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Population Parameter vs. Sample Statistic

Anger is a stronger motivator than happiness, in my experience. In contrast, it would be rather surprising if the large differences between Hite's results and those of the other surveys were due to dishonest responses to the other surveys. Only 4, of the over , women who were sent questionnaires responded 4. Roughly 95, of the people from whom a response was solicited did not respond to the survey: They are called nonresponders. The nonresponse rate in the Hite survey is thus at least.

This is a very high rate of nonresponse. The 95, nonresponders might be quite different from the 4, responders with respect to the issues the survey sought to explore, even though the 4, responders were much like the general population of women with respect to basic demographic characteristics, such as age, ethnicity, income, and place of residence. If so, the difference between the responders and the nonresponders could bias the results.

This is called nonresponse bias. Even if the , women who were sent surveys were a representative subset of all american women, the 4, who responded might not be. In fact, that is a plausible explanation for the differences between the results of the Hite report and the results of the other studies cited.

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We can bound the extent to which nonresponse affects estimates of percentages by imagining what would have happened had all the nonresponders answered one way or the other. For example, if the nonresponders had all had extramarital affairs, the estimated rate of extramarital affairs would have been.

On the other hand, if none of the nonresponders had had an extramarital affair, the estimated rate of extramarital affairs would have been. The following exercise checks your ability to calculate the possible size of nonresponse bias. The Hite report might be evidence that women's dissatisfaction in their relationships with men and perhaps infidelity is fairly evenly distributed throughout our society; but, primarily because of nonresponse, the survey says very little about the prevalence of dissatisfaction and infidelity.

Proportional representation in the sample of various subgroups of the population does not ensure that the sample is like the population with respect to the variables of interest. In the Hite survey, it is reasonable to conclude that those women who responded to the questionnaire were not typical of the general population of U.

There are many other potential sources of bias in sample surveys. The following list summarizes some of them:. See Huff for more discussion and more examples. Hite was concerned primarily with the third and fourth of these sources of bias: People tend to color their responses when the topic is sensitive, and when they are worried that the interviewer is judging them, or that their responses could have negative repercussions for them.

There are techniques that try to reduce this bias, but it is hard to eliminate completely. Conscious or unconscious bias in selecting subjects to interview can be eliminated by selecting subjects at random.

Types of Sampling: Sampling Methods with Examples

This section introduces terminology and a taxonomy of sampling designs , strategies for drawing a sample from a population to draw inferences about a population of people or other units from a sample. The terminology and classification apply not only to sample surveys, but to sampling generally. The sample size is the number of units the sample contains.

Commonly, the sample is chosen not from the entire population of units, but from a subset of the population, or a different population, called a frame or sampling frame. If the value of the parameter differs for the population and the frame, this can introduce frame bias into estimates computed from the sample, as described earlier in this chapter.

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Throughout the remainder of this chapter, n will denote the sample size and N will denote the number of units in the frame. Sometimes the units are not sampled directly, one at a time; rather, clusters of units are selected. The basic element sampled is called the sampling unit. The sampling units can be the same as the population units, but it is quite common for the sampling units to be clusters of population units; then the sample is called a cluster sample. Sometimes the population is divided into non-overlapping groups, called strata singular: stratum , and a sample is taken separately from each stratum.

This is called stratified sampling ; the sample is called a stratified sample. If the variable of interest varies within the population in a way that is associated with membership in different strata, stratified sampling can yield smaller errors than simpler sampling designs, for a given sample size. However, it is generally harder to quantify the errors rigorously than it is for a sample drawn at random directly from the entire population e.

Sometimes it is easier to draw the sample in stages. For example, to draw a sample of persons in the United States, we might proceed as follows:. Such an approach is called multistage sampling. It can be much more economical than trying to sample directly from the population. In this example, the multistage approach needs a list of persons in a few dwellings, a list of dwellings in a few blocks, a list of blocks in a few counties, a list of counties in a few states, and a list of states.

Constructing or obtaining these lists is much easier and much less error-prone than trying to construct a list of all persons in the United States, which we would need to sample persons directly in a single stage. There are also more complicated sampling designs that combine these strategies.

Methods of sampling from a population | Health Knowledge

For example, in the description of multistage sampling in the previous section, had we taken all the residents of the selected housing units to be in the sample, instead of just one resident of each housing unit in the sample, we would have been sampling clusters of people instead of individuals. This is called multistage cluster sampling. Whether we sample individuals or clusters of individuals, sample in one stage from the frame or in several stages, sample from the frame as a whole or from strata separately, we need to pick the sampling units that comprise the sample.

How the sampling units are selected is crucial in determining whether the sample is representative, and whether it is possible to quantify the uncertainty estimates of parameters of the population based on the sample.

Sampling Theory Part-1

A convenience sample is a sample that consists of units that are readily accessible to the investigator or data collector—units it is convenient to examine. The data collector has complete latitude in deciding which units to include in the sample. For example, suppose I seek to estimate the fraction of University of California at Berkeley faculty who are registered Republicans. I might just start at the beginning of the campus telephone directory, and call faculty until I reach people who are willing to answer my question.

Alternatively, I might go to the Faculty Club at lunchtime and interview the first faculty who consent. Either would be a convenience sample. A convenience sample typically is not representative of the population, and usually it is not possible to quantify the error in extrapolating from a convenience sample to the entire frame or population.

For example, in the second case, if the membership of the Faculty Club is disproportionately Republican compared with the faculty at large, the sample would tend to be biased. The Hite study essentially used a sample of convenience. A quota sample is a sample picked to match the population with respect to some summary characteristics. For example, in an opinion poll, one might want the proportions of various ethnicities in a sample to match the proportions of ethnicities in the overall population.

Like convenience samples, quota samples leave latitude for the data collectors to select the individuals who will comprise the sample—subject to the constraint that the summary characteristics of the sample match their target values. Generally, this is a bad idea: Unconscious biases in the interviewers' selections can have strong effects on which individuals end up in the sample, which can cause the sample to be unrepresentative of the population with respect to the variable being studied.

This is called selection bias. As with a sample of convenience, usually it is not possible to quantify how closely representative of the population a quota sample is likely to be. Although the Hite study did not use quota sampling, the demographics of its sample matched the demographics of the population extremely well, but the results did not seem to be representative of the population if the contemporaneous studies using random samples are trustworthy.

Towards Data Science

This shows that matching some characteristics of the sample to characteristics of the population does not guarantee that the sample is representative of the population with regard to the variables of interest. A systematic sample results from taking every k th unit from the frame, where k is chosen to give a sample of the desired size. For example, if there are 20, units in the frame and we want a sample of size , we would take every th unit to be in the sample. To take a systematic sample, the units in the frame have to be listed in some order.

If the order is essentially haphazard, a systematic sample behaves much like a simple random sample, described later in this chapter. If the order of the units in the list is related to the value of the variable under study, a systematic sample can be biased. Systematic samples are cluster samples—the frame is divided into k clusters, and one of those k clusters comprises the sample.

It is difficult to quantify the error that results from using a systematic sample. Systematic samples do not leave latitude for the data collector to select the units that comprise the sample, which can reduce deliberate and unconscious biases compared with convenience samples and quota samples. A probability sample is a sample drawn using a random mechanism to select the units from the frame to comprise the sample; that is, whether each unit in the frame is in the sample is a random event, with a specified probability. In a probability sample, one can specify ahead of time before the sample is drawn the chance that each unit in the frame will end up in the sample.

The probability of being selected need not be the same for every unit in the frame.

Probability vs. Non-Probability Samples

A statistic computed from a probability sample is a random variable , because its value depends upon which units happen to be in the sample, and those units are chosen randomly. In a probability sample, the person collecting the data has no discretion in about which units to include in the sample, so deliberate and unconscious biases cannot affect the choice of units.

As a result, probability samples tend to be more representative of the general population than convenience samples and quota samples are, if the probability of drawing each unit is the same. Moreover, it is possible to quantify the error of estimators computed from a probability sample, which is not possible for samples of convenience, quota samples, or systematic samples. A simple random sample of size n from a frame containing N units is a probability sample drawn in such a way that every subset of n of the N units in the frame is equally likely to be the sample.

This is like writing a unique identifier for each unit in the frame on one of N otherwise identical cards, shuffling the cards well, then dealing the top n cards. Equivalently, taking a simple random sample is like writing an identifier for each of the N units in the population on N otherwise identical tickets, putting the tickets into a box, stirring them vigorously, and drawing n of the tickets without looking; then considering the sample to consist of those units whose identifiers were on the tickets drawn.

Conceptually, a simple random sample is a sample drawn without replacement as follows: In the first step, each of the N units is equally likely to be drawn. After n steps, we have a simple random sample of size n. In practice, simple random samples are drawn using a computer to generate pseudo-random numbers, as follows: Each unit in the population is assigned independently a random number between zero and one.

The sample consists of those units that were assigned the n largest random numbers. If there are ties, they are broken randomly and independently e. All the elements of the cluster are used for sampling. Clusters are identified using details such as age, sex, location etc. Cluster sampling can be done in following ways:. Entire cluster is selected randomly for sampling.

Here first we randomly select clusters and then from those selected clusters we randomly select elements for sampling. Systematic Clustering.

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