Here is the problem.

 Sample size calculation is only an estimate. It is the minimum sample size necessary to achieve your objectives given the values that you provide. Yet you probably cannot claim that the variance that you entered into the sample size calculation is the variance of the studied population. So what is the 95% confidence interval about your estimated variance? Entering that will give a range of sample sizes. Really, you can use any sample size that you want, subject to the following reservations:

1) Smaller sample sizes increase the chance that your results cannot be duplicated.

2) Smaller sample sizes have less power to detect significant effects.

3) Smaller sample sizes limit your options in terms of the types of analyses that can be done.

4) Smaller sample sizes increase the chance your manuscript will get rejected.

All that said, sometimes there is no choice. If done honestly, there should not be a penalty for discovering that some of the initial assumptions were wrong, and consequently (in hindsight) your sample size was too small. So you, your advisor, and committee all thought "this" but you collected the data and the assumption was wrong. That happens in research. What you do then depends on many factors, but sample size is a major consideration. Your goal was 335. You managed to get 320, and estimate that you really needed 1200? You managed to get 20, and estimate that really needed 1200? In the latter case I would either start over, or abandon the project. In the former case, I don't see a major problem.

I figured out that 1 lakh=100,000. I don't know what UT stands for.

Hi Anoop,

If it is not possible to reach this number, your chances of representing the population will diminish. You can reach accurate statistical results with fewer individuals, but you have to reach the number you find to generalize to the population. I hope I could help.

Best wishes.

Here is the problem.

 Sample size calculation is only an estimate. It is the minimum sample size necessary to achieve your objectives given the values that you provide. Yet you probably cannot claim that the variance that you entered into the sample size calculation is the variance of the studied population. So what is the 95% confidence interval about your estimated variance? Entering that will give a range of sample sizes. Really, you can use any sample size that you want, subject to the following reservations:

1) Smaller sample sizes increase the chance that your results cannot be duplicated.

2) Smaller sample sizes have less power to detect significant effects.

3) Smaller sample sizes limit your options in terms of the types of analyses that can be done.

4) Smaller sample sizes increase the chance your manuscript will get rejected.

All that said, sometimes there is no choice. If done honestly, there should not be a penalty for discovering that some of the initial assumptions were wrong, and consequently (in hindsight) your sample size was too small. So you, your advisor, and committee all thought "this" but you collected the data and the assumption was wrong. That happens in research. What you do then depends on many factors, but sample size is a major consideration. Your goal was 335. You managed to get 320, and estimate that you really needed 1200? You managed to get 20, and estimate that really needed 1200? In the latter case I would either start over, or abandon the project. In the former case, I don't see a major problem.

I figured out that 1 lakh=100,000. I don't know what UT stands for.

Thanks Professor, Your explanation to my query has given clarity to my problem. UT is union territory. (UT is a measurement for a area) A union territory is a type of administrative division in the Republic of India. Unlike states, which have their own elected governments, union territories are ruled directly by the Union Government (Central Government), hence the name "union territory"

Dear Anoop

The sample size depends on the type of your population, is it finite population or infinite population.

In the case of finite population, you can use the attached table to estimate the suitable sample size. Or use Slovin formula:

n= N / ( 1+ N * e^2 ) 

But in the case of an infinite population: 

The sample size for any study depends on the standard deviation of the variable ( from previous studies ) and the margin of error you decided. The formula:

n= ( Z^2 * S^2) / E^2

where : Z  ( 1.96 for 0.05 and 2.58 for 0.01 )

S = standard deviation from previous studies or pilot  study

E = significant level 

Also, you can use software to calculate sample size ( SPSS , Minitab , G*power )

My advice to use G*Power .

G*Power software is effective tool to calculate sample size for many ranges of experiments. Also, you can determine effect size and power of the test, G*Power is free to download and easy to use after reading the manual, the download link:

http://download.cnet.com/G-Power/3000-2054_4-10647044.html

The link to download G*Power manual:

http://www.gpower.hhu.de/fileadmin/redaktion/Fakultaeten/Mathematisch-Naturwissenschaftliche_Fakultaet/Psychologie/AAP/gpower/GPowerManual.pdf

I hope that be useful for you.

Good Luck

Hello Anoop -

Are you looking at continuous data, or are you looking at proportions (yes/no data)?  You must be careful of online calculators which are often only for simple random sampling, and only for yes/no data.  They also (for yes/no data) often then circumvent the most important thing to know, an 'estimate' of population standard deviation (or better, such 'guesses' by stratum).  They instead often just give you a worst case, and this does not apply at all to continuous data.  I may be misreading your question, but it also sounds like you may not be using a finite population correction (fpc) factor, when perhaps you should.

Perhaps you might benefit by obtaining a copy of one of these books:

Thompson, S.K.(2012), Sampling, 3rd ed, John Wiley & Sons, or

Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons. 

A simpler book, which may not explain everything you need to know, but might be a good start, would be the following:

Blair, E. and Blair, J(2015), Applied Survey Sampling, Sage Publications.

Further, the bibliography I have below,  for a more specific project, may also contain a reference you might use if you cannot obtain one, or both, of the first two above.  That is, I note other textbooks in survey statistics which you may find in your library or elsewhere. 

 https://www.researchgate.net/publication/317914104_Handout_Bibliography_for_Comparison_of_Model-Based_to_Design-Based_Ratio_Estimators_Poster

Best wishes - Jim

PS -  The book by Thompson above is often referenced in the Pennsylvania State University online statistics course websites, which I have found are often very good.  If you do an online search for a topic related to the above, and such a PSU site presents itself, i recommend looking into it.  

For example, if you go to the following URL, there are three links at the bottom which look like they may be of interest to you, to get you started:

 https://onlinecourses.science.psu.edu/stat506/node/7

PSS -  I just took a look at the URL given in your question, and it is only for yes/no data.  Though it is probably better than most such calculators, if you are not looking exclusively at yes/no data using simple random sampling, it is still definitely not what you want.  

Data Handout Bibliography for "Comparison of Model-Based to Desig...

Anoop:

I think that Jim gave in the point of interest, is important to define what kind of variable you will measure, or maybe you will perform a multipurpose study with more than one variable of interest.

Derived from your explanation about States and UT like the objective populations, maybe a stratified or by conglomerates sample design will be necessary, and this is another factor that you will look in the sample size calculation, the majority of sample size calculators on line are based on a simple random sample,but you must to adapt your sample size to the sample selection design according to the population characteristics; on the references sited by Jim you will find this.

Best regards,

Federico