If I understand correctly the approach you used in selecting your sample of universities, it does not fall in either stratified or cluster sampling. Rather, as you mentioned, it is convenience sampling. 

In both stratified and cluster sampling, the presence of "random" selection is required. For example, in stratified random sampling, you need to divide your target population into some strata (based on your 'stratification variable', e.g., age, education, income etc.). These strata can be of same size or different size, which is another issue. Afterwards, you have to choose some strata (depending on your sampling plan) RANDOMLY from all strata and then select the respondents RANDOMLY from each of your selected stratum.

Same fundamental approach is used for cluster sampling, but the clusters are usually divided on the basis of geographical coverage. That's why this technique is also known as "area sampling". There are some differences between the characteristics of clusters and strata, but the key issue to be maintained is RANDOM selection.

Elahe -

What kind of data are you looking to collect: continuous, yes/no (proportions), likert scale, qualitative?  I am not familiar with the latter two, and mostly familiar with the first, continuous data, but if you are doing anything quantitative where you can estimate standard errors, you should do so.  If you compare simple random sampling to cluster (randomized) sampling and to stratified random sampling, you would find that stratified random sampling is more efficient than simple random sampling, but cluster sampling is less efficient. Here a design is more efficient if lower variance is obtained with the same overall sample size, or you could say that it takes a smaller sample size to reach a standard error goal.  Leslie Kish made popular the study of 'design effect,' where you generally see how much better you can do than a simple random sample. The reason for cluster sampling is that it may be very helpful for handling logistical issues.  The reason for randomization techniques is to improve chances of having a sample which is 'representative' of the population, and also, variance estimation based on randomization can be done.  That is very important.  Regression modeling can also lead to such results, making a big improvement where applicable, but i doubt that it would apply to your case.  -  If you are doing a qualitative study, then I suppose that you still want to use randomization of selection techniques to collect data hopefully 'representative' of the population. 

But it sounds like you are looking at two universities which may be compared to each other, though they may not be very 'representative' of other universities. It also sounds like you have divided the population of each university into four strata (the four strata sounding very much like they make up a contingency table).  Further, these four strata may also need to be reported separately.  If they do not, then you can be more efficient by looking only at the overall variance, assuming quantitative data, and not worrying if any individual stratum might yield low enough standard errors for every variable. That is what is considered when you look at optimal allocation of your sample by methods found in statistics books. If you need to publish for each group, that is not really stratification. You are just publishing for each category.  Regardless, variances differ by variable of interest (question on a survey), and category, and equal sample allocation is not generally very efficient. But if you do not have an estimate of how variable the data are, by variable and stratum or category, then a small pilot study with equal allocation might be needed to start. A pilot study could help you with this and to test your survey instrument.  It could be a good learning experience before the actual survey. 

So it sounds like you have a convenience sample of two universities, which can be compared to each other,  but may not be close to the way other universities would behave.  And you have the population for each university stratified or categorized into four parts which collectively make up all of each university. And then within each stratum/category/group, you probably are taking what amounts to a simple random sample of that group. At least that is what it seemed to me that you are doing.  I may have misread you, however.

I suggest that you consult a sampling book such as one of the following:

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 these three represent a range of types,  except for modeling, and also I am thinking of continuous data, or even estimating proportions, but if you need likert scales or qualitative data, perhaps others can give you some references.

I hope that at least some of this relates to your question and is helpful.

Cheers - Jim 

PS -  It sounds like what you are doing is very much different from cluster sampling. An example of cluster sampling could be that if you wanted to look at information about buildings, and you needed to send people to the buildings to collect data, it may be logistically more feasible to divide your population into city blocks (thus in this example, clusters of buildings), and select blocks at random.  You would then either census the buildings in each selected city block, or do a second stage random sample within each randomly chosen block.  Both stages could basically in themselves be simple random samples, or perhaps it might make sense in this example to make the first stage selection a PPS (probability proportional to size) selection if blocks are known to be of different 'sizes' (perhaps population or some other measure). 

At any rate, it does not sound like you are doing a cluster sample. 

I agree with Khan and James. We don't clearly understand your research objectives, so it is diffcult to give you detailed suggestion. But anyway, it is necessary to read a book about sampling technique, then you can understand the basci concepts of stratified random sampling and cluster sampling, and know the difference between the two sampling techniques.

It sounds like you are looking at two universities which may be compared to each other. It also sounds like you have divided the population of each university into four groups and selected randomly almost equal number of samples, which may also be compared to each other. If your target population is a university, then the four groups are defined as four strata, and the effective samples selected from each stratum should be proportional to the stratum size, not almost equal to each other. This is a stratified random sampling.

Hope it is helpful to you

Good luck.

Dear Wei, James and Khan

Thanks for your answers. In fact I dont intend to compare universities, I want to compare a dependent variable (which is self efficacy) in four groups of students who are different in university major (EFL and Non-EFL) and level (undergraduate and post graduate) to see whose self efficacy is higher. I have selected the two universities based on convenient sampling, though the students in the two were selected randomly for the four groups, The four groups are somehow equal in number whereas the two universities are quite different in the number of students they have. I want to know this, now that the participants in the four groups (which i think are four strata) are not proportionately comparable with the two universities (but are randomly selected) can the sampling be called stratified random sampling or not. 

I remember having read somewhere that it can be stratified random even though the strata size is not proportionally comparable with the population bcz the participants in the strata are randomly selected. Is this true?

This is like stratified random sampling but actually not, as I noted above, if you really want to compare the four categories. You can get descriptive statistics on each of these categories, for each university.

You may not have wanted to compare universities, but that is all you can do.  You can see if your descriptive statistics vary much between them and only speculate about the others.

So you can compare results by category and university, but beyond that, as just noted, it is more speculative. 

PS -  How do you measure "self efficacy?"  Is this a continuous variable?  It does not sound like it.  You did mention it was a dependent variable.  Does that mean that there independent variables so that regression models can be compared? 

PSS -  The sample sizes in conjunction with innate variance (sigma-square) are part of what determines accuracy. If two categories have equal sample sizes, then the one with higher sigma is generally less accurately measured.  But there is no rule about sample sizes being equal or not.  The relevant concept is accuracy.  Variance is not all there is to it though. Bias can be a concern.  Also measurement error can sometimes be a huge concern, and though a larger sample size tends to lower sampling error, it can also increase nonsampling error. 

Elahe -

One other thing of note:  It was not clear to me, but it sounds like perhaps part of your question has to do with cases where two groups (categories) have different finite population sizes, say N_sub_1, and N_sub_2, that are very diferent, but the respective sample sizes, n_sub_1, and n_sub_2, are about the same. As I indicated above, if all else were considered even (sigmas, bias, nonsampling errors), then the case where n/N is largest would yield the more accurate results. This difference for finite populations is made even greater in cases where you consider a finite population correction (fpc) factor: 

 https://www.researchgate.net/publication/262970761_FINITE_POPULATION_CORRECTION_%28fpc%29_FACTOR

Cheers - Jim 

Article FINITE POPULATION CORRECTION (fpc) FACTOR

Dear Elahe,

Now it is bit clear what you've done regarding your sampling. My comment is just about your sampling, NOT on what you are measuring.

In my understanding, you used both convenience sampling and stratified sampling. In your report, you need to explicitly mention that you've chosen the universities using convenience sampling and you've selected the respondents using stratified sampling. You should also clarify that you stratified your population in terms of "major" (EFL and Non-EFL) and "level" (undergrad and postgrad). Technically, these are called stratification variables.

YES, stratified sampling can be proportionate and disproportionate. This is explained on page#350 on the following reference:

• Malhotra, N. K. (2008). Marketing research: An applied orientation, 5/e. Pearson Education India.

Hope this helps.

Because the first stage was a convenience sample, you cannot call this cluster sampling. (Even if it was that the two universities were randomly sampled so that the estimators from cluster sampling would apply, a drawing at that level of n=2 would not be very stable).  You need randomization for inference ( unless you are using regression modeling).  This is not cluster sampling because the convenience part means the estimators do not apply, variance in particular. Also, you are looking for more than one result.  You want results by category. So it isn't exactly stratified random sampling either, though that is much closer to what you did.  You can consider it stratified random sampling for overall results for each university examined, but I think your point is actually to compare categories  ("strata" here).  Cluster sampling is even further removed from your goals.  

Thanks dear Khan

This source was exactly what i needed. 

Best 

Dear Ellahe,

In stratified sampling, all the non overlapping subgroups(strata) making up the population of interest are individually sampled , studied and results obtained,  combined using appropriate weights. In cluster sampling however, only the subgroups(clusters), selected by random sampling are studied. If all the elements in the selected clusters are studied, we have single stage, otherwise we have multi stage.

Since the selection of Universities is not through Probability sampling procedure, cluster sampling is out, so your work may be seen as a comparative study of results from the two  selected Universities if the four groups(4 strata) exhaust the University Community (population of interest).You can have equal selection from each stratum, ie (nh=n / L) , remember that proportional allocation is (nh = nNh/ N)

Yes, it could be taken the equal assignation nh = n/L, being L the number of strata. The proportional assignation, nh = nNh/N (h = 1, 2, ..., L), gives a better performance than simple random sampling with replacement of the same total sample size n. If Nh = N/L = constant, both sampling assignations are the same.

The equal size assignation, mentioned by Mariano, usually produce test with more power for performing Test of Hypothesis on the parameters of the different strata, but for the estimation of the Population parameters usually is better the proportional assignation.

Elahe -

In my first response I asked what kind of data you have.  Assuming you have appropriate quantitative data, you could estimate proportional and also cost optimum allocation between strata, but you need to have variance estimates by strata.  That is important information for you anyway.  Thus it is another reason that a pilot study may often be useful.

There are a number of survey statistics textbooks which include the proportional allocation technique, and other useful information.

For stratified random sampling, you could see Chapter 5 and 5a in Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons.

Also, Chapter 5 in

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

covers stratified random sampling.

Both of those books also cover cluster (random) sampling.

An insightful and well written book, but perhaps harder to borrow as it may be expensive, would be the following:

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

Of the books above, the least expensive, and perhaps more elementary would be Blair and Blair.

Of course, these are my opinions from my experience, and there are many other sampling textbooks.

Best wishes - Jim 

Hello

The difference between stratified sampling and cluster sampling is as follows:

stratified sampling has to be sampled from all floors, but cluster sampling does not need to be sampled from all floors

If we are interested in knowing how many samples are taken from each strata , there is a discussion of allocations