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#1




How to solve this confidence interval question ?
A prospective study was conducted to assess the role of daily alcohol consumption in the occurrence of breast carcinoma. The investigator reported a 5 year relative risk of 1.4 for people who consume alcohol compare to those who do not.
The 95% confidence interval was 1.02 to 1.85. Which of the following 'p' values is most consistent with the results described above ? A.0.04 B.0.06 C.0.09 D.0.11 E.0.20 Tell me how to solve this so confused. I am trying to understand Confidence Interval and P value no where it explains properly. Is it worth wasting my time on this for Step 1 ? 
#2




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So no, you are not wasting your time There are a lot of picky definitions in stats, but I like to keep things simple, so at the risk of offending my fellow stats nerds out there: pvalue: this is the chance you got your results by pure chance. You know how you can flip a coin and have it come up on the same side 56 times in a row? That's just a sampling error and if you flip the coin enough times, you'll end up with a 5050 split like you would expect. So in stats, the pvalue just says what percent of the time your answer could be due to pure chance. For whatever reason, the field of science and medicine has decided that 0.05 (aka 5%) is the cutoff value for something being "statistically significant." 95% CI: This is the range of values where you are 95% sure the TRUE value of whatever you're measuring actually lies. For the example above it was Relative Risk, but you can construct of CI around just about anything. Obviously, the small the CI, the better because it means our result is more likely to be accurate. **notice how the CI is 95% and the pvalue cutoff is 5%  that's not a coincidence** Now, lets take a hypothetical and I'm going to ask you to calculate these values in your head. Room A has 100 people in it; I measured ALL of them; their average height is 160cm with a standard deviation of 5 cm Room B has 100 people in it; I measure ALL of them; their average height is 155cm with a standard deviation of 3cm. From this I conclude that the people in room A are, on average, 5 cm taller than the people in Room B. Calculate the pvalue and the 95% CI. Go! ... ... ... Time's up! The answer is that there IS NO PVALUE or CI! In my example, I measured EVERYBODY. There's no sampling error to be had because I measured the entire population in question. Now if I had measured only 10 people in each room, I may or may not have found the same thing depending on who exactly I measured. In this case, I would have a pvalue and a CI. As I measured more and more people in each room, the pvalue and CI would get smaller and smaller until I measured everyone and then they would disappear. I would know "the truth." So back to the original question at hand: We're given a RR of 1.4 (95%CI 1.02  1.85) and asked to estimate the pvalue. Remember that RR here means that people who consume EtOH are 1.4x more likely to get breast cancer. If the RR was 0.70, then people who consume EtOH would only be 0.7x as likely to get breast cancer; in other words, they would be LESS likely to get it. So for Relative Risk, 1.0 is a big important number because that's where your stat completely changes its meaning. Since I have a 95% CI that never crosses 1.0, I know that my RR has less than a 5% chance of being the complete opposite of what I'm saying (ie. more vs less likely of developing breast cancer). Remember that pvalue of less that 5% is significant? So since my 95% CI never crosses 1.0, I know my pvalue MUST be less than 5% or 0.05. Now all I have to do is pick the answer choice that is less than 0.05, so AA is the correct answer. The faster ways to answer this one: 1) know that CI for RR or OR or HR that doesn't cross 1.0 is statistically significant; only one pvalue on the list would be consider significant (A) 2) Use test strategy that says "which of these is not like the other?" Since only one pvalue is significant and all the others are not AND they didn't give you enough information to actually calculate a pvalue, you could assume they want you to pick the different one. Hope this helps  stats can be tricky! 
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#3




Thanks so much for detailed explanation.
What about this ? this is confusing me The 95% confidence interval was 1.02 to 1.85. you are not using 1.85 any where or 1.02. 
#4




And how is RR and OR tied with confidence Interval ?
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#5




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For ANY stat, all the CI is saying is this: I'm 95% certain that the TRUE value of whatever I calculated lies in this range of numbers. In the question above, the actual numbers of the CI are not important. Only the fact that the interval does not include the number 1.0. This is what tells us the result is significant, and by our universally accepted definition of significance, the pvalue must be less than 0.05. Maybe this will help: If the confidence interval in the question was 0.98 to 1.85, then BB would be the correct answer. In this hypothetical case, our CI would include the number 1.0. What 1.0 means in a RR is that there is not difference. If I'm 95% sure the RR could also mean there is no difference at all, then my pvalue would have to be greater than 0.05. Basically they just want you to understand that CI's that cross 1.0 are not significant. 
#6




You can calculate a confidence interval for ANY statistic. Relative risk, odds ratio  doesn't matter. I just listed examples of other stats where you can also see CIs. There are many others too.

#7




So since my 95% CI never crosses 1.0, I know my pvalue MUST be less than 5% or 0.05. Now all I have to do is pick the answer choice that is less than 0.05, so AA is the correct answer.
it is more than 1.02 so it crossed 1 right ? Or I am i missing something ? also what does not significant mean ? not important ? Last edited by ezguy; 05122015 at 04:34 PM. 
#8




Quote:
Significant is just an arbitrary term. It means that your results are most likely real and not just from random chance. 
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