How to draw a sample

Most of the methods described in this manual arc qualitative, that is, they describe without necessarily quantifying observations. There might be times, however, when more quantitative data is required. Maybe you suspect that your observations, if systematically recorded and analyzed, will reveal patterns or associations which are not obvious without special testing. This involves the use of statistical analysis, a subject outside the scope of this manual; there are plenty of good books on the subject as well as powerful and easy-to-use computer applications.

In short, statistical tests allow you to draw informative conclusions about very large groups of people, things, or occurrences by observing a small representative sample of these people, things, or occurrences. Since this manual is about collecting information, it is worthwhile knowing what constitutes a representative sample.

Imagine that the population you are studying is a pot of stew with all sorts of vegetables, beans, and meat. Taking a spoonful from the top might lead one to believe that the stew is thin. A spoonful scraped from the bottom of the pot might suggest an especially hearty stew. To learn the true nature of a stew, you must fires stir, then sample. In terms of your population under study, this means you will need information which adequately represents the diversity of the population. It does not mean you have to stir people in a big pot! But it does mean you have to know something about the population before you start.

1 Determine Your Population. What do you want to study? In what area? For instance, you might decide to study the indigenous cropping practices in the Western Highlands in your country. Your population might therefore be crop raisers in that region.

2 Decide on the unit of study. Are you interested in individuals, couples, households, families, organizations, or villager? In plants, animals, herds, fields, farms, or watersheds? (For the crop variety study, the unit of study might be households—though you need to determine who in the household—male or female, old or young—you should interview.)

3 Determine Your unit of measure. For the study on crop varieties, this could be the yield per hectare (or the local unit of area) of each variety. It is likely that you'll be interested in other unite of measure, too. For instance, you might also want to measure the number of varieties grown, the level of organic and inorganic fertilizer used, the time of planting and harvesting, the number of days labor put into a unit area, and other characteristics.

4 Work out how large the sample size will have to be. The sample must be big enough, otherwise your data, no matter how carefully collected, and your statistical analysis, no matter how skillfully
performed, will be useless.

The minimum sample size depends on several things:

- How much time and money do you have?

- How big is the population that you want to generalize?

- How much variability is there in the population?

- How many subgroups do you want to split the population into during your analysis?

- How confident do you want to be that your findings are correct? (This is measured by the confidence level: a confidence level of 90% means that you can be 90% confident that the true value of a mean will be reasonably accurate. Gee a statistics book for details.)

The following table shows the minimum sample sizes required for various population sizes with a 90% confidence levels.

Note that these are minimum numbers required. If-you divide the sample into subgroups for analysis, or if you need a higher level of confidence, you will need to sample more than this. For a 95% confidence level, you need to sample about four times the number n shown in the table. In general, for populations of more than 5000, a sample size of about 100 is enough for most simple statistical analyses at 90% level of confidence (400 for 95% confidence level). You should not use samples of less than about 30 for statistical analysis.

Note
Draw a bigger sample than you need

It is usually a good ides to draw a bigger sample than you actually need (say, 15 to 20% larger than you need). You need to do this because some people may not be in when you visit, may refuse to answer your questions, or give responses that you decide you cannot trues. If you start off with a bigger sample than you need for the statistical analytic, you can always replace these people with the extra respondents.

In many instances, you might be tempted to go to the house next door if someone is not at home when you visit for an interview. You can do this as long as you are consistent. Beware of introducing bias—for instance, by interviewing a disproportionate number of elderly people, since these are the ones who arc at home when you call.

5 Make a list of all members of me population. This is your sampling frame. You can make such a list in several ways:

- Ask local people to make such a list. Make sure that they include "invisibles" such as low-caste families or landless people.

- Develop the list through one of the other techniques described in this manual, such as Mapping or Sorting and ranking.

- Obtain a list from local authorities. Possibilities include the village leader, local land records, lists of school children (from the local school), patients (from the clinic), or cooperative members (from the coop). Beware: these lists might be biased to one section of the community. But they can be a good basis on which to build a more complete list with the help of local people.

Making a reasonably complete list can be very difficult, especially for large populations. If you cannot do 50, don't worry; you can use other methods of sampling (described below).

6 Draw the sample to study. You can use one of the techniques described below.

Drawing lots

1 Write all the names of the people (households, farms) in your sampling frame on small pieces of paper.

2 Fold the papers uniformly, put them in a big pot and mix them well. (For a stratified sample [see below], put the names for each subgroup in a different pot).

3 Then reach in the pot, without looking at the names, and pull out at random the number of pieces of paper (n) you need.

4 It is a good idea to pull out extra pieces of paper (extra households) to serve as substitutes in case some households have moved or cannot be located or contacted after several attempts. After two or three follow-upe without success, you can use the substitutions. These should also be chosen randomly.

Cards

This method can be used for drawing samples where there are less than 52 (the number in a deck of carafe) individuals in the sampling frame.

1 On a piece of paper, list the names of all individuals in your sampling frame.

2 Number the list (1, 2, 3, etc.).

3 Shuffle a deck of ordinary playing carafe. and draw out n cards at random from the deck.

4 Write down the figures that correspond to the carafe you have drawn, according to the following table.

Cards

5 Select the names from the list that correspond to the numbers you have written down.

Calculator

Some calculators can generate random numbers at the push of a button. These numbers arc typically a decimal between 0 and 1. To use the numbers generated, you can either:

- Multiply each number by the number in the population, plus 1. For instance, if there are 500 people in the population, multiply each of the random numbers generated by 501. (The extra 1 is necessary to make sure that the 500th individual also has a chance of being selected, since the random numbers generated range from 0.000 to 0.999, not 1.000).

- Alternatively, you can ignore the decimal point in the random numbers, and ignore any numbers that are higher than the total of your population.

Random number table

1 Make a list of all individuals in your sampling frame.

2 Number the fat (1, 2, 3, etc.).

3 Decide how many individuals you need to sample. This is your sample size, n.

4 In the table of random numbers on page 35, locate a starting point by closing your eyes and pointing with a pencil to any position on the page.

5 Starting at the number you have just chosen, read downward vertically and choose the next n numbers in the column. If you need fewer than 100 individuals, take the first two digits in the column (or the middle two, or the last two: it doesn't matter, as long as you're consistent). When you get to the bottom of the column, go to the top of the next column.

6 Select the names from the list that correspond to the numbers you nave chosen from the table.

Systematic random sample

This method is easier than random sampling if your list contains a large number of individuals (say, more than 500).

1 Obtain a fiat of all individuals in your sampling frame. Count how many there are (say, there are 15,000 people).

2 Decide how many individuals you want to sample (say, you want to sample 200 people).

3 Divide the number of individuals by the number in the sample (i.e., 15,000/200 = 75). This is the sampling interval.

4 Select one individual from the list at random as a starting point.

5 Select every subsequent 75th person (or whatever your sampling interval is) from the list.

If you cannot get a list of the members of the population

You can still generate a sample that will be approximately random. Here are some suggestions.

Using a map

1 Obtain a map of the area (or ask local people to make one—see Mapping)

2 Select locations at random from the map. For instance, you can draw a grid of squares over the map, number the squares, and select squares at random using one of the techniques described in this section. You can then go to the locations chosen and select the nearest house (field, farm) to the chosen location.

Random route

1 Select a location at random.

2 Identify further addresses (fields, farms) by taking alternate left and righthand turns at road junctions and calling at every nth address (field, farm, etc.) en route. (The number n depends on the sampling interval, see above under Systematic random sample.) Alternate between the right and left sides of your path.

Using a transect

1 Identify a series of transects at random (possibly using a map, ace above).

2 Walk along each transect and select every nth house (field, farm). Alternate between the right and left sides of your path.

Cluster sampling

Perhaps you want to interview a sample of people who live in villages scattered over a large area. There is no list of all the people in the area, and it would be impossible to make one. This is where cluster sampling can help.

1 Make a list of all the villages in the area (these are the "clusters").

2 Decide how many villages you can afford to visit (this may depend on money or time available). In general, select as many as possible.

3 Select this number of villages at random.

4 Within the villages you have selected, choose people at random using one of the other methods described in this section.

5 It may be necessary to draw a multistage cluster sample in some instances. For instance, you could select several districts at random, then choose villages at random within the districts, and choose people at random within each village.

Snowball sampling

Snowball sampling does not produce a sample that can be analyzed using standard statistical tools. But it is a useful way of identifying hard-to-find individuals. See Identifying indigenous specialists for a description of how to use this sampling method.

Stratification

Your population might contain an important subpopulation that might be underrepresented in a simple random sample. For instance, you might be interested in the indigenous knowledge of large landowners compared to smaller-scale farmers But if there are only 20 large landowners with more than 2 hectares of land and 5000 Small farmers with leas than 2 hectares, you would need to sample a very large number of people at random in order to be reasonably sure of interviewing enough large landowners.

The answer to this problem is called stratification. You first divide the population into subsets, or strata. You can get local people to help you do this (ace Identifying indigenous specialists and Sorting and ranking). Then randomly select individuals from within each subset. for instance, you might select 100 households with less than two hectares and all 20 of those with more than two hectares.

Compiled by Ricky G. Anunciacion, David Abbess and Paul Mundy Sources: Krejcie and Morgan, 1970, (Bernard, 1988, Babbie 1986

Table of random numbers

This table contains 1000 4-digit random numbers. See How to draw a sample for how to use the table to select a sample at random.

Table of random numbers