PakMediNet Discussion Forum : Biostatistics : How to Calculate Sample Size?
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How to Calculate Sample Size?
CPSP has recently acquired a new way to 'bounce' your synopsis. "How have you calculated your sample size?" and all your effort is wasted.
(When we attended the so called RMBDW workshop we were told that 30 is the minimum possible sample size, nothing regarding the damn formula.
Please somebody should clarify this formula
n = (Z1-alpha/2)2 x p (1- p)
__________________________
d2
Please clarify this with respect to confidence interval, proportion and margin of error. Thanks.
Posted by: doctocPosts: 20 :: 18-05-2008 :: | Reply to this Message
Re: How to Calculate Sample Size?
No. Although we statisticians like the number 30 but it is not the magic word. There are hundreds of formulas depending on what you want (mean, proportion, coefficient of variation etc. name it and it is there). It seems that you want to find sample size formula for single proportion.
To make life easy you can assume:
(Z1-alpha/2)2 = (1.96)2 (ie square of 1.96) this is normal value corresponding 95%
d2 is the square of the margin of error
p is the proportion of success
(1-p) is the proportion of failure
Example: Suppose we want to take a sample of citizens of city A to determine the percentage of people who have or are carrying , Hepatitis C. Level of precision we require is such that 95% confidence interval is no wider than 5%. Assume that phat is 0.45. This is another problem). Putting these values I hope we will find that minimum size of the sample is 381.
I dont know how to attach the files here, please write me I can explain in detail.
Hope it will help.
Anwer
Posted by: anwer_khurPosts: 30 :: 18-05-2008 :: | Reply to this Message
Re: How to Calculate Sample Size?
you have got the correct reply from Dr. Anwer except that the "d'is called the bond of error and it is actually half of the width of confidence interval which will vary in different studies
Moreover for two samples other formula will be applied
Posted by: asadfPosts: 2 :: 18-05-2008 :: | Reply to this Message
Re: Re: How to Calculate Sample Size?
@ dranwer
Thanks for your quick reply.
I understood everything except the example (I m a complete noob, so please forgive me).
What is phat?
I think one more example d be helpful.
Posted by: doctocPosts: 20 :: 18-05-2008 :: | Reply to this Message
Re: How to Calculate Sample Size?
Ok. Here is another example.
Suppose that a study is to be conducted to estimate the smoking rate among women. We want to estimate this proportion to within 2% (i.e d=0.02) with 95% confidence. Now two cases can be considered:
Case 1: Assume that by previous experience, research or by pilot survey, we know that smoking rate among women is about 29%. So plugging the values in the formula we have
n=[(Z)^2*p*(1-p)]/d^2
where Z is degree of confidence (ie 95% which yields 1.96)
p is proportion (here it is 0.29)
d is maximum tolerated error or upper bound for the margin of error
n1 = [(1.96)^2 *(0.29)*(0.71)]/(0.02)^2
= 1977.46
or a sample of size 1988 is needed.
Case 2: If we dont have any idea about current smoking rate among women ie we dont have the figure of 29%, we can still conversatively take
n2=[(1.96)^2(0.25)]/(0.02)^2
=2401
We can sample 2401.
Comments: Note the difference between two sample sizes. The sample size n2 is adequate regardless of the true value of the unknown proportion
Value of n1 and n2 will be clsoe when p is near 0.5
Where does the 0.25 come from? This is the maximum value when you multiply two fractions together.
Hope it will clarify.
[Please note that
* is notation for multiplication,
/ is notation for division
^ is notation for raising the power]
Posted by: anwer_khurPosts: 30 :: 19-05-2008 :: | Reply to this Message
Re: How to Calculate Sample Size?
Thank you very much sir. You have saved many fcps candidates from re-writing the synopsis again and again. Both examples were excellent.
I think we d ask you regular questions in this forum (if you consider answering). Thanks once again.
Posted by: doctocPosts: 20 :: 19-05-2008 :: | Reply to this Message
Re: Re: How to Calculate Sample Size?thanx alot
Posted by: dr saimaPosts: 3 :: 04-06-2008 :: | Reply to this Message
Re: Re: How to Calculate Sample Size?sir what is ment by taking value of p conservatively?
Posted by: dr saimaPosts: 3 :: 04-06-2008 :: | Reply to this Message
Re: Re: Re: How to Calculate Sample Size?
OK. Let's look at the formula again ie
{{n=[(Z)^2*p*(1-p)]/d^2
where Z is degree of confidence (ie 95% which yields 1.96)
p is proportion (here it is 0.29)
d is maximum tolerated error or upper bound for the margin of error}}
Please note that here p is proportion or probability. Probability of any event (in my example smoking among women is an event) lies between 0 (minimum) and 1 (maximum)[In no case it can be smaller than 0 and greater than 1]. Now just concentrate on p* (1-p) bit of the above formula. Just give different values to p. Here is a table with some values. You can check with in between values. What will happen to p * (1-p).
p (1-p) p * (1-p)
0 1 0
0.25 0.75 0.1875
0.5 0.5 0.25
0.75 0.25 0.1875
1 0 0
It is clear that it p * (1-p) will be maximum (ie 0.25) when p=0.5. Now statisticians are smart. Remember they don’t have any idea about the value of p but they estimate it and call it conservative estimator of p.
Hope it will help.
Anwer
Posted by: anwer_khurPosts: 30 :: 05-06-2008 :: | Reply to this Message
Re: How to Calculate Sample Size?Hyder, I want to know is it possible for you to take sometime and become PakMediNet Expert in the analysis of Research Synopsis posted on the website? Let me know if you are interested.
Posted by: docosamaPosts: 333 :: 11-06-2008 :: | Reply to this Message
Re: How to Calculate Sample Size?
Sure doc. I get stuff for correction, supervisor rejects, 'hapless trainee' all the time. So, ya I think I can help out here as well.
[Edited by Hyder on 15-06-2008 at 04:23 PM GMT]
Posted by: HyderPosts: 9 :: 15-06-2008 :: | Reply to this Message
Re: How to Calculate Sample Size?
An excellent resource on sample size calculations for cross sectional studies is this article
http://www.ijo.in/article.asp?issn=0301-4738;year=2000;volume=48;issue=3;spage=245;epage=50;aulast=Naduvilath
Posted by: HyderPosts: 9 :: 15-06-2008 :: | Reply to this Message
Re: How to Calculate Sample Size?
@ All
Thank you very much for showing much needed interest in the plight of fcps trainees like me.
[Edited by doctoc on 20-06-2008 at 08:37 PM GMT]
Posted by: doctocPosts: 20 :: 17-06-2008 :: | Reply to this Message
Re: How to Calculate Sample Size?
I read following problem in a book of biostatistics regarding calculation of size of sample.
Ministry of health wants to conduct a survey regarding hypertension amongst those 60 years old and above . With previous experience they know that prevalance of hypertension is 25%. How large the sample size should be so that the resulting estimate falls with in 10 % of true proportion with 95% confidence interval.
In proposed solution of this question, concept of relative precision is introduced.
Formula is z2(1-alpha/2)(1-p)/D2p
Now for 95% confidence interval 1-alpha is 1.96 and p is 0.25 so 1-p is 0.75 so putting in the values
it gives.
(1.96)2(0.75)/(0.05)2(0.25). This is relative precision formula.
Can anybody please explain how did the author put the denominator values. Especially How did he calcaulte relative precision value i.e. 10% of 25%.
Posted by: drfarhanPosts: 93 :: 11-06-2009 :: | Reply to this Message
Re: Re: How to Calculate Sample Size?is there any calculator to calculate sample size?
Posted by: samreenqmcPosts: 140 :: 17-06-2009 :: | Reply to this Message
Re: How to Calculate Sample Size?aoa,i want to know the website used by cpsp for the sample size calculation for estimation of single proportion with absolute precision. the site with the calculators shown to us in the research methodology workshop. thanks
Posted by: surgeonPosts: 2 :: 24-02-2010 :: | Reply to this Message
How to Calculate Sample Size?
my study is cross-sectional study of factors influencing immunization coverage
so i see many formules and iconfused which to choice, the immunization coverage in area is 35% so plz help me which formule to chioce
Posted by: drcawlPosts: 2 :: 07-01-2011 :: | Reply to this Message
Re: How to Calculate Sample Size?The sample size calculation is not a difficult task, you may contact me on phone, all services are free M.Ibrahim 0300-4668681
Posted by: ibrahim_apPosts: 138 :: 09-01-2011 :: | Reply to this Message
Re: Re: How to Calculate Sample Size?I want to carry out a study titled - Evaluation of malaria preventive strategies in pregnancy in Abia state university teaching hospital. Number of deliveries is about 1000 per annum. Subjects will be pregnant women in labour.what will be my sample size
Posted by: chinagoromPosts: 3 :: 26-10-2011 :: | Reply to this Message
Re: Re: Re: How to Calculate Sample Size?Dear Dr, Please forward one fresh research paper on your title to this email, so to able calculate the sample size. Given information are incomplete. mob: 0300-4668681 ibrahim_ap98@yahoo.com
Posted by: ibrahim_apPosts: 138 :: 28-10-2011 :: | Reply to this Message
Re: How to Calculate Sample Size?if a proportion is 2.08 or 4.5% than what should be the confidence interval. kindly some one give me idea about this. as cpsp has returned my synopsis as sample size was too much
Posted by: waqashqPosts: 2 :: 22-11-2011 :: | Reply to this Message
Re: Re: How to Calculate Sample Size?Dear Sir, the provided information to calculate confidence interval is incomplete. Please call me so advise you. M.Ibrahim 03004668681
Posted by: ibrahim_apPosts: 138 :: 23-11-2011 :: | Reply to this Message
Re: Re: Re: How to Calculate Sample Size?When someone calculate sample size he/she must consider power of test in calculation. Muhammad Ibrahim 03004668681
Posted by: ibrahim_apPosts: 138 :: 13-12-2011 :: | Reply to this Message
Re: How to Calculate Sample Size?
Thanx ... trying to understand.
is anyone here active ?
I want help ....
Posted by: israianPosts: 4 :: 11-03-2012 :: | Reply to this Message
Re: How to Calculate Sample Size?I need help to calculate sample size of case control study with help of odd ratio by using WHO 2.2a formula as OR 0.49,95% Cl 0.29,0.84. Any genius mind?
Posted by: dr.ainaPosts: 3 :: 12-04-2012 :: | Reply to this Message
Re: Re: How to Calculate Sample Size?
Dear Dr
I will calculate the sample size for given information, however you may consult with me for more understanding M.Ibrahim 0300 4668681
Posted by: ibrahim_apPosts: 138 :: 13-04-2012 :: | Reply to this Message
Re: Re: Re: How to Calculate Sample Size?Expected sample size is 314
Posted by: ibrahim_apPosts: 138 :: 13-04-2012 :: | Reply to this Message
Re: Re: Re: Re: How to Calculate Sample Size?Thanks alot.but I want to understand this calculation sothat I can apply on other studies to get better sample size.
Posted by: dr.ainaPosts: 3 :: 16-04-2012 :: | Reply to this Message
Re: Re: Re: Re: Re: How to Calculate Sample Size?Dear Dr , u may contact on cell for detailed information
Posted by: ibrahim_apPosts: 138 :: 26-04-2012 :: | Reply to this Message
Re: Re: Re: Re: Re: Re: Re: How to Calculate Sample Size?Dear Dr Tariq, i am servicing the health community since a long time, and i think that Pakmedinet is good forum to help and serve the community. All health professionals who are regular user of pakmedinet are also access me for help. This is Allah's blessing on me for servicing the nation through pakmedinet
Posted by: ibrahim_apPosts: 138 :: 04-05-2012 :: | Reply to this Message