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I realized a large research with Brazilian physics high-school teachers and I wanted that my sample could be representative of the Brazilian physics high-school teachers population. However, nobody in Brazil knows how many teachers there are, in which cities they are or who they are to provide contact.

So, during one year, I contacted teachers, schools, universities, governmental secretaries, labor unions, and event organizers and I reached more than 7000 names of possible teachers.

To build my sample, knowing that a lot of them wouldn’t not answer the survey, I invited 33% of this 7000 names to participate of the research. I chose randomly this 33%, but I can’t contact many of them and others didn’t fit with my population (they are no more teachers, they teach only in Universities and so on). In the end of one year trying to contact this 33%, I got about 300 valid responses.

But now, with all data collected, I’m not sure if my sample could be considered a simple random sampling (SRS) and how I can modify and fix my results to extend them to all population if my sample is not a SRS (or another previously known sampling method). Someone could help me?

Thank you, Alysson Ramos Artuso

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  • $\begingroup$ Of the six sources for names that you mention - Individual teachers - schools - universities - gov secretaries - labor unions - event organizers • How many of the original 7,000 names came from each? • How many of the 33% sample of names (~2,333) came from each • How many of the final 300? $\endgroup$ – Steve Samuels Apr 27 '14 at 16:19
  • $\begingroup$ Focusing on High schools • How many high schools did you contact? How did you select them? Did they include private as well as public schools? In what way, if any, would you consider them representative of high schools which might teach physics? • How many schools provided any information? Of these, how many had physics programs? $\endgroup$ – Steve Samuels Apr 27 '14 at 16:28
  • $\begingroup$ Hello, Steve. Thank you for your help! Let’s me explain better some points. We don’t have an educational census, so nobody knows how many high-schools or teachers there are. My contact with individual teachers, schools, universities and so on (‘the sources’) was a tried to estimate how many physics high-school teachers are in Brazil and how I can contact them (every high-school has physics, it is a mandatory discipline). $\endgroup$ – Alysson Artuso May 2 '14 at 19:13
  • $\begingroup$ I didn’t count or separate how many ‘sources’ a contacted or how many names which of them provide to me. I just contacted as many as I could. In this contact, I just pretend to have a better estimative of how many physics high-school teachers I could consider as my population (About 1,000? About 50,000? I estimate the answer is about 10,000) and how I can contact them. These teachers are in private and public schools. I got about 7,000 names. $\endgroup$ – Alysson Artuso May 2 '14 at 19:14
  • $\begingroup$ Considering these 7,000 as my population, I send a survey for 2,500 approximately, choosing randomly this 2,500. 343 teachers answered the survey and I’m considering that this is my sample (n = 343). In this sample, 57% teachers teach in public schools, 29% in private and 14% in both - these numbers are probably close to real. 73% are male teachers and 27% are female teachers, but I have no parameter to know if this is close to real or not. $\endgroup$ – Alysson Artuso May 2 '14 at 19:15
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Alysson's sample can't be considered a random population sample, because the list of names doesn't qualify as a valid sampling frame. The best that Alysson can do, I think, is to state that he had a diverse study group, but that he cannot say that it is a random sample.

Any applied sampling text will tell you that the design of a sample starts with one (or more) sampling frames. You can think of a frame as a list of "slots", or "listings". Each "slot" contains none, one, or more of the target population. A random number selects from among the eligible slots. In an ideal frame would be in a 1-1 correspondence of slots with member, but this rarely occurs.

For example, slots may contain no members of the target population. Some slots might reference units who are not members of the population. Duplicate listings are also a problem, because then the frame over-represents the multiply-listed units.

Since random numbers draw frame units, the probability of selection is known for every selected unit. This is the hallmark of a "probability sample", also known as a "representative" or "scientific" sample.

In Arturo's case, the ideal frame would be a list of all high school physics teachers. Such a list doesn't exist. Therefore In its place, he gives a list of names collected from different sources. This list might contain all the physics teachers, but there's no way of telling.

I make a stab, knowing little about Brazil, about how a professional sampler there might design the study. In place of trying to construct a frame of names, the sampler would employ a multi-stage design. The country would be stratified into regions and into principal cities. In each stratum, smaller geographical units, primary sampling units, or "PSUs" , would be listed (this is the initial frame) and a sample of these would be selected with probability proportional population size. Within each PSU, even smaller geographic units (second stage sampling units SSUs) might be listed (another frame!), and a sample of these selected. Finally, an effort would be made to locate every high school in each SSU (another frame) and all, or a sample of physics teachers would be contacted. An effort would be made to interview a sample, or all, teachers in the selected school. Though three-or-four stages of sampling might be necessary, the probabilities of selection would be known at every stage. I would guess that 20-40 PSUs would be sufficient to cover the entire county, with maybe 100 high schools. If recruitment is successful, the sample would yield at least 100 physics teachers.

The main feature of the multistage design is that there is no attempt to list all the physics teachers in the country or all the high schools in the country or even in a PSU. Even if little is known about the population, a valid representative sample can still be drawn. There are examples in the classic book "Sampling Design in Business Research by WE Deming (Wiley, 1960). The virtue of studying a smaller number of high schools is that resources and time be concentrated on achieving contact and gaining cooperation of respondents.

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