Another option is probability proportional to size 'PPS' sampling, in which the selection probability for each element is set to be proportional to its size measure, up to a maximum of 1. In a simple PPS design, these selection probabilities can then be used as the basis for Poisson sampling. However, this has the drawback of variable sample size, and different portions of the population may still be over- or under-represented due to chance variation in selections.
Systematic sampling theory can be used to create a probability proportionate to size sample. This is done by treating each count within the size variable as a single sampling unit.
Samples are then identified by selecting at even intervals among these counts within the size variable. This method is sometimes called PPS-sequential or monetary unit sampling in the case of audits or forensic sampling. The PPS approach can improve accuracy for a given sample size by concentrating sample on large elements that have the greatest impact on population estimates.
PPS sampling is commonly used for surveys of businesses, where element size varies greatly and auxiliary information is often available—for instance, a survey attempting to measure the number of guest-nights spent in hotels might use each hotel's number of rooms as an auxiliary variable.
In some cases, an older measurement of the variable of interest can be used as an auxiliary variable when attempting to produce more current estimates.
Sometimes it is more cost-effective to select respondents in groups 'clusters'. Sampling is often clustered by geography, or by time periods. Nearly all samples are in some sense 'clustered' in time — although this is rarely taken into account in the analysis. For instance, if surveying households within a city, we might choose to select city blocks and then interview every household within the selected blocks.
Clustering can reduce travel and administrative costs. In the example above, an interviewer can make a single trip to visit several households in one block, rather than having to drive to a different block for each household. It also means that one does not need a sampling frame listing all elements in the target population.
Instead, clusters can be chosen from a cluster-level frame, with an element-level frame created only for the selected clusters. In the example above, the sample only requires a block-level city map for initial selections, and then a household-level map of the selected blocks, rather than a household-level map of the whole city.
Cluster sampling also known as clustered sampling generally increases the variability of sample estimates above that of simple random sampling, depending on how the clusters differ between one another as compared to the within-cluster variation. For this reason, cluster sampling requires a larger sample than SRS to achieve the same level of accuracy — but cost savings from clustering might still make this a cheaper option.
Cluster sampling is commonly implemented as multistage sampling. This is a complex form of cluster sampling in which two or more levels of units are embedded one in the other.
The first stage consists of constructing the clusters that will be used to sample from. In the second stage, a sample of primary units is randomly selected from each cluster rather than using all units contained in all selected clusters. In following stages, in each of those selected clusters, additional samples of units are selected, and so on. All ultimate units individuals, for instance selected at the last step of this procedure are then surveyed.
This technique, thus, is essentially the process of taking random subsamples of preceding random samples. Multistage sampling can substantially reduce sampling costs, where the complete population list would need to be constructed before other sampling methods could be applied.
By eliminating the work involved in describing clusters that are not selected, multistage sampling can reduce the large costs associated with traditional cluster sampling. In quota sampling , the population is first segmented into mutually exclusive sub-groups, just as in stratified sampling.
Then judgement is used to select the subjects or units from each segment based on a specified proportion. For example, an interviewer may be told to sample females and males between the age of 45 and It is this second step which makes the technique one of non-probability sampling. In quota sampling the selection of the sample is non- random. For example, interviewers might be tempted to interview those who look most helpful. The problem is that these samples may be biased because not everyone gets a chance of selection.
This random element is its greatest weakness and quota versus probability has been a matter of controversy for several years. In imbalanced datasets, where the sampling ratio does not follow the population statistics, one can resample the dataset in a conservative manner called minimax sampling.
The minimax sampling has its origin in Anderson minimax ratio whose value is proved to be 0. This ratio can be proved to be minimax ratio only under the assumption of LDA classifier with Gaussian distributions. The notion of minimax sampling is recently developed for a general class of classification rules, called class-wise smart classifiers.
In this case, the sampling ratio of classes is selected so that the worst case classifier error over all the possible population statistics for class prior probabilities, would be the. Accidental sampling sometimes known as grab , convenience or opportunity sampling is a type of nonprobability sampling which involves the sample being drawn from that part of the population which is close to hand. That is, a population is selected because it is readily available and convenient. It may be through meeting the person or including a person in the sample when one meets them or chosen by finding them through technological means such as the internet or through phone.
The researcher using such a sample cannot scientifically make generalizations about the total population from this sample because it would not be representative enough. This type of sampling is most useful for pilot testing. Several important considerations for researchers using convenience samples include:. In social science research, snowball sampling is a similar technique, where existing study subjects are used to recruit more subjects into the sample.
Some variants of snowball sampling, such as respondent driven sampling, allow calculation of selection probabilities and are probability sampling methods under certain conditions. The voluntary sampling method is a type of non-probability sampling. A voluntary sample is made up of people who self-select into the survey. Often, these subjects have a strong interest in the main topic of the survey. Volunteers may be invited through advertisements on Social Media Sites .
This method is suitable for a research which can be done through filling a questionnaire. The target population for advertisements can be selected by characteristics like demography, age, gender, income, occupation, education level or interests using advertising tools provided by the social media sites. The advertisement may include a message about the research and will link to a web survey. After voluntary following the link and submitting the web based questionnaire, the respondent will be included in the sample population.
This method can reach a global population and limited by the advertisement budget. This method may permit volunteers outside the reference population to volunteer and get included in the sample. It is difficult to make generalizations about the total population from this sample because it would not be representative enough. Line-intercept sampling is a method of sampling elements in a region whereby an element is sampled if a chosen line segment, called a "transect", intersects the element.
Panel sampling is the method of first selecting a group of participants through a random sampling method and then asking that group for potentially the same information several times over a period of time. Therefore, each participant is interviewed at two or more time points; each period of data collection is called a "wave". The method was developed by sociologist Paul Lazarsfeld in as a means of studying political campaigns. Panel sampling can also be used to inform researchers about within-person health changes due to age or to help explain changes in continuous dependent variables such as spousal interaction.
Snowball sampling involves finding a small group of initial respondents and using them to recruit more respondents. It is particularly useful in cases where the population is hidden or difficult to enumerate. Theoretical sampling  occurs when samples are selected on the basis of the results of the data collected so far with a goal of developing a deeper understanding of the area or develop theories. Sampling schemes may be without replacement 'WOR'—no element can be selected more than once in the same sample or with replacement 'WR'—an element may appear multiple times in the one sample.
For example, if we catch fish, measure them, and immediately return them to the water before continuing with the sample, this is a WR design, because we might end up catching and measuring the same fish more than once. However, if we do not return the fish to the water, this becomes a WOR design. If we tag and release the fish we caught, we can see whether we have caught a particular fish before. Sampling enables the selection of right data points from within the larger data set to estimate the characteristics of the whole population.
For example, there are about million tweets produced every day. It is not necessary to look at all of them to determine the topics that are discussed during the day, nor is it necessary to look at all the tweets to determine the sentiment on each of the topics. A theoretical formulation for sampling Twitter data has been developed. In manufacturing different types of sensory data such as acoustics, vibration, pressure, current, voltage and controller data are available at short time intervals.
To predict down-time it may not be necessary to look at all the data but a sample may be sufficient. Survey results are typically subject to some error. Total errors can be classified into sampling errors and non-sampling errors. The term "error" here includes systematic biases as well as random errors. Non-sampling errors are other errors which can impact the final survey estimates, caused by problems in data collection, processing, or sample design.
After sampling, a review should be held of the exact process followed in sampling, rather than that intended, in order to study any effects that any divergences might have on subsequent analysis. A particular problem is that of non-response. Two major types of non-response exist: In this case, there is a risk of differences, between respondents and nonrespondents, leading to biased estimates of population parameters.
This is often addressed by improving survey design, offering incentives, and conducting follow-up studies which make a repeated attempt to contact the unresponsive and to characterize their similarities and differences with the rest of the frame. Nonresponse is particularly a problem in internet sampling. Reasons for this problem include improperly designed surveys,  over-surveying or survey fatigue ,   and the fact that potential participants hold multiple e-mail addresses, which they don't use anymore or don't check regularly.
In many situations the sample fraction may be varied by stratum and data will have to be weighted to correctly represent the population. Thus for example, a simple random sample of individuals in the United Kingdom might include some in remote Scottish islands who would be inordinately expensive to sample.
A cheaper method would be to use a stratified sample with urban and rural strata. The rural sample could be under-represented in the sample, but weighted up appropriately in the analysis to compensate. More generally, data should usually be weighted if the sample design does not give each individual an equal chance of being selected. For instance, when households have equal selection probabilities but one person is interviewed from within each household, this gives people from large households a smaller chance of being interviewed.
This can be accounted for using survey weights. Similarly, households with more than one telephone line have a greater chance of being selected in a random digit dialing sample, and weights can adjust for this. Random sampling by using lots is an old idea, mentioned several times in the Bible. In Pierre Simon Laplace estimated the population of France by using a sample, along with ratio estimator. He also computed probabilistic estimates of the error. His estimates used Bayes' theorem with a uniform prior probability and assumed that his sample was random.
Alexander Ivanovich Chuprov introduced sample surveys to Imperial Russia in the s. In the USA the Literary Digest prediction of a Republican win in the presidential election went badly awry, due to severe bias . More than two million people responded to the study with their names obtained through magazine subscription lists and telephone directories. It was not appreciated that these lists were heavily biased towards Republicans and the resulting sample, though very large, was deeply flawed.
The textbook by Groves et alia provides an overview of survey methodology, including recent literature on questionnaire development informed by cognitive psychology:.
The other books focus on the statistical theory of survey sampling and require some knowledge of basic statistics, as discussed in the following textbooks:. The historically important books by Deming and Kish remain valuable for insights for social scientists particularly about the U.
From Wikipedia, the free encyclopedia. For computer simulation, see pseudo-random number sampling. This section needs expansion. You can help by adding to it. How to conduct your own survey. Model Assisted Survey Sampling. The" panel" as a new tool for measuring opinion. The Public Opinion Quarterly, 2 4 , — Analysis of Sampling Algorithms for Twitter.
International Joint Conference on Artificial Intelligence. Survey nonresponse in design, data collection, and analysis. Internet, mail, and mixed-mode surveys: The tailored design method. Nonresponse in web surveys. New directions for institutional research pp. Moore and George P. Mean arithmetic geometric harmonic Median Mode. Central limit theorem Moments Skewness Kurtosis L-moments.
Grouped data Frequency distribution Contingency table. Pearson product-moment correlation Rank correlation Spearman's rho Kendall's tau Partial correlation Scatter plot. Then the population is randomly sampled within each category or stratum. How to Construct a probability representative sample. As they are not truly representative, non-probability samples are less desirable than probability samples. However, a researcher may not be able to obtain a random or stratified sample, or it may be too expensive.
A researcher may not care about generalizing to a larger population. The validity of non-probability samples can be increased by trying to approximate random selection, and by eliminating as many sources of bias as possible.
A researcher is interested in the attitudes of members of different religions towards the death penalty. In Iowa a random sample might miss Muslims because there are not many in that state. However, the sample will no longer be representative of the actual proportions in the population. This may limit generalizing to the state population. But the quota will guarantee that the views of Muslims are represented in the survey.
A subset of a purposive sample is a snowball sample -- so named because one picks up the sample along the way, analogous to a snowball accumulating snow. A snowball sample is achieved by asking a participant to suggest someone else who might be willing or appropriate for the study. Snowball samples are particularly useful in hard-to-track populations, such as truants, drug users, etc. Non-probability samples are limited with regard to generalization.
Because they do not truly represent a population, we cannot make valid inferences about the larger group from which they are drawn. Validity can be increased by approximating random selection as much as possible, and making every attempt to avoid introducing bias into sample selection. Examples of nonprobability samples. Using the random numbers table. Two of each species. Random sample The term random has a very precise meaning.
The defining characteristic of a quota sample is that the researcher deliberately sets the proportions of levels or strata within the sample. This is generally done to insure the inclusion of a particular segment of the population. The proportions may or may not differ dramatically from the actual proportion in the population.
A stratified sample is a mini-reproduction of the population. Before sampling, the population is divided into characteristics of importance for the research. For example, .
Ultimately, though, the sampling technique you choose should be the one that best allows you to respond to your particular research question. Let's review four kinds of probability sampling techniques.
Sampling Methods. Sampling and types of sampling methods commonly used in quantitative research are discussed in the following module. Learning Objectives: Define sampling and randomization. Explain probability and non-probability sampling and describes the different types of each. In probability sampling it is possible to both determine which sampling units belong to which sample and the probability that each sample will be selected. The following sampling methods are examples of probability sampling: Of the five methods listed above, students have the most trouble.
There are many methods of sampling when doing research. This guide can help you choose which method to use. Simple random sampling is the ideal, but researchers seldom have the luxury of time or money to access the whole population, so many compromises often have to be made. Types of Probability Sampling Methods. Simple Random Sampling. This is the purest and the clearest probability sampling design and strategy. It is also the most popular way of a selecting a sample because it creates samples that are very highly representative of the population.. Simple random is a fully random technique of selecting subjects.