Mirghani -

If by 'pilot study' you mean an exploratory study to see what it is that you might want to learn, then the sample size needed would be very subjective. As Eddie noted, cost would be a consideration, so you would need to avoid using too much of your resources on such a probe, but some effort spent here could be very important to a more useful result later. Once you know what items (variables of interest) for which you want to collect data, the kind of pilot study needed at that stage is to estimate the inherent variance in a given category or stratum. Those variance estimates - noted by Eddie - are important information needed to plan your final study well.

Your sampling and estimation methodology should be either (1) randomized (design-based), or (2) model-assisted design-based (better, as it uses correlated 'auxiliary' data, already available on the population, to improve results of your randomized sample), or else (3) model-based (regression-based) estimation could be used without randomized sampling, but then good stratification can be very important, and you must have regressor data on the entire population (say administrative data, or a related census).

I'll assume you are doing a random sample, the first of the three major headings above, and that for every data category you want to publish, there will be either a simple random sample, or a stratified random sample. It would be best to find a copy of a survey sampling book. One very good older book that might be more easily found, which has a great deal of very good information packed into a small book, is Cochran, W.G.(1977), Sampling Techniques, 3rd ed., John Wiley & Sons. In there, in chapters 4 and 5, I think you will find what you need. Section 4.4 tells you about simple random sample needs for proportions, and 4.6 is for continuous data. Sections 5.10, 5.11, and 5.12 are for stratified random sampling for proportions, and 5.5, 5.6, and 5.7 are for continuous data.

Cochran mentions four ways of obtaining estimates of inherent data variance (such as your pilot study, or repeated similar surveys, as in the official statistics on which I expended a great deal of effort) in a section on that topic. These are the "guesses" needed on page 77, in Cochran, for example. (I did something similar for model-based estimation in the paper at the attached link, but as I said, I think you are probably using strictly design-based sampling. It does demonstrate the need for the same kind of information, but I think you need a primarily design-based methods book, like Cochran.)

Stratification will help lower sample size needs, but do not confuse the strata for separate samples you would need, if you want to publish at that lower level of aggregation.

If you strain your resources in your final study, and try to collect a final sample size that is too large, or requires too much of your participants either, you will likely encounter more nonsampling error, such as measurement error (lower data quality), which will invalidate the sample size estimates (from 'formulae') you have made from your pilot study. This is because those variances you had estimated will now be larger. So you need to only collect what you can collect well, which may reduce the scope of your final results. (You might want to do an Internet search on "total survey error.")

There are several good survey sampling (and estimation) statistics books available. A more recent one that is very well written (but expensive, i think) is Lohr, S.L.(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.

Cochran should cover what you likely need to know, including what is mentioned above and more.

Cheers - Jim 

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

Dear Mohamed,

As such there is no formula for pilot study. A rule of thumb (practice) is max 5% of your sample size is pilot tested.

regards

Logistically, the determinant of a sample size is cost.

Technically, the factors determining sample size are: population size (if population is known), margin of error, confidence level and assumptions on variance (for formulae estimating population mean) and proportion (for formulae estimating population proportion).

It will not matter if you have a pilot study, or the “real” study, same factors will apply and the technical factors they are population size, margin of error, confidence level, and the assumptions you make.

For easy-to-use sampling formulae try

https://www.researchgate.net/publication/262564897_Easy-to-use_Sampling_Formulae

Data Easy-to-use Sampling Formulae

Mirghani -

If by 'pilot study' you mean an exploratory study to see what it is that you might want to learn, then the sample size needed would be very subjective. As Eddie noted, cost would be a consideration, so you would need to avoid using too much of your resources on such a probe, but some effort spent here could be very important to a more useful result later. Once you know what items (variables of interest) for which you want to collect data, the kind of pilot study needed at that stage is to estimate the inherent variance in a given category or stratum. Those variance estimates - noted by Eddie - are important information needed to plan your final study well.

Your sampling and estimation methodology should be either (1) randomized (design-based), or (2) model-assisted design-based (better, as it uses correlated 'auxiliary' data, already available on the population, to improve results of your randomized sample), or else (3) model-based (regression-based) estimation could be used without randomized sampling, but then good stratification can be very important, and you must have regressor data on the entire population (say administrative data, or a related census).

I'll assume you are doing a random sample, the first of the three major headings above, and that for every data category you want to publish, there will be either a simple random sample, or a stratified random sample. It would be best to find a copy of a survey sampling book. One very good older book that might be more easily found, which has a great deal of very good information packed into a small book, is Cochran, W.G.(1977), Sampling Techniques, 3rd ed., John Wiley & Sons. In there, in chapters 4 and 5, I think you will find what you need. Section 4.4 tells you about simple random sample needs for proportions, and 4.6 is for continuous data. Sections 5.10, 5.11, and 5.12 are for stratified random sampling for proportions, and 5.5, 5.6, and 5.7 are for continuous data.

Cochran mentions four ways of obtaining estimates of inherent data variance (such as your pilot study, or repeated similar surveys, as in the official statistics on which I expended a great deal of effort) in a section on that topic. These are the "guesses" needed on page 77, in Cochran, for example. (I did something similar for model-based estimation in the paper at the attached link, but as I said, I think you are probably using strictly design-based sampling. It does demonstrate the need for the same kind of information, but I think you need a primarily design-based methods book, like Cochran.)

Stratification will help lower sample size needs, but do not confuse the strata for separate samples you would need, if you want to publish at that lower level of aggregation.

If you strain your resources in your final study, and try to collect a final sample size that is too large, or requires too much of your participants either, you will likely encounter more nonsampling error, such as measurement error (lower data quality), which will invalidate the sample size estimates (from 'formulae') you have made from your pilot study. This is because those variances you had estimated will now be larger. So you need to only collect what you can collect well, which may reduce the scope of your final results. (You might want to do an Internet search on "total survey error.")

There are several good survey sampling (and estimation) statistics books available. A more recent one that is very well written (but expensive, i think) is Lohr, S.L.(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.

Cochran should cover what you likely need to know, including what is mentioned above and more.

Cheers - Jim 

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

There is no formula for Pilot Study sample size. Use about 10 (Rule of Thumb) - also be clear what pilot study is for - I quote: "A pilot study, pilot project or pilot experiment is a small scale preliminary study conducted in order to evaluate feasibility, time, cost, adverse events, and effect size in an attempt to predict an appropriate sample size and improve upon the study design prior to performance of a full-scale research project.

Pilot experiment - Wikipedia, the free encyclopedia

en.wikipedia.org/wiki/Pilot_experiment"

It depends what you want to achieve, and what level of detail you have in mind.

Essentially you need about 25-30 responses pe unit of interest (called "cell"), e.g. if you want a pilot study to look at the possible differences between men and women and youths vs others you need a sample that has min 25 men, 25 women, 25 youths and 25 other age groups. This is called quota sampling and is used frequently in market research.

There is no need to waste your potential pool of respondents by setting the pilot size as a fixed percentage of it. Also, issues of nonresponse, margin of error, confidence level need to be considered.

What Adrian is proffering is not for a pilot study. Adrian's advice is for doing the actual final survey exploratory, explanatory, etc. If you use the definition of Pilot Study as written in my previous post, then you don't need that many respondents. For actual survey for which you need a representative sample check the posts from Eddie and James.

Sometimes it is easy to gather 20 items samples. Othertimes it would be hard to get more than 8 items, like in medicine, so in these cases it would be enough for a preliminar study, warning that the risk of error is higher. But the purpose of a preliminar study is not to get a precise answer, it is to gain a sense of the main question. Ok, emilio

@ Josh, 

Not sure about the language used (proferring?), and it is not for an actual study, but for an informative pilot study that will give meaningful information about the actual study. Otherwise how can one expect to "predict an appropriate sample size and improve upon the study design prior to performance of a full-scale research project¨?

By the way, this also complies with your definition so why not check what you understand by ¨evaluate feasibility, time, cost, adverse events, and effect size ¨?

And next time please be more civil in replying to posts that you disagree with!

Adrian - Emilio has proffered a practical answer to Mirghani's question.

I demand that you retract your last statement.

OK, looks like there is some confusion about this word. Retraction and apologies are in order, but  "proffer" is most frequently used together with "insults", at least in Continental Europe, hence my reaction.