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p-value

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Ujk
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07/27/07 - 01:36 PM

A group of researchers conducted a large double blind, randomized trial comparing the efficacy of a new antibiotic with penicillin in treating streptococcal pneumonia. The results showed 95% of the patients taking the new antibiotic cleared their pneumonia, while 90% of those taking penicillin cleared their pneumonia. A large sample size was chosen in order to generate a statistical power of 80% with a p value of 0.21. Which of the following represents the probability that there is a difference between the two treatment groups despite the study's failure to show this difference (p-value <0.05)?

A 0.05

B 0.20

C 0.21

D 0.80

E 0.90

F 0.95

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titly
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07/27/07 - 10:06 PM

0.2

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sfk
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07/28/07 - 11:02 AM

type 2 error. 1-power, i.e 1-0.8

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Ujk
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07/28/07 - 01:06 PM

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vnty
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09/10/07 - 09:57 AM

Why is it a typep II error UJK? Please clarify.

Null hypothesis: There is no different btw 2 trials.
Type I error: Probability the a variable is different when none exist.
Type II error: There is not an effect when one exists.

Is the question asking about type I ?

Jackofknives
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09/11/07 - 01:47 AM

Alfa is significance level and 1 – beta is power.

Power is the probability for discovering that null hypothesis is wrong.

So in this question the null hypothesis is false although we have accepted it. Because power = 1 – beta => beta = 1 – power = 1 – 80% = 20%

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Jackofknives
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09/11/07 - 06:06 AM

Oops its not this simple, ill investigate in this.

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Jackofknives
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09/13/07 - 10:40 AM

This is the answer I got from the head of Copenhagen Trial Unit.

In short, "the question is unanswerable given the information above"

then he gave me a 1 page long explanation on alfa, beta, P and such what could as well make you more confused. So dont bother with this question

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vnty
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09/13/07 - 11:12 PM

I beleive B is correct

Study result is no different, but reality is different => beta = 0.02.

Pls see FA page 64.

Jackofknives
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09/18/07 - 02:03 AM

#10

The question is peculiar and maybe unawerable because it is very rare that a sample size has been calculated to show "this difference". If the sample size had been calculated to show this difference then the p-value would have been < 0.05 which it is not so! The difference according to which the sample size has been calculated must inevitably have been another and which? Obviously a greater absolute difference than 95-90% clearance! We are in the area of post-hoc power calculation which is risky business! So yes on some premises you may say that the answer is 20% that we got the actual result or something more extreme, but in reality it depends on the difference that we were originally looking for to detect or reject.

so basically either the question is flawed or there is a typo and 80% power should accompany with p<0.05 and 20% should go with p=0.21

Edited by Jackofknives on 09/18/07 - 07:21 AM

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edie
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09/18/07 - 07:38 AM

#11

Jackofknives wrote:
Alfa is significance level and 1 – beta is power.

Power is the probability for discovering that null hypothesis is wrong.

So in this question the null hypothesis is false although we have accepted it. Because power = 1 – beta => beta = 1 – power = 1 – 80% = 20%

You got it right the first time.

Jackofknives
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09/18/07 - 01:40 PM

#12

edie wrote:

You got it right the first time.

it seems as if you didnt understand what i wrote

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edie
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09/18/07 - 09:56 PM

#13

Jackofknives wrote:

so basically either the question is flawed or there is a typo and 80% power should accompany with p<0.05 and 20% should go with p=0.21

Would the correct answer then be 0.8?

Jackofknives
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09/20/07 - 12:03 PM

#14

Ok i put this straight forward

A group of researchers conducted a large double blind, randomized trial comparing the efficacy of a new antibiotic with penicillin in treating streptococcal pneumonia. The results showed 95% of the patients taking the new antibiotic cleared their pneumonia, while 90% of those taking penicillin cleared their pneumonia. A large sample size was chosen in order to generate a statistical power of 80% with a p value of 0.21. Which of the following represents the probability that there is a difference between the two treatment groups despite the study's failure to show this difference (p-value <0.05)?

Question is flawed and unanswerable

A group of researchers conducted a large double blind, randomized trial comparing the efficacy of a new antibiotic with penicillin in treating streptococcal pneumonia. The results showed 95% of the patients taking the new antibiotic cleared their pneumonia, while 90% of those taking penicillin cleared their pneumonia. A large sample size was chosen in order to generate a statistical power of 80% with a p value of below 0.05. Which of the following represents the probability that there is a difference between the two treatment groups despite the study's failure to show this difference (p-value <0.05)?

Answer is 20%

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