This happens very frequently in social or consumer research. Your sample is still valid (but if the numbers you report are the true ones it is very very small). In principle to secure representativity of your stratified sample you should weight the sample you obtained back to the original dimension of the strata. In this way you will have the right percentages by gender and still can use all the responses. Hope this helps.

Your stratified sampling would not be random probabilistic because they have responsed a part of the drawn sample initially of size n = 40. But if it is probabilistic the selection and the n = 25 people respond, you could use stratified sampling with fixed allocation n1 = 10 and n2 = 15. This would not be proportional allocation, but it could be used too.

In your case, having sample szies large enough will be more important than implementing stratified sampling. Use all data.

Muhammad -

If you have data missing at random, then I agree with Massimo that you can reweight your survey weights, but it seems like a lot of nonresponse. If you had more data, you might be able to look for response propensity groups for the weighting if you had other characteristics to use, but your sample size seems rather thin.

Your sample size should be determined by the standard errors you obtain, and with such n/N ratios, you best look into the finite population correction factors. 

Stratification is often done to obtain a lower overall variance, but if you want to publish numbers by stratum, that is a different story.

You could look into a book such as Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons. 

I assume you are looking at continuous data, or at proportions. If not, you still need to be concerned if the cases are not missing at random. You could check into any characteristics that seem to be over or under represented in your sample, based upon what you know about the populatuin, and at least make note of it in your findings.

If you have auxiliary (regressor) data for the population, you might try something here:

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

Or for each stratum, with regressor data, I have something on sample size on my ResearchGate page, but it is really for skewed establishment surveys.

Best wishes - Jim

As per your statement, for the sample size of 40, there should have been 24 males and 16 females while your sample has 10 males and 15 females. This means all the non-responses are from the side of males and it is around 57% which is very high. Considering the data is like compromising with the sample size. In case of non-response, it is always argued that non-responders very often behave differently from those who have responded. If you are sure that non-responders are not different from responders in males with respect to important characteristics  than probably using the weights would be appropriate not otherwise. How to ensure that non-responders are comparable with that of responders, to do so you may take few important characteristics like age and some other variables and compare. In case you are not able to do so, the sample size should be taken as inadequate and analysed data should be interpreted with caution. 

Dear Muhammad, 

I hope you find this document useful

Dear Muhammad,

"Särndal, CE, Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlang" is a very good reference for sampling. I recommand it.

Sample selection: Case 1 or 2?

1. you selected 40 from 100 persons (i.e. simple random sample selection)

2. you selected 24 from 60 men and 16 from 40 women (i.e, stratified sample selection.)

In both cases: the probability of selection is 40/100=24/60=16/40=0.4 for all 40 selected persons. Therefore, the sample weigths are all: 1/0.4=2.5. The difference is that case 2 has a better control of the gender variable.

After data collection you will apply an overall correction for nonresponse or a poststratification (correction different between men and women). You'll obtain the final weights (larger than 2.5). Look at Särndal et al , or other reference, for the detailed procedure. In any case, you'll have to work with weights in your analysis if you have different weights for men and women.

Best wishes

Dear Mr. Imran Khan,

I suggest you PPS (Probability Proportion to size) sampling to conduct the sample for this case.

Best Wishes 

You would have a 41% response rate among the women and a 93% response rate among the women.  This is a very large difference in response rates so you would need to look at why there was this difference in response rates to determine whether it is non-random.  For instance, if calls were made during the work day in an area where most men work and most woman do not, you would have a non-random effect.  At a minimum you would need to caution the reader of your report that there was differential response rates and any results should be looked at with great caution.

However, as Raid said your sample sizes are too small for analysis.

Replacement is part of random sampling. But for a 100 population size in a survey, census is a better option than a sample survey. With complete enumeration you will not have to contend with inferential analysis issues.

You have lot of suggestion, almost all seems to be good. If the situation as specified by Ramnath Takiar, I have one more suggestion: you may draw a boot strap sampling among male to make your 40 size sample and then you may try to draw some conclusion based on this  last information. If the ten male observation is not random then I think you have to rethink about your experiment.

In social sciences, more than 40% response rate is acceptable.

Hope attached one is helpful.

Article Refined Stratified Sampling for efficient Monte Carlo based ...