The likelihood that the difference is due to chance

[nativedoc2]

two experimental drugs are being researched for the treatment of CHF

patients getting drug X have a cardiac index of 2.5L/m with a 95% confidence interval between 1.5 to 3.5.
patients getting drug y have cardiac index with 95% confidence interval between 0.7 to 3.7. a teat of significance of difference shows a p-value of 0.1. which of the following is the likelihood that the difference in mean cardiac index of patients getting drugs x and y is due to chance:
a.0%
b.2.5%
c.5%
d.7.5%
e10%
f.66.7%
g.95%

i would really appreciate a concise explanation as i have no idea what they are talking about,i have read statistics in FA
thanks

[bebix]

which of the following is the likelihood that the difference in mean cardiac index of patients getting drugs x and y is due to chance:

This is the same as saying "we fail to reject H0"

H0 = difference =0
HA = difference =! 0

So, you preset an alpha value of 5% (0.05)
Then you did the test statistics under the null hypothesis and you got a p value = 0.10 (10%) = post-test

Conclusions = you fail to reject the null hypothesis

When the p-value is < 0.05, reject the null hypothesis. With such a low probability for the p-value, there is little likelihood that the observed difference between the sample mean and hypothesized mean is due to chance - it must be do to some program, process change, intervention or other effect.

When the p-value is > 0.05, fail to reject the null hypothesis. There is a high probability for the p-value that the observed difference between the sample mean and the hypothesized mean is so small that it must be do to chance involved in sampling error.

In this case, the answer is 10%

[drnrpatel]

Here difference in mean is due to chance is null hypothesis.

Now, p = probability of making alpha error or Rejecting the null hypothesis when it was true. = 0.1 = 10%

When p>0.05 we do not reject null hypothesis.

So yeah difference was definitely due to chance and 10% chance were there we may have rejected it. And also 10% is likelihood of difference is due to chance!!!!!!

[bebix]

Originally Posted by drnrpatel

Here difference in mean is due to chance is null hypothesis.

Now, p = probability of making alpha error or Rejecting the null hypothesis when it was true. = 0.1 = 10%

When p>0.05 we do not reject null hypothesis.

So yeah difference was definitely due to chance and 10% chance were there we may have rejected it. And also 10% is likelihood of difference is due to chance!!!!!!

Be carful though.

the probability of a Type I error here is equal to alpha = 0.05
alpha is NOT the same as p-value (in this case 0.10)

[nativedoc2]

thanks for the explanations

[struggle]

This is NBME form 3 question..
Posting NBME qs is not allowed.

[dinosaur108]

Originally Posted by bebix

Be carful though.

the probability of a Type I error here is equal to alpha = 0.05
alpha is NOT the same as p-value (in this case 0.10)

Alfa crieterion is hypothesized - .05
alfa error is p value - .1 in this case

[bebix]

Originally Posted by dinosaur108

Alfa crieterion is hypothesized - .05
alfa error is p value - .1 in this case

no, they are not the same.

alpha is the probability of a type I error. In this case is a PREtest probability equal to 0.05 (something that an investigator can manipulate BEFORE do the actual experiment)
(probability alpha = Probability to reject the Null given the Null is true)

p-value is a POSTtest probability...you cant change this...is is the probability that you get with the data that you have in that particular time! (in this case 0.1)

The interpretations are completely different.

So first you preset an alpha = 0.05....then you do the test statistic and you get a p-value...if this p-value is less than you preset alpha, you'll reject the null hypothesis (there is little likelihood that the observed difference between the sample mean and hypothesized mean is due to chance)

[dinosaur108]

Originally Posted by nativedoc2

two experimental drugs are being researched for the treatment of CHF

patients getting drug X have a cardiac index of 2.5L/m with a 95% confidence interval between 1.5 to 3.5.
patients getting drug y have cardiac index with 95% confidence interval between 0.7 to 3.7. a teat of significance of difference shows a p-value of 0.1. which of the following is the likelihood that the difference in mean cardiac index of patients getting drugs x and y is due to chance:
a.0%
b.2.5%
c.5%
d.7.5%
e10%
f.66.7%
g.95%

i would really appreciate a concise explanation as i have no idea what they are talking about,i have read statistics in FA
thanks

can anyone tell me what is the chance that study result don't match the effect in large population?

[bebix]

Originally Posted by dinosaur108

can anyone tell me what is the chance that study result don't match the effect in large population?

I dont understand your qs. (large population)

here we have a 95% CI...so, we are talking about population parameters ("mu" and not "mu hat")....we are 95% confident that the population parameter mu lies between the lower and the upper bound...

[dinosaur108]

Originally Posted by bebix

I dont understand your qs. (large population)

here we have a 95% CI...so, we are talking about population parameters ("mu" and not "mu hat")....we are 95% confident that the population parameter mu lies between the lower and the upper bound...

likelihood that the difference in mean cardiac index of patients getting drugs x and y is due to chance is type 1 error = p = 10%

when there is failure to reject null hypothesis (P>5%) as here which is 10% chance of alfa error is 0 bcz we dont put that drug in practical life.............but what is the chance of beta error( difference in mean cardiac index of patients may be due to drug and not due to chance)?
what is the power ?

[bebix]

Originally Posted by dinosaur108

likelihood that the difference in mean cardiac index of patients getting drugs x and y is due to chance is type 1 error = p = 10%

when there is failure to reject null hypothesis (P>5%) as here which is 10% chance of alfa error is 0 bcz we dont put that drug in practical life.............but what is the chance of beta error( difference in mean cardiac index of patients may be due to drug and not due to chance)?
what is the power ?

Again. Type 1 error is not the same as p-value.

Type 1 error = reject the null given the null is true
Alpha = probability of a type 1 error

In this case: type 1 error (PRE-SET) = 0.05
p-value (POST)= 0.10

The term significance level (alpha) is used to refer to a pre-chosen probability and the term "P value" is used to indicate a probability that you calculate after a given study.

Beta again is something that you must decide before you run your experiment (since you´ll need that value and the alpha value to calculate the sample size). Typically we use beta = 0.1 (power = .9) or 0.2 (power = 0.8).

Here you can find more info:
http://www.statsdirect.com/help/basics/pval.htm

if you want, you can send me a pm.