Dear Alysson

Let me name to the teachers of your initial list, (Alysson Population). Your objective population was not this but the population of Professors of Physic in Brasil. May be many professors of your objective population that were lacking in your list, but most of the professors of your list are members of the objective population. Your statistic inference is limited to Alysson Population but you may extrapolate the inference (substantive inference) to the objective population, if you can show that the reasons that explain the lack of some professors in Alysson Population are not related to the questions under study and if there are not other geographical obvious limitations in your list that are limiting this inference. For example if in your list, you have not teachers from the north of Brasil, it would be better to adjust your substantive inference to the south of Brasil.

You did a SRS of your list and selected 7000/3 teachers but some teachers were not members of the objective population, then you can adjust the size of your list with the proportion of answer that were not members. You could consider Alysson Population as formed by two subpopulations: The subpopulation of collaborative teachers that if contacted would respond at first, and the subpopulation of non collaborative, your sample would be a SRS from the first subpopulation, you should try to contact in person, by email, or phone a subsample of that noncollaborative subpopulation because they may be very different of that of the other subpopulation. After doing this you can use an stratified estimator of the parameters of the Alysson Population.

Dear Alysson

Let me name to the teachers of your initial list, (Alysson Population). Your objective population was not this but the population of Professors of Physic in Brasil. May be many professors of your objective population that were lacking in your list, but most of the professors of your list are members of the objective population. Your statistic inference is limited to Alysson Population but you may extrapolate the inference (substantive inference) to the objective population, if you can show that the reasons that explain the lack of some professors in Alysson Population are not related to the questions under study and if there are not other geographical obvious limitations in your list that are limiting this inference. For example if in your list, you have not teachers from the north of Brasil, it would be better to adjust your substantive inference to the south of Brasil.

You did a SRS of your list and selected 7000/3 teachers but some teachers were not members of the objective population, then you can adjust the size of your list with the proportion of answer that were not members. You could consider Alysson Population as formed by two subpopulations: The subpopulation of collaborative teachers that if contacted would respond at first, and the subpopulation of non collaborative, your sample would be a SRS from the first subpopulation, you should try to contact in person, by email, or phone a subsample of that noncollaborative subpopulation because they may be very different of that of the other subpopulation. After doing this you can use an stratified estimator of the parameters of the Alysson Population.

you may consider a non-response calibration if you have some information on your 7000 teachers (totals of men/women, age structure, ...). You will result in weights for each observation.

ypou can choose cluster sampling which do not require any sampling frame. First decide how many teachers you want to include. One area or city or zone will work as cluster for you. Select the cluster by SRS then covered the complete cluster. By this method your sample will be representative one.

Alysson, from your story, I see that your possible population actually started with the 7000. On the basis of your judgment, you invited a quota of 33 percent (judgmental, quota are not probability samples). It turned out later that even the 2310 were not all qualified to be part of the intended population. Hence, even the 2310 are not appropriate as a representative sample from the onset.. Your size of 300 is statistically appropriate at a margin of error of 5.39 percent, a proportion of 0.5 and a confidence level of 95.44 percent on the basis of a population of 2310 (assuming that you assume it to be your population).

As to whether your 300 are simply randomly selected, let us go back to the definition and ask this question- in the selection of the 300, were all the members of the population (assuming the 2,310 as the sampling frame) given an equal chance to be selected? Ed

Dear Aggarwal

The Cluster Sampling Design requires a frame of clusters. In this example he would need a list of all the cities or zones in Brasil where there are teachers of Physic.

From the random sample of clusters, you could cover completely each cluster if you can obtain a list of all its teachers, but may be that some teachers were lacking in the list of his/her cluster, and that although they were there, they were unavailable as here.

Also it may be that the set of cities do not cover all the Objective Population.

You may read this as reference

https://www.researchgate.net/publication/260082130_R_D_Management_in_State_Universities_and_Colleges_in_the_Philippines_Sampling_in_Business_and_Management_Research?ev=prf_pub

Data R& D Management in State Universities and Colleges in the Ph...

Or you may use these quick solutions

https://www.researchgate.net/publication/262564897_Easy-to-use_Sampling_Formulae?ev=prf_pub

Data Easy-to-use Sampling Formulae

Thank you all!! I did what you suggested Guillermo Enrique Ramos, now I have just to organize and compare tha data. Thank you a lot.