard.edu/AstroStat/slog/2007/spurious-sources/#comment-94 <p>I saw many students and some clients from consulting class were confused with how to set the null and alternative hypotheses, and defining type I and II errors accordingly. Hypothesis testing looks very arbitrary and most likely appears as a method to reject the null hypothesis by collecting data. I was not sure it was a pyto of typo, or a confusion between null and alternative (or type I and II), which led me to write about it.</p> I saw many students and some clients from consulting class were confused with how to set the null and alternative hypotheses, and defining type I and II errors accordingly. Hypothesis testing looks very arbitrary and most likely appears as a method to reject the null hypothesis by collecting data. I was not sure it was a pyto of typo, or a confusion between null and alternative (or type I and II), which led me to write about it.

]]> By: hlee http://hea-www.harvard.edu/AstroStat/slog/2007/spurious-sources/comment-page-1/#comment-93 hlee Thu, 20 Sep 2007 04:42:00 +0000 http://hea-www.harvard.edu/AstroStat/slog/2007/spurious-sources/#comment-93 Type II error is claiming no signal when there is signal (failing to reject the null hypothesis when the alternative is true). Type I error is rejecting the null hypothesis when the null is true, i.e. detecting signal under no signal. The null hypothesis is a subset of combined hypotheses (union of null and alternative). I think no signal should be the null hypothesis and the existence of signal is the alternative. The other way around, the existence of signal is null and no signal is alternative, is an improper statement for hypothesis testing. <b>[Response: </b> Thanks for the catch. That was a pyto. -vlk<b>]</b> Setting 3оѓ or 5оѓ thresholds become important when you study the power of the test, defined by one minus the size of type II error, once you reject the null hypothesis, or say signal is significant. Besides many factors, power depends on the sample size. With the same rejection region of the null hypothesis based on 3оѓ (smaller sample size) or 5оѓ (larger sample size) thresholds, the power of larger sample is larger than the power of smaller sample; in other words, type II error is smaller with larger sample. Setting high number оѓ helps to reduce type II error, false negative, or the chance of saying no signal when there is signal. Unfortunately, other factors also determine the power of the test so that a larger оѓ threshold is not an optimal choice for a reliable source detecting rule, not to mention the cost of collecting large sample and systematic errors. Type II error is claiming no signal when there is signal (failing to reject the null hypothesis when the alternative is true). Type I error is rejecting the null hypothesis when the null is true, i.e. detecting signal under no signal. The null hypothesis is a subset of combined hypotheses (union of null and alternative). I think no signal should be the null hypothesis and the existence of signal is the alternative. The other way around, the existence of signal is null and no signal is alternative, is an improper statement for hypothesis testing.

[Response: Thanks for the catch. That was a pyto. -vlk]

Setting 3оѓ or 5оѓ thresholds become important when you study the power of the test, defined by one minus the size of type II error, once you reject the null hypothesis, or say signal is significant. Besides many factors, power depends on the sample size. With the same rejection region of the null hypothesis based on 3оѓ (smaller sample size) or 5оѓ (larger sample size) thresholds, the power of larger sample is larger than the power of smaller sample; in other words, type II error is smaller with larger sample. Setting high number оѓ helps to reduce type II error, false negative, or the chance of saying no signal when there is signal. Unfortunately, other factors also determine the power of the test so that a larger оѓ threshold is not an optimal choice for a reliable source detecting rule, not to mention the cost of collecting large sample and systematic errors.

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