If you take a good sample of participants from the Shikarpur district, then you can generalize the results to the universe of participants belonging to that district. If you would want to make generalizations to the universe of students from the Sindh Province as a whole, your would have to sample the 250 colleges. 

Let's assume your study is focused just on the Shikarpur district. You have 4 colleges, with N1, N2, N3 and N4 participants (let's say N is the sum of them all). Then, if you take a sample of "n" participants, you can take a sample of n x (N1/N) .individuals from college 1, n x (N2/N) individuals from college 2 and so on.  You can also stratify the participants using one o more criteria. . 

From the quantitative side it all depends what your target of inference is. Are you interested in the college as a setting or is it  a convenience in the design that may become a nuisance in the analysis?

https://www.researchgate.net/publication/256802442_Multilevel_approaches_to_modelling_contexuality_from_nuisance_to_substance_in_the_analysis_of_voting_behaviour

If you are interested in how colleges differ then you would only have a sample of 4 if you only survey 4 colleges. That would be very small if you are interested in the effect of say college ethos or spending on pupil attainment. So you would increase the number of colleges and reduce the number in each but I understand that there are cost and time implications of doing this.

For general orientation on this - see

http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#datadesign

You can use the following software to do the power calculations

http://www.bristol.ac.uk/cmm/software/mlpowsim/

and

Optimal Design for Longitudinal and Multilevel Research Documentation for the “Optimal Design” Software

http://www.stat.cmu.edu/~brian/463/week14/od/od-manual-20111016-v300.pdf

http://sitemaker.umich.edu/group-based/optimal_design_software

From my perspective it would be unethical not to undertake a study with sufficient power  as you would asking people to take part in something that would be doomed to not being able to detect effects.

Of course qualitative often have small n - the samples then should be theoretically representative - some of the issues are considered here

http://berkeleyroundtable.weebly.com/uploads/2/1/9/9/21997192/seawright_multi-method_book_chap_1.pdf

Article Multilevel approaches to modelling contexuality: from nuisan...

What kind of mixed methods design you are planing (sequential/concurrent/multi-phase) as this will have implications on the purpose of the quantitative study. I agree with Kelvyn that your research context suggests some kind of multi-level approach where the number of colleges (2nd level) should be much larger than the number of students you sample in each college (1st level). I used HLM in my PhD and from memory the number of level 2 units should be > 50 but the number of nested level 1 respondents could be lower than 20 see: Maas, C. J. M., & Hox, J. J. (2005). Sufficient Sample Sizes for Multilevel Modeling. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 1(3), 86-92.

Hope that helps. 

Like Matthew I am unclear where your mixed methods design comes in here. There is a lot of literature on the need to develop a thorough framework for conducting mixed methods research to ensure quality and integration in mixed methods research. I have cited some of these references in my work on mixing methods, so maybe have a look at the reference list. https://www.researchgate.net/publication/258172849_Integrating_Mixed_Method_Data_in_Psychological_Research_Combining_Q_Methodology_and_Questionnaires_in_a_Study_Investigating_Cultural_and_Psychological_Influences_on_Adolescent_Sexual_Behavior

Article Integrating Mixed Method Data in Psychological Research Comb...

Dear All,

I am grateful to your response on the question or problems faced by me. I am Planning cluster sampling for the sake of convenience and access. However, the number of respondents may be increased because each college enrolls more than one thousand students.   

Dear Anke and Matthew,

I am designing a mixed methods research design in which qualitative and quantitative research strategies will be used. However, I have designed two surveys for the students and teachers to investigate the problems of reading discourse and teaching reading discourse. I have also designed classroom observation sheets to have a deeper understanding of the issue in real phenomenon. I hope you understand the matter and guide me how to plan sampling for my research. 

I am wondering if you need to think about the type of MMR that you would like to do - sequential or concurrent seem the obvious ones to me - and how the two different types of data will be integrated to 'add more than the sum of the two' types of research methods. The two design forms that spring to mind are concurrent - collecting both quant and qual data together to see how these provide a holistic story of teaching English, or sequential - collect quant, do cluster analysis and then select classrooms for each cluster to see what is happening in depth. For both of these you need to be very clear from the design stage how you will integrate quant and qual and to what end - what does MMR add in contrast to single-method studies. Hope this is useful.

Sheeraz

again from the quantitative side and in relation to what you have now written in terms of further explanation - there is a need to consider a further level -  the classroom . So that students (at level 1) are seen as nested in classes (at level 2) and colleges (at level 3). There may be further complexities if the class is taught by more than one teacher. The class or teacher is a 'cluster' and the population is clustered and not just the sample - there is a social process going on - students learn in a class and this produces a dependency.

This paper is a classic example of how to study styles of  teaching and how this impacts on student achievement - the issue is that students in the same classroom tend to be alike and to be taught by the same method and you have to take this dependency into account in the analysis  -it considers teachers/classes and pupils (not colleges)

 Murray Aitkin, Dorothy Anderson and John Hinde (1981) Statistical Modelling of Data on Teaching Styles Journal of the Royal Statistical Society. Series A (General)

Vol. 144, No. 4 (1981), pp. 419-461,  DOI: 10.2307/2981826

Dear Anke and Kelyn,

I am happy for seeking such a professional guidance on my work. I would go through the literature on Mixed Method Approach to get a clear and fair idea about it.

Hi Shiraz

to the best of my knowledge.

cluster sampling would be a good method only if you feel that there would be significant demographic or psychograhic difference between the cluster areas which can be variables that can affect your DV . other wise just take university register as a sample frame and go with randon sampling.

Hello Sheeraz

If the students are your target respondents, then you can cluster the intermediate colleges into four clusters (if you target all the four hotels). You can then employ proportionate sampling to have a representative sample and may be follow it up with stratified sampling depending on what strata you want to use.

A good example of proportionate sampling is demonstrated by José Eduardo Jorge above

Thank you George. I appreciate your cooperation.

Regards

I see several themes running through this discussion. One is the possibility of doing hierarchical linear analysis (HLM) to see how factors at the higher levels are related to those at the school or classroom level. But if your main interest is to get a representative sample, then you may not need to get into the complexity of HLM.

Another question is the relationship between MMR and the kind of sampling that you do. In that regard, I agree with others that it would help to specify your overall design. If part of that design is a quantitative study that should be able to stand on its own (rather than simply supplementing a major qualitative study), then there would indeed be advantages to having a representative sample, and cluster sampling would be an efficient way to achieve that.

Note, however, that if you are asking about whether to do cluster sampling to select your observation sites, I think that involves a different set of issues. In particular, unless you do observations at a large number of sites, your estimates will have high standard errors, regardless of the sampling technique you use. This issue was also raised early under the heading of "statistical power." So, it is one thing to do a survey that generates a substantial N for your analysis versus doing a smaller number of observations.

I will have another go at my point - even if you took a simple random sample and there was more than one pupil in the class this will be 'clustered' or potentially auto-correlated or dependent. Think of twins - it is an attribute of the thing you are studying as well as how you plan to collect your data.   This is because the POPULATION  has a structure with pupils at level 1 learning in classes at level 2. I can conceive that the type of instruction that they have had - your predictor  is a level 2 macro variable  while their individual attainment - the response - is a micro variable. You need situations where the macro variable varies/ differs if you are going to assess its effect.  

Typically in school effects studies about 10% of the variation lies at the school level - this (rho = the rate of homogeneity = ρ= 0.1) is a lot. If you collect data on 50 schools (J) and 25 pupils (nj) in each you might think you have 50 * 25 = 1250 effective degree of freedom but you do not - you have an effective degree of freedom of 368 - Kish's (1965) Design Effect would be 3.40 in this case 

ESS=  (J* nj)/DEF=(J* nj)/(1+ρ(nj  -1))

 So we cam anticipate quite a large reduction in how many bits of independent information that you have.

If rho is 0.25 and you collect data on 50 pupils in 25 schools your effective sample size is not 1250 but 94 - so this can be a big issue in terms of power for detecting effects. 

Firstly, in the quantitative facet, you must consider the convenient Effect Size on reading skills. Then for determining sample size you can use Table M in the classical Shavelson’ s book (Statistical reasoning for the behavioral sciences, pp. 693-3, in 1988 edition), or the Power Analysis module in STATISTICA software package.

If you read Spanish, in:

Fernández Cano. A. y Fernández Guerrero, I. Mª (2009). Crítica y alternativas a la significación estadística en el contraste de hipótesis. Colección Cuadernos de Estadística, nº 37. Madrid: Arco Libros-La Muralla. ISBN: 978-84-7133-786-3.