1. Sampling and Randomness
Chapter 8
Sampling and Randomness

2. Sampling, Random Sampling, and Representativeness
Two definitions of random sampling:
1.Random sampling is that method of drawing a portion (or sample) of a population or universe so that each member of the population or universe has an equal chance of being selected.
2.The method of drawing samples from a population such that every possible sample of a particular size has an equal chance of being selected is called random sampling, and the resulting samples are random samples.
The first definition, then, is a special case of the second general definition—the special case in which n=1.

3. Sampling, Random Sampling, and Representativeness
Sampling without replacement
Sampling with replacement
A representative sample means that the sample has approximately the characteristics of the population relevant to the research in question.
The characteristics typical of a population are those that are the most frequent and therefore most likely to be present in any particular random sample.

4. Randomness
Randomness means that there is no known law, capable of being expressed in language that correctly describes or explains events and their outcomes.
In different words, when events are random we cannot predict them individually. However, we can predict them quite successfully in the aggregate.

5. Randomization Randomization means random assignment.
While some people believe that random assignment removes variation, in reality it only distributes it.
Individuals with varying characteristics are spread approximately equally among the treatments so that variables, have “equal” effects in the different treatments.

6. Randomization
The principle of randomization may be stated as the following. Since, in random procedures, every member of a population has an equal chance of being selected, members with certain distinguishing characteristics—male or female, high or low intelligence, conservative or liberal, and so on—will, if selected, probably be offset in the long run by the selection of the characteristics.
We say that subjects are assigned at random to experimental groups, and that experimental treatments are assigned at random to groups.

7. Sample Size
Whenever a mean, a percentage, or other statistic is calculated from a sample, a population value is being estimated. A question that must be asked is: How much error is likely to occur in statistics calculated from samples of differing sizes?
Figure 8.1
Table 8.5, 8.6
Statistics calculated from large samples are more accurate (other things being equal) than those calculated from small samples.

8. Kinds of Samples
Probability samples use some form of random sampling in one or more of their stages.
Nonprobability samples do not use random sampling. Their weakness can to some extent be mitigated by using knowledge, expertise, and care in selecting samples, and by replicating studies with different samples.

9. Nonprobability sampling
Quota sampling: The knowledge of the strata of the population—sex, race, region, and so on—is used to select sample members that are representative, “typical,” and suitable for certain research purpose. But quota sampling is difficult to accomplish because it requires accurate information on the proportions for each quota, and such information is rarely available.

10. Nonprobability sampling
Purposive sampling: purposive sampling is characterized by the use of judgment and a deliberate effort to obtain representative samples by including presumably typical areas or groups in the sample.
Accidental sampling: one takes available sample at hand

11. Probability sampling
Stratified sampling: the population is first divided into strata. Then random samples are drawn from each strata. This design is recommended when the population is composed of sets of dissimilar groups. Stratified random sampling is often accomplished through proportional allocation procedures (PAP).

12. Probability sampling
Cluster sampling: A cluster can be defined as a group of things of the same kind. In cluster sampling, the universe is partitioned into clusters. Then the clusters are sampled randomly. Each element in the chosen clusters is then measured.
Cluster sampling is most effective if a large number of smaller size clusters are used.

13. Probability sampling
Two-stage cluster sampling: we begin with a cluster sampling as described above. Then, instead of measuring every element of the clusters chosen at random, we select a random sample of the elements and measure those elements.

14. Probability sampling
Systematic sampling: This method assumes that the universe or population consists of elements that are ordered in some way. If the population consists of N elements and we want to choose a sample of size n, we first need to form the ratio N/n. This ratio is rounded to a whole number, k, and then used as the sampling interval. Here the first sample element is randomly chosen from numbers 1 through k and subsequent elements are chosen at every kth interval.
The representativeness of the sample chosen in this fashion is dependent upon the ordering of the N elements of the population.