In probability sampling, every member of the population has a known probability of selection to be in the sample.Although more difficult to execute than nonprob- ability sampling, it has the benefit of allowing the researcher to generalize the results obtained to the population of interest.
Drawing a sample from a population requires devising some type of sampling frame, which allows the researcher to identify and sample members of the popula- tion.Sometimes an obvious sampling frame exists: if the population is students enrolled at a particular school, a list of all enrolled students could serve as the sampling frame.Other times a less optimal sampling frame must be used: for instance, a telephone directory or block of phone numbers in use may be employed for a survey carried out by telephone.A problem with either frame is that people without phone service are not included in the population from which the sample is drawn, although they may be included in the population of interest. Weighting and other procedures can be used during analysis to make results from the study sample more applicable to the population of interest.
The most basic type of probability sampling issimple random sampling(SRS).In SRS all samples of a given size have an equal probability of being selected. Suppose you wanted to draw a random sample of 50 students attending a partic- ular school.You obtain a list of the students and select 50 at random from the list, using a random number table or random number generator.Because the list represents an enumeration of the entire population and the choice of who to include in the sample is completely random, every student has an equal proba- bility of being selected for the sample, as does every combination of students up to the size of the sample.
In most cases, SRS has the most desirable statistical properties of any kind of sampling, including the smallest confidence intervals around parameter esti- mates, and requires the least complex procedures to analyze.However, SRS is impossible or prohibitively expensive to execute in some contexts, so other methods of probability sampling have been developed to deal with situations where SRS is not possible or practical.
Systematic samplingis very similar to SRS.To draw a systematic sample, you need
a list or other enumeration of your population.You then choose a start number between 1 andnat random, and include in that sample thenth object and every nth object following,nbeing chosen to produce the sample size desired.Suppose you want to draw a random sample of 100 objects from a population of 1,000. The steps to draw a systematic sample are:
1. Setn = 10, because 1000/100 = 10.
2. Choose a number at random between 1 and 10.
3. Select the object with that number, and every 10th object thereafter.
If the number chosen at random was 7, your sample would include the 7th, 17th, 27th, and so on, up to the 997th object.
Systematic sampling technique is particularly useful when the population accrues over time and there is no predetermined list of objects.For instance, if you want to survey people who will be making court appearances in the upcoming year, at the start of the study you will not know who those people will be.So you could make an estimate ofnbased on the court caseload in the previous year, keep an ordered list of people making court appearances, and then survey every nth person who appears in court.If you determine thatnis 14, you would then survey the 14th person, 28th person, 42nd person, and so on.
One caution when using systematic sampling is that you must ensure that the data is not cyclic in a way that corresponds withn.For instance, if particular hours or days in court were reserved for particular types of cases, and your choice of n meant that people whose court dates were scheduled for those times had no possi- bility of being selected, then your sample would not be random.
There are many types ofcomplex random samples, an umbrella term for proba- bility sampling methods that impose one or more layers of complexity beyond that of SRS.In a stratified sample, the population of interest is divided into nonoverlapping groups or strata based on common characteristics.For people, these characteristics might be gender or age, for cities they might be population size or type of government, for hospitals they might be type of organization or number of beds.If comparing different strata is a primary goal of the study, strati- fied sampling is a good choice because it can be designed to ensure adequate sampling from each strata of interest.For instance, using SRS might not produce sufficient elderly people to accurately compare their results with middle-aged people, while a stratified sample can be designed to oversample the elderly to ensure sufficient sample size, then correct statistically for the oversampling.
In acluster sample, the population is sampled making use of pre-existing groups.
This technique is often used in national surveys that require in-person interviews or the collection of physical specimens (e.g., blood samples), because it would be prohibitively expensive to send survey personnel to interview one person in Ruck- ersville, Virginia, one in Chadron, Nebraska, one in Barrow, Alaska, and so on.A more economical procedure is to create a sampling plan that incorporates several levels of random selection.On a national level, this could be executed by selecting geographic regions, then states within regions, cities within states, and so on down to individual households and individuals within households.Precision is decreased with cluster sampling because objects that are clustered within units (for instance, households within cites and cities within states) tend to be more similar than objects selected through SRS.Offsetting this loss of precision is the fact that the cost savings of cluster sampling are usually substantial, so a larger sample can be collected.