If you have no knowledge about the population, then a random sample is at least statistically "safe" to -statistically- represent the population.

If you do know some things about the population (e.g. male/female ratio, age distribution, etc.) then you should use this knowledge to get a better sample. The technique is called "stratification" ("take stratified samples"). You will find a lot about that in the internet and in stats books.

For a random sample of this small size, the standard error would be quite large (even after allowing for a finite population correction), but if you don't have any way of drawing a systematic sample, then that is probably your best bet.

If you do have information on the characteristics of your larger population, then the favored approach in qualitative research is purposive (or purposeful sampling). The best known typology of purposeful sampling is from Michael Patton's book on Qualitative Evaluation, and I have attached a summary from the 3rd edition.

Jan -

Stratified random sampling is a more efficient way to sample overall.  (That is, you can obtain a lower overall variance, i.e., aggregate level variance, for the same overall total sample size.)  But keep in mind that if you want to actually infer for each of the strata, you will find that you are really doing a simple random sample by category.  This is not really what is meant by "stratified random sampling," a technique often used for continuous data, and perhaps yes/no data.  Sample allocation schemes to improve overall results can leave some such categories with too little data to estimate well enough for that category.  Keeping that in mind, however, if you are interested in stratification for improvement at the most aggregate level, there are many sampling books which cover such stratified random sampling, for quantitative purposes. 

Here are a few good sampling book examples:

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

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

Lohr, S.L(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.

There are many others, but those represent a great classic, a simpler and less expensive new book, and a well-written, in-depth, fairly new book, respectively. 

If you have auxiliary (actually regressor) data, say perhaps in your case some administrative data, correlated with your population of interest, you can make vast improvements with model-assisted design-based methods.  See the following:

Särndal, CE, Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlang.  

I imagine that the strata you may consider may also be categories that you want to publish separately.  In that case, the estimated standard errors for each such 'stratum,' or 'category' really, will need to be considered carefully, and you might shift the category sample sizes around a little. 

[Later added note:  Categorical administrative data, such as sex of patient, can be used to determine the part of N =  500 in each category.] 

Your sample actually sounds more like a pilot study, as the sample design assumes you know something about the inherent variances, sigma.  You can use information here to do a better sample in the future, if needed.  You can even use information you learn at any point to poststratify, but the more you plan ahead, the better.

Because you want to use a small sample, I assume that resources (including timeframe) for your project are tight.  If you try to increase your sample size, you may incur more nonsampling error, such as measurement error, which may have the affect of inflating your estimate of sigma(s).  If you can sample more for a category where needed without straining resources too much, that might be helpful.

Right now, you might consider using your small sample resources by doing a simple random sample, and considering it a pilot study, if your estimated standard errors turn out to be unsatisfactory (too large).   If you really want to know data at a lower level, you can break into categories, but you will more likely need more data. 

Note that the estimated means or totals, whatever, and their estimated standard errors, are not only overall and/or by category, but also for each variable of interest.  Some variables will need larger samples than others to be estimated well.  If sample size needs are large enough to cause nonsampling error issues, there may be some information that may not be reasonably estimable without special efforts, or even at all.

Best wishes - Jim  

For quantitative purposes for continuous data, purposive sampling can be used if you have regressor data, and can separate data into groups for modeling purposes. 

Here, using the link below, are examples of looking at one modeling group and category at a time, to determine sample size needs.  It is written with skewed data, an establishment survey, in mind, but works the same way in your case, except your x would be administrative data on all 500 cases (well, the part of the 500 within a given modeling group) in the population. 

 https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements

........

However, you could just do a simple random sample first, and see what kind of estimated standard error results you obtain, for each variable of interest.  This is especially true as I do not know what kind of data you are collecting, but I am still assuming that you are collecting some kind of numerical data.

Standard errors, bias, sampling and nonsampling errors are all important considerations for quantitative data, and one should generally at least estimate standard errors.  For continuous data (my expertise), and yes/no data, it is essential. 

....

Even if you are only collecting qualitative data, you are more likely to obtain more 'representative' results if you sample from each of the different categories.  So that would be like stratified random sampling, as Jochen noted, as you could think of it as a way for your qualitative data to be more representative overall.  

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

1. The most valid sample is the most representative of the population (which retains the same parameters of interest), but this analysis is only possible knowing the frame census.

2. If you limit the sample to restricted conditions, you would change the frame of your population, and the inference would not be correct for the original frame. Random sample is better.

I am surprised by the number of people who are recommending random sampling on general principles, without considering the associated size of the standard errors for using this technique with such a small sample.

I ran the numbers, and a sample of 15 from a population of 500 gives a confidence interval of 25% for a 95% confidence level on a 50-50 split in the population. In other words, if the population percentage is 50%, then the sample estimate would be between 25% and 75%.

I personally would consider such a poor estimate to be not worth the effort, and would instead concentrate on knowing more about some particularly interesting subset of the original population.

David -

A "50-50 split?"  Are you talking about proportions?  Perhaps that is appropriate.  I'm sure I generally think in terms of continuous data, which may not be appropriate.

Jim 

Most sample calculators use a 50% proportion for the estimating because it is the highest variance for a two-category variable. That is much simpler than trying to devise an equivalent set of parameters for a continuous variable. (FYI that is the basis for the confidence estimates you see when polls are reported in the media.)

Yes, but assuming p = q = 0.5 is generally going to overestimate sample size needs, even for proportions, but I get your point. 

 -  For a poll, for estimating sample size needs, p = 0.5 would generally make sense.  If one expected it to be much different from that, you'd hardly need a poll. 

There are many good suggestions but the choice of sample units and the sample size depends on many things.

The most important questions here are (because you already said that you have determined the sample size):

What is the aim of the survey?

Are you going to repeat the same survey to see effects before and after the treatment?

What is expected response rate?

Is there a real need to stratify the population according to sex or age (or something similar)?

Maybe you could even give a brief questionnaire to each patient and invite them to the interview?

Ok, there are more questions which came to my mind, but I think that you have to determine what's your aim and what you want to inspect (do you inspect some rare event?).

A lots of answers already added and may be the purpose already been served. However, I have a simple thinking on this issue. If there is no periodic variation in your outcome to be measured systematic sampling would be the best to represent the population.

It's depending on the aim of the survey. However 15-18 units are enough to apply statistical tests basad on normality of the distribution. It's better to have almost 25 patients. If you want to compare patients with different ages, you have to consider a block "age" and, within each age class, carry out a random sample.

Use te SYSTAT or MYSTAT statistical software. Using the BOOTSTRAP tehnique. This is a good instrument for design of experiment.......

Even randomly picking 15 or 18 cases for analysis may face serious limitations. For example, you would need to convince your "audience" that these 500 are representative. 

the question is what do you looking for on the patient? Any way if you have a list I suggest to use simple random sampling because it gives good, and easy, inferential properties

Jan - 

By the way, by the very nature of a "small sample" (relative to what would be large for your application and purposes), one would not expect a short confidence interval using three standard errors (even less so for standard deviations in general).  One would expect to live with less accuracy, such as one or two standard errors.  If this does not meet your needs, then more data collection would be required, if it can be done reliably. 

Cheers - Jim 

PS - This is for quantitative data, but qualitative data should not just be purely anecdotal in the sense that if the sample is too small to obtain somewhat reasonable quantitative data, I would be wary of qualitative data as well. 

Adding to James post scriptum:

Qualitative (ordinal or nominal scaled) data can alsways be quantititatvely analyzed by their relative frequencies and proportions (so inference aimes at the "probability to observe the respective values/categories", leading to odds ratios and all that). It is possible and useful to consider the precision of such estimates (frequencies, proportions, odds, odds ratios). These precisions also depend on the sample size, but they also depend on the mean (expected value), and the common normal-approximations can severely fail for small samples (one should better use the appropriate models [binomial or multinomial] to assess the precision of estimates.