Alpha Risk

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Alpha Risk

When testing a hypothesis, the risk of rejecting a piece of data that should have been accepted. Many tests reject some data as unusable or irrelevant. Alpha risk is the probability that the wrong data will be eliminated from the sample. It is also called type I error or alpha error. See also: Beta risk.
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However, we also need to recognize that there are usually consequences to type I errors as well (i.e., the ripples).
A precautionary approach for public health appears to be opposite to the conventional scientific bias in hypothesis testing that critics have claimed favors type II over type I errors (Cranor 1993; M'Gonigle et al.
Type I errors involve rejecting material that is actually good while Type II errors occur when accepting material that is actually bad.
The type I errors in Figure 1A were obtained by testing the significance of [beta] using the S-Plus standard error estimate at the 0.05 level of significance; the type I error increases dramatically with the degree of concurvity.
Figure 3 shows the type I errors observed when using t-tests based on the S-Plus estimate and the alternative estimate, respectively, to test the true null hypothesis that [beta] = 0.0087 at the 0.05 level of significance.
(2002), increased concurvity in the data used to fit a semiparametric spatial GAM leads directly to increased downward bias in the estimated standard error of the fitted linear parameter and, consequently, to inflated type I error in the standard significance test of this effect.
A consequence of this inability to detect concurvity is that using the S-Plus standard error estimate to test the significance of a fitted linear parameter can result in inflated type I error.
The first simulation study was conducted to verify that increased concurvity does result in increased standard error bias and, therefore, to inflated type I error. For each j in the set {0,0.1,0.2, ...
It should be noted that although both the type I error and the concurvity [R.sup.2] statistic are measured on a scale of 0 to 1, the two curves in Figure 1A do not measure the same thing.
For the 1,000 data sets simulated with j = 0.3, the type I error was 0.246, the sample standard deviation was about 0.0063, the average estimated standard error estimate was about 0.0036, and 95% of the standard error estimates were < 0.0052.
Simulation data sets constructed from the same preconcurvity data set are connected by lines, and the large blue points in Figure 3 represent the overall type I error for a single value of the concurvity parameter.
Using the S-Plus standard error estimate to test the true null hypothesis that [beta] = 0.0087 resulted in an observed type I error rate > 0.05 (the expected value) for 24 of the 30 models for which j = 0.3.