For NHST vs , theoretically, is s.t. , rather than zero. Nevertheless, pratically a large t, rejecting both and , should not be counted as any evidence to retain or reject .

To verify the shape of --

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# Tag: Hypothesis Test

## Unexpectedly, the theoretically best reject-region of T-test is bounded.

## Classic Neyman-Pearson approach demo

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## 习题：一类错误的注水

## The tail(s) of p value

For NHST vs , theoretically, is s.t. , rather than zero. Nevertheless, pratically a large t, rejecting both and , should not be counted as any evidence to retain or reject .

To verify the shape of --

It notes here that N-P approach does not utilize the information in the accurate *p* value. Actually, at the time N-P approach was firstly devised, the accurate *p* value was not available usually. Now almost all statistic softwares provide accurate *p* values and the N-P approach becomes obsolete. Wilkinson & APA TFSI (1999) recommended to report the accurate *p* value rather than just significance/insignificance, unless *p* is smaller than any meaningful precision.

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Wilkinson, L. & APA TFSI (1999). Statistical methods in psychology journals: Guidelines and explanations. *American Psychologist, 54*, 594-604.

一个研究者每次都先看一下计算出的统计量再决定对零假设做单尾检验还是双尾检验。如果统计量，就设对立假设为；如果统计量，就设对立假设为。假如他的请问他真实的一类错误率是多少？具体说，有许多次的实验，真实情形都是，他能检验出显著拒绝的比例会趋近于多少？

For any given vs , the p value of any given point x is , Where

-- See R. Weber's Statistics Note (Chap 6.2 & 7.1)

I made some wrong comment on the pdf Null Ritual (Gigerenzer, Krauss, & Vitouch, 2004) Where three types of significance level (rather than p value) were discussed. I had written the comment to note that the chapter had ignored the role of in definition of p value. In almost every textbook, the two-tail p vs single-tail p are differentiated. Usually, the two-tail p is defined by like .

Here I demonstrate a three-tail p value case on R platform.

z=(-1000:1000)*0.02;

f=0.5 * dchisq(abs(z),df=5);

h=dchisq(10,df=5)*.5;

plot(z,f,type="h",col=c("black","grey")[1+(f>h)]);

lines(c(-20,20),c(h,h));

## is * binomial(-1 vs 1) ##

Do you agree the region nearby zero under the "V" curve (which is below the horizontal line) should be the 3rd tail? I think so, if only includes all other possible distributions in the same shape.

You'll also agree there will be two asymmetrical tails if includes just two asymmetrical curves, for example, and () while is the standardized normal distribution.