Chapter 5.
1. Distinguish between probability and non-probability sampling and discuss the advantages and disadvantages of each.
If you can not specify the probability that any given individual will be in the sample, you have a non-probability sample. Some combinations of individuals may be more likely to be selected than others. Some individuals may have absolutely no chance of being selected. Since you don?t know which members of the population have a chance to be included in your sample, you don?t know whether or not your sample accurately represents the population. You can?t generalize your results to the population. In fact, there is no way to tell which population (if any) a non-probability sample represents.
If you know the probability of being included in the sample for each and every member of the population, you have a probability sample. With probability samples you can make valid generalization to the population from which the samples are drawn. Probability samples are usually more representative (i.e. they have higher external validity) than non-probability samples because there is less bias. With probability samples you can estimate the accuracy of the sample; that is, you can estimate the level of confidence you can have that your sample statistics differ from the population parameters by no more than a given level of error. Because you can do this, you can generalize to the population from which the sample was drawn. You can't do this with non-probability sampling methods.
2. Discuss the main types of probability sampling methods and explain their strengths and weaknesses.
If you construct your sample by randomly choosing members of the population, you will have a simple random sample. In a simple random sample, all combinations of population members are equally likely. The simple random sample is the ideal against which all other probability samples must be judged. Its strengths include its simplicity, lack of bias, and relatively straightforward math. The main weakness of this method is that it requires that you have a list of all the members of the population and that you are able to get access to any members who may be chosen. Because there are many research situations in which such a list doesn?t exist or isn?t available— situations in which you thus can?t randomly select a sample from the population—systematic methods were developed.
If you are able to line up all members of your population and move down the line one member at a time, you can draw a systematic sample by taking every kth member (for example, every tenth member) of the population. If the first member selected is chosen randomly, your sample becomes a systematic sample with a random start, which, although much easier to do, is almost as valuable as a simple random sample. Although many combinations of members are not possible with this method, the characteristics of equal probability and, to an extent, independence, are still present, which means that these samples are essentially equivalent to simple random sampling. This method has two potential weakness. The first one is that it requires that there be a way to line up all members of the population so you can count them off and choose every kth one. This is not always possible. The second one is that the members of the population may be organized in some sort of cyclical or periodical fashion so that every, say, tenth member is different from the others in a systematic way.
If you divide your population into a number of strata (sub-populations), where each stratum is internally homogeneous with respect to the characteristic being studied, and you take a random sample from each stratum you have a stratified random sample. A stratified random sample will be more efficient than a simple random sample when the population can be divided into a small number of strata such that the strata differ from one another in terms of variables related to the issue being studied, and the members of any given stratum are relatively similar to one another in terms of these variables.
You will have a proportionate stratified sample if the sampling ratio is the same for all strata. This means that the sample you draw from a stratum that has more members should be larger than the sample you draw from a stratum that has fewer members. A proportionate random stratified sample is equivalent to a simple random sample, in terms of its ability to represent the population.
If the population is organized into groups or clusters of people, you may want to sample clusters of people instead of individuals. This is a cluster sample. You take either all the members of a given cluster or none of the members. You would choose clusters randomly; then take everyone in each chosen cluster. Cluster samples are less efficient than simple random samples or stratified random samples; there is more variability from sample to sample with cluster samples; and the math needed to do statistics with cluster samples is more complex than the math for simple random and systematic samples. Like disproportionate stratified samples, cluster samples are not likely to have equal probability.
3. Explain how to select a sample with each of the probability sampling methods.
This is answered in the answer to question 2.
4. List all the essential qualities of a simple random sample. (do not include non-essential qualities!)
This kind of sample has two essential characteristics: equal probability and independence.
1)Equal probability. All members of the sampling frame have an equal chance of being selected, which means that the probability that any particular person will be selected (pi) is the same as the probability that any other person will be selected (pj), and this probability is equal to the number of people in the sample (n) divided by the number of people in the sampling frame (N).
2)Independence. The fact that one member is selected has no effect on any other member's chance of being selected.
5. List all the essential qualities of a probability sample. (do not include non-essential qualities!)
A sample in which the probability of being included in the sample is known for each and every member of the population is a probability sample. This is the one feature that clearly distinguishes them from non-probability methods.
6. Under what conditions would you use systematic sampling with a random start instead of simple random sampling?
The main weakness of simple random sampling is that it requires that you have a list of all the members of the population and that you are able to get access to any members who may be chosen. Because there are many research situations in which such a list doesn?t exist or isn?t available — situations in which you thus can?t randomly select a sample from the population — systematic methods were developed. If you are able to line up all members of your population and move down the line one member at a time, you can draw a systematic sample by taking every kth member (for example, every tenth member) of the population.
7. What is stratified random sampling and under what conditions would you want to do it instead of simple random sampling?
Stratified random sampling is when you divide your population into a number of strata (sub-populations), where each stratum is internally homogeneous with respect to the characteristic being studied, and you take a random sample from each stratum. A stratified random sample will be more efficient than a simple random sample when the population can be divided into a small number of strata such that the strata differ from one another in terms of variables related to the issue being studied, and the members of any given stratum are relatively similar to one another in terms of these variables.
8. Why are non-probability samples not likely to be representative of the populations from which they were drawn?
With a non-probability sample, some combinations of individuals may be more likely to be selected than others. Some individuals may have absolutely no chance of being selected. Since you don?t know which members of the population have a chance to be included in your sample, you don?t know whether or not your sample accurately represents the population. You can?t generalize your results to the population. In fact, there is no way to tell which population (if any) a non-probability sample represents.
9. What factor(s) affect the efficiency of a sampling method?
The efficiency of a sample of a given size is a function of only one thing — the degree of heterogeneity or the variance of the population from which it is drawn. The size of the population generally doesn't matter. Cluster sampling is less efficient than simple random sampling because there is more variability between clusters of people than there is between individual people. Stratified random sampling is more efficient than simple random sampling because stratifying, when properly done, can produce subsets of the population that are more homogeneous than the population as a whole is.