PakMediNet Discussion Forum : Biostatistics : How to Calculate Sample Size?

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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: ** doctoc Posts: 20** :: 18-05-2008 :: | Reply to this Message

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_khur Posts: 30** :: 18-05-2008 :: | Reply to this Message

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: ** asadf Posts: 2** :: 18-05-2008 :: | Reply to this Message

@ 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: ** doctoc Posts: 20** :: 18-05-2008 :: | Reply to this Message

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_khur Posts: 30** :: 19-05-2008 :: | Reply to this Message

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: ** doctoc Posts: 20** :: 19-05-2008 :: | Reply to this Message

thanx alot

Posted by: ** dr saima Posts: 3** :: 04-06-2008 :: | Reply to this Message

sir what is ment by taking value of p conservatively?

Posted by: ** dr saima Posts: 3** :: 04-06-2008 :: | Reply to this Message

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 donâ€™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_khur Posts: 30** :: 05-06-2008 :: | Reply to this Message

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: ** docosama Posts: 333** :: 11-06-2008 :: | Reply to this Message

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: ** Hyder Posts: 9** :: 15-06-2008 :: | Reply to this Message

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: ** Hyder Posts: 9** :: 15-06-2008 :: | Reply to this Message

@ 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: ** doctoc Posts: 20** :: 17-06-2008 :: | Reply to this Message

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: ** drfarhan Posts: 93** :: 11-06-2009 :: | Reply to this Message

is there any calculator to calculate sample size?

Posted by: ** samreenqmc Posts: 140** :: 17-06-2009 :: | Reply to this Message

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: ** surgeon Posts: 2** :: 24-02-2010 :: | Reply to this Message

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: ** drcawl Posts: 2** :: 07-01-2011 :: | Reply to this Message

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_ap Posts: 138** :: 09-01-2011 :: | Reply to this Message

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: ** chinagorom Posts: 3** :: 26-10-2011 :: | Reply to this Message

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_ap Posts: 138** :: 28-10-2011 :: | Reply to this Message

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: ** waqashq Posts: 2** :: 22-11-2011 :: | Reply to this Message

Dear Sir, the provided information to calculate confidence interval is incomplete. Please call me so advise you. M.Ibrahim 03004668681

Posted by: ** ibrahim_ap Posts: 138** :: 23-11-2011 :: | Reply to this Message

When someone calculate sample size he/she must consider power of test in calculation. Muhammad Ibrahim 03004668681

Posted by: ** ibrahim_ap Posts: 138** :: 13-12-2011 :: | Reply to this Message

Thanx ... trying to understand.

is anyone here active ?

I want help ....

Posted by: ** israian Posts: 4** :: 11-03-2012 :: | Reply to this Message

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.aina Posts: 3** :: 12-04-2012 :: | Reply to this Message

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_ap Posts: 138** :: 13-04-2012 :: | Reply to this Message

Expected sample size is 314

Posted by: ** ibrahim_ap Posts: 138** :: 13-04-2012 :: | Reply to this Message

Thanks alot.but I want to understand this calculation sothat I can apply on other studies to get better sample size.

Posted by: ** dr.aina Posts: 3** :: 16-04-2012 :: | Reply to this Message

Dear Dr , u may contact on cell for detailed information

Posted by: ** ibrahim_ap Posts: 138** :: 26-04-2012 :: | Reply to this Message

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_ap Posts: 138** :: 04-05-2012 :: | Reply to this Message