What do you do when you don’t have neat clusters and neat sampling frames printed out on a computer by a reliable government agency? The answer is to place your trust in randomness and create maximally heterogeneous clusters from which to take a random sample.

Draw or get a map of the area you are studying. Place 100 numbered dots around the edge of the map. Try to space the numbers equidistant from one another, but don’t worry if they are not. Select a pair of numbers at random and draw a line between them. Now select another pair of numbers (be sure to replace the first pair before selecting the second) and draw a line between them. In the unlikely event that you choose the same pair twice, simply choose a third pair. Keep doing this, replacing the numbers each time. After you’ve drawn about 50 lines, you can begin sampling.

Notice that the lines drawn across the map in figure 5.1 create a lot of wildly uneven spaces. Because you don’t know the distribution of population density in the area you are studying, this technique maximizes the chance that you will properly survey the popula-

FIGURE 5.1.

Creating maximally heterogeneous sampling clusters in the field.

tion, more or less PPS. By creating a series of (essentially) random chunks of different sizes, you distribute the error you might introduce by not knowing the density, and that distribution lowers the possible error.

Number the uneven spaces created by the lines and choose some of them at random. Go to those spaces, number the households, and select an appropriate number at random. Remember, you want to have the same number of households from each made-up geographic cluster, no matter what its size. If you are doing 400 interviews, you would select 20 geographic chunks and do 20 interviews or behavioral observations in each.

My colleagues and I used this method in 1986 to find out how many people in Mexico City knew someone who died in that city’s monster earthquake the year before (Bernard et al. 1989). Instead of selecting households, though, my interview team went to each geographic chunk we’d selected and stopped the first 10 people they ran into on the street at each point. This is called a street-intercept survey (box 5.3).

BOX 5.3

STREET- AND M A L L -1 N T E R C E P T SAMPLING

K. W. Miller et al. (1997) sampled blocks of streets in a city and did a street- intercept survey of African American men. They compared the results to a random-digit dialing telephone survey in the same city. The street-intercept survey did a better job of representing the population than did the telephone survey. For one thing, the response rate for the street intercept survey was over 80%. Compare that to the typical telephone survey, where half or more of the respondents may refuse to be interviewed. Also, with telephone surveys, the socioeconomic profile of respondents is generally higher than in the population (partly because more affluent people agree more often to be interviewed on the telephone). A variant of this method is mall-intercept sampling, used widely in marketing (Further Reading: street and mall intercept surveys).

Handwerker (1993) used a map-sampling method in his study of sexual behavior on Barbados. In his variation of map sampling, you generate 10 random numbers between 0 and 360 (the degrees on a compass). Next, put a dot in the center of a map that you will use for the sampling exercise, and use a protractor to identify the 10 randomly chosen compass points. You then draw lines from the dot in the center of the map through all 10 points to the edge of the map and interview people (or observe houses, or whatever) along those lines. (See Duranleau [1999] for an empirical test of the power of map sampling.)

If you use this technique, you may want to establish a sampling interval (like every fifth case, beginning with the third case). If you finish interviewing along the lines and don’t have enough cases, you can take another random start, with the same or a different interval and start again. Be careful of periodicity, though (box 5.4).

Camilla Harshbarger (1995) used another variation of map sampling in her study of farmers in North West Province, Cameroon (1995). To create a sample of 400 farmers, she took a map of a rural community and drew 100 dots around the perimeter. She used a random number table to select 50 pairs of dots and drew lines between them. She numbered the points created by the crossing of lines, and chose 80 of those points at

BOX 5.4

COMBINING MAP SAMPLING AND CLUSTER SAMPLING

In chapter 4, I mentioned a study in which Lambros Comitas and I compared Greeks who had returned from what was then West Germany as labor migrants with Greeks who had never left their country (Bernard and Comitas 1978). There were no lists of returned migrants, but we thought we could do a cluster sample by locating the children of returned migrants in the Athens schools and then use the children to select a sample of their parents.

The problem was, we couldn't even get a list of schools in Athens. So we took a map of the city and divided it into small bits by laying a grid over it. Then we took a random sample of the bits and sent interviewers to find the school nearest each bit selected. The interviewers asked the principal of each school to identify the children of returned labor migrants. (It was easy for the principal to do, by the way. The principal said that all the returned migrant children spoke Greek with a German accent.) That way, we were able to make up two lists for each school: one of children who had been abroad, and one of children who had not. By sampling children randomly from those lists at each school, we were able to select a representative sample of parents.

random. Then, Harshbarger and her field assistants interviewed one farmer in each of the five compounds they found closest to each of the 80 selected dots. (If you use this dot technique, remember to include the points along the edges of the map in your sample or you’ll miss households on those edges.)

There are times when a random, representative sample is out of the question. After Harshbarger did those interviews with 400 randomly selected farmers in North West Province, Cameroon, she set out to interview Fulani cattle herders in the same area. Here’s what Harshbarger wrote about her experience in trying to interview the herders:

It was rainy season in Wum and the roads were a nightmare. The grazers lived very far out of town and quite honestly, my research assistants were not willing to trek to the compounds because it would have taken too much time and we would never have finished the job. I consulted X and he agreed to call selected people to designated school houses on certain days. We each took a room and administered the survey with each individual grazer.

Not everyone who was called came for the interview, so we ended up taking who we could get. Therefore, the Wum grazer sample was not representative and initially that was extremely difficult for me to accept. Our team had just finished the 400-farmer survey of Wum that was representative, and after all that work it hit me hard that the grazer survey would not be. To get a representative sample, I would have needed a four- wheel drive vehicle, a driver, and more money to pay research assistants for a lengthy stay in the field. Eventually, I forgave myself for the imperfection. (personal communication)

The lessons here are clear: (1) If you are ever in Harshbarger’s situation, you, too, can forgive yourself for having a nonrepresentative sample. (2) Even then, like Harshbarger, you should feel badly about it (Further Reading: space sampling).