There are several methods could be use to determine the sample size of the study:

1- Krejcie and Morgan table(Krejcie, R. V., & Morgan, D. W. (1970). Determining sample size for research activities. Educational and psychological measurement, 30(3), 607-610).

2- Range Rule of Thumb 30 to 500

3- Use previous studies results(mean and standard deviation)

4- Use raosoft website -http://www.raosoft.com/samplesize.html

So, u can either consider ur population or previous related studies to calculate ur sample size.

Best regards

Abdulrab

There is another way to calculate sample size:

Due to the fact that there is a total of "m" predictors in the survey (you have to define the number of predictors based on the purpose of your research and the elements assigned to the hypotheses); the ideal minimum sample size for this study will be calculated.  This number is computed using the formula from Green (1991) which states that the minimum sample is based on 50+8(m) where m is the number of predictors to be studied [for example, if the number of predictors is 23, then the minimum sample size is = 50+8(23) = 234].

Green, S. (1991). How many subjects does it take to do a regression analysis? Multivariate Behavioral Research, 26(3), 499-510.

Netra - 

The estimated variance of the prediction error, for continuois data, from econometrics, may be helpful for you, if you are looking at continuous data.  Note that for an individual case, the square root is STDI in SAS PROC REG. The first few pages of the paper at the first link below will show you the difference between this measure for an individual vs estimated total. 

If you are doing a survey to estimate totals for continuous data, and you want to estimate a needed sample size, you might - for that purpose - combine your predictors in some way, and see if the paper at the second link might possibly give you any ideas. 

Cheers - Jim 

Article Using Prediction-Oriented Software for Survey Estimation

Conference Paper Projected Variance for the Model-based Classical Ratio Estim...

I think I am not able to communicate my question correctly. I have mentioned that formula for calculating sample size is

n = z2 (sd)2 / E2

Let us assume hypothetically I have a big questionnaire for my survey research. Not necessarily I am using regression analysis. Further assume that I have collected data of five demographics such as age, income, gender, qualification, and profession. There are many research questions. Researcher need to find out answer to these questions.

Further assume I have collected data on 10 attribute of the cars/ vehicles and it is Likert scale data or interval scale data. I am keen to know differences in mean scores for which I need to test null hypotheses. I am also keen to go for factor analysis. I may also go for factorial experiment set up for collecting data.

My question is how I will calculate estimate for population variance to be used in the above formula.

(sd)2 in the above formula is population variance. One need an estimate of population variance to be used in the formula.

I thank you for answering the question.

Determining Sample Size: How to Ensure You Get the Correct Sample Size

How many responses do you really need? This simple question is a never-ending quandary for researchers. A larger sample can yield more accurate results — but excessive responses can be pricey.

Consequential research requires an understanding of the statistics that drive sample size decisions. A simple equation will help you put the migraine pills away and sample confidently.

Before you can calculate a sample size, you need to determine a few things about the target population and the sample you need:

Population Size — How many total people fit your demographic? For instance, if you want to know about mothers living in the US, your population size would be the total number of mothers living in the US. Don’t worry if you are unsure about this number. It is common for the population to be unknown or approximated.

Margin of Error (Confidence Interval) — No sample will be perfect, so you need to decide how much error to allow. The confidence interval determines how much higher or lower than the population mean you are willing to let your sample mean fall. If you’ve ever seen a political poll on the news, you’ve seen a confidence interval. It will look something like this: “68% of voters said yes to Proposition Z, with a margin of error of +/- 5%.”

Confidence Level — How confident do you want to be that the actual mean falls within your confidence interval? The most common confidence intervals are 90% confident, 95% confident, and 99% confident.

Standard of Deviation — How much variance do you expect in your responses? Since we haven’t actually administered our survey yet, the safe decision is to use .5 – this is the most forgiving number and ensures that your sample will be large enough.

Okay, now that we have these values defined, we can calculate our needed sample size.

Your confidence level corresponds to a Z-score. This is a constant value needed for this equation. Here are the z-scores for the most common confidence levels:

90% – Z Score = 1.645

95% – Z Score = 1.96

99% – Z Score = 2.576

If you choose a different confidence level, use this Z-score table* to find your score.

Next, plug in your Z-score, Standard of Deviation, and confidence interval into this equation:**

Necessary Sample Size = (Z-score)² * StdDev*(1-StdDev) / (margin of error)²

Here is how the math works assuming you chose a 95% confidence level, .5 standard deviation, and a margin of error (confidence interval) of +/- 5%.

((1.96)² x .5(.5)) / (.05)²

(3.8416 x .25) / .0025

.9604 / .0025

384.16

385 respondents are needed

http://www.qualtrics.com/blog/determining-sample-size/

"Standard of Deviation — How much variance do you expect in your responses? Since we haven’t actually administered our survey yet, the safe decision is to use .5 – this is the most forgiving number and ensures that your sample will be large enough."

If suppose I want to conduct a pilot survey to know the variance of the populations or I have conducted a pilot survey. I have data now on large number of variables. Which variable variance I will take as an estimate in the formula of sample size.

I thank you very much for your answer & look forward for more input.

Sample size from finite population can be estimate by :

n= N / ( 1+ N * e^2 ) 

and from infinite population by :

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 , Gpower )

I hope that be useful for you 

Netra -

The 0.5 'safe' value indicates to me that you are looking at yes/no questions. A pilot study could help if you want to have a better answer for What is an adequate sample size?  

If your questions can be ranked by importance, then I suggest you have a survey sample size large enough to answer any of your critical questions. 

More is not necessarily better with sample sizes, as you increase cost and may increase nonsampling error. 

I am still not certain that your actual questions are being addressed. Are they? 

Jim 

Dear Prof. Khalid Hasan

Thank you very much for your answer. I appreciate your time and concern for the topic. You have mentioned that estimate of variance could be as

S = standard deviation from previous studies or pilot  study

My question is

if i need to study 12 variables. Which variable S I will use as an estimate for variance of the population.

Regards

N P Singh

Dear Singh 

The key component to estimate sample size ( when we fixed the other ) is variance of the trait , when the study include many traits , we depend on the trait of higher variance which give us estimation sufficient sample size suitable for other traits.

Good luck 

Dear Professor Khalid Hassan

Thank you very much for your answer. May I know source of your statement which seems to be correct in my view also. But it may have an impact on cost of the survey. As it is clear from formula, higher the estimate of the variance higher the sample size.

With regards

I think one would say that the source of Khalid's statement on multiple variables is rather common sense common practice among statisticians doing surveys. Textbooks perhaps generally do not address this, but when one has to report for multiple questions on a survey, you have to at least have a large enough sample size to do well with your most important questions. I've advised that on ResearchGate before. However, the sigma you might get for any one of the variables/questions, say in a pilot study, may not hold up if you try to gather too large of a sample in the full study, which may not only be costly, but also increases nonsampling error, say measurement error, which inflates sigma. 

Sometimes, when collecting data for one question may or may not involve a respondent for which other questions are relevant, the situation gets even more complex, and has been treated as something of an operations research problem.  However, the flaw there is that because we are dealing with random variables, we cannot be so exact. For a related note on model-based sampling and estimation, see the letter at the link attached.

Note that these arguments primarily deal with continuous data, and I still do not think that the exact nature of your particular application has been made clear. 

.

PS -  Yes, the higher the sigma, the greater the variance (and measurement error can inflate this).  With multiple attributes/variables of interest/questions/items on a survey, if you make sure the most important questions are covered, if possible, then that may be rather straightforward with simple random or stratified random sampling, but more complex with probability proportionate to size (PPS) sampling, as you can not use but one measure of size. (Regression model-based estimation does not have that problem, as a different 'size' can be used for each variable in the estimation phase.) 

Article JOS Letter - Cutoff Sampling and Total Survey Error

There are some useful working papers published online by the US Federal Committee on Survey Methodology, such as the 2001 paper, listed first under "Survey Quality" found through the first link below, where on page 3-8, it states that "The principal difficulty with the computation and presentation of sampling error occurs because of the multipurpose nature of many federal surveys."  But this is just generally glossed over with the implication then that one just does the best that can be done, as implied above by Khalid. 

Cochran(1977), Sampling Techniques, has a nice chapter on sample size, and so do others, but as with Blair and Blair(2015), Applied Survey Sampling, where on page 111 they mention a "given sample characteristic" for "some variable," literature generally discusses one attribute at a time. 

http://fcsm.sites.usa.gov/reports/policy-wp/

But you can't know the variance until you've done the sampling. A better approach is to draw a power curve, which will give the correct sample size. But n = 30 usually works! :-)

Dear Professor Andrew Paul Mckenzie Pegman,

I request you to provide some reference of power curve used for the purpose. It will help me in understanding the process of drawing power curve and finding optimal sample size.

Regards

N P Singh

Most work with  minimum of n=30

The power of any test of statistical significance will be affected by four main parameters:

The effect size

The sample size (N)

The alpha significance criterion (α)

The statistical power, or the chosen or implied beta (β)

All four parameters are mathematically related. If you know any three of them you can figure out the fourth.

Let's say we want to know the minimum sample size required to give us a reasonable chance (e.g. 0.80) of detecting an effect of certain size given a conventional level of alpha (0.05). You can then look up a power table  to find out.

I hope this helps :-)

Thank for your kind reply

I will revert back to you

Regards

N P Singh

Dear DR. Agevi Humphrey

I am looking for scientific justification.

Regards

N P Singh

The number of samples depends on the nature of the subject. Whenever certainly have been many more had it well.

Whether you use a confidence interval or power of a test, the key is to estimate standard error from standard deviation and sample size (perhaps by stratum).  To estimate standard deviation, if you have no other information for "guessing," you could try a pilot study ... even if just a few data points.  

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

Dear RG colleague,

Determining the sample sizes involve resource and statistical issues. Usually, researchers regard 100 participants as the minimum sample size when the population is large. However, In most studies the sample size is determined effectively by two factors: (1) the nature of data analysis proposed and (2) estimated response rate.

For example, if you plan to use a linear regression a sample size of 50+ 8K is required, where K is the number of predictors. Some researchers believes it is desirable to have at least 10 respondents for each item being tested in a factor analysis, Further, up to 300 responses is not unusual for Likert scale development according to other researchers.

Another method of calculating the required sample size is using the Power and Sample size program (www.power-analysis.com).

Regards,

There are several methods could be use to determine the sample size of the study:

1- Krejcie and Morgan table(Krejcie, R. V., & Morgan, D. W. (1970). Determining sample size for research activities. Educational and psychological measurement, 30(3), 607-610).

2- Range Rule of Thumb 30 to 500

3- Use previous studies results(mean and standard deviation)

4- Use raosoft website -http://www.raosoft.com/samplesize.html

So, u can either consider ur population or previous related studies to calculate ur sample size.

Best regards

Abdulrab

I feel you are looking for selection of sample size based on an estimate of a population size, tolerable error and confidence level. If yes then here is the answer that works very well:

https://www.surveymonkey.com/mp/sample-size-calculator/

It does not need SD.

Derivation:

https://onlinecourses.science.psu.edu/stat414/node/264/

Netra Pal Singh ji pl check and revert.