# ȤP value(ֵ) ֪R6}Сy򞣬

822 Ķ 2022-1-25 16:47 |˷:|ϵͳ:бʼ

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• 0ֻ򿴲ģ6}]дhنһδyӋW

• 16-50ֻµ1-3}ģhنһδTʿ׃ MAyӋW

• 51-83 1-2 }]дx״ Haller and Krauss (2002); Gigerenzer (2004); Cohen (1988,1992)

• 100ֵģMaster̫.

Rigor & Relevance(֔P)оăɴ֧оPϣоˆT඼оԼIPĆ}P(Relevance)ˣ҂۽о֔(Rigor)P@p valueĽጣЩ⣬磬܌Pֵ^ȽxyӋ⡣ǰ1yӋоyԇоˆT_PֵGigerenzer 2004 Ӣԭ£

Suppose you have a treatment that you suspect may alter performance on a certain task. You compare the means of your control and experimental groups (say 20 subjects in each sample). Further, suppose you use a simple independent means t-test and your result is significant (= 2.7, d.f. = 18, = 0.01). Please mark each of the statements below as true or false. False means that the statement does not follow logically from the above premises. Also note that several or none of the statements may be correct.

1.You have absolutely disproved the null hypothesis (that is, there is no difference between the population means).

[] true/false []

2. You have found the probability of the null hypothesis being true.

[] true/false []

3. You have absolutely proved your experimental hypothesis (that there is a difference between the population means).

[] true/false []

4. You can deduce the probability of the experimental hypothesis being true.

[] true/false []

5.You know, if you decide to reject the null hypothesis, the probability that you are

making the wrong decision.

[] true/false []

6. You have a reliable experimental finding in the sense that if, hypothetically, the experiment were repeated a great number of times, you would obtain a significant

result on 99% of occasions.

[] true/false []

ӢĽ£

Which statements are in fact true? Recall that a p-value is the probability of the observed data (or of more extreme data points), given that the null hypothesis H0 is true, defined in symbols as p(D|H0).This definition can be rephrased in a more technical form by introducing the statistical model underlying the analysis (Gigerenzer et al., 1989, chapter 3).

Statements 1 and 3 are easily detected as being false, because a significance test can never disprove the null hypothesis or the (undefined) experimental hypothesis. They are instances of the illusion of certainty (Gigerenzer, 2002).

Statements 2 and 4 are also false. The probability p(D|H0) is not the same as p(H0|D), and more generally, a significance test does not provide a probability for a hypothesis.

The statistical toolbox, of course, contains tools that would allow estimating probabilities of hypotheses, such as Bayesian statistics. Statement 5 also refers to a probability of a hypothesis. This is because if one rejects the null hypothesis, the only possibility of making a wrong decision is if the null hypothesis is true. Thus, it makes essentially the same claim as Statement 2 does, and both are incorrect.

Statement 6 amounts to the replication fallacy (Gigerenzer, 1993, 2000). Here, p=1% is taken to imply that such significant datawould reappear in 99% of the repetitions. Statement 6 could be made only if one knew that the null hypothesiswas true. In formal terms, p(D|H0) is confused with 1p(D).

To sum up, all six statements are incorrect. Note that all six err in the same direction of

wishful thinking: They make a p-value look more informative than it is.

f

PֵĶxǣ̓oOO棬cӱYͬĸʣʾPD/H0

-----------------------

OƜyһNίSԸ˂ĳNyϵĿЧOӋһо^ˌսM͌MOÿM20ӱľʹ˪ӱtz򞣬@½Y: t = 2.7, d.f. = 18, p = 0.01, Ոeش}ĿeǱʾԓ}cǰоY߉݋

1.     ȫ̓oOO̓oOOָǃɂwľû /e

2.     ҵ̓oOOĸʡ/e

3.     ȫCˌffָǃɂwľڲ/e

4.     Ɣfĸʡ/e

5.     Ҫܽ^Oѽ֪@eĸʡ/e

6.     õһɿоYԭ飺@򞱻}˷ǳΣ㌢99%Ŀܫ@һ@ĽY/e

Ҫh Statements (abbreviated)

1)     H0 is absolutely disproved

2)     Probability of H0 is found

3)     H1 is absolutely proved

4)     Probability of H1 is found

5)     Probability of Type I error

6)     Probability of replication

_Ĵ𰸣@}fe

PֵĶxOr^ֵĸ÷̖ʾP(D/H0)

}1}3eģһ@ĜyԇδH0H1

}2}4PֵʾP(D/H0)}2}4ָP(H0/D)ǲһӵ˼

}5Ҳeģ}5}3OĎʣY}2ͬeġ

}6eģ}6P = 1%ָ@Y}99%Ҳ1-P(D)ԭʼPֵʾP(D/H0)1-P(D)

οף

• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.

• Cohen, J. (1992). A Power Primer. Psychological Bulletin, 112(1), 155-159.

• Haller, H., Krauss, S., 2002. Misinterpretations of significance: a problem students share with their teachers? Methods of Psychological Reseach.

• Gerd Gigerenzer, Mindless statistics, The Journal of Socio-Economics 33 (2004) 587C606

https://m.sciencenet.cn/blog-3444471-1322621.html

һƪ20220114 ´ϲ1ƪESI 1% ߱
һƪSEM Power analysis (no type II error )
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