Since it is generally impossible to study an entire population (every individual in a country, all college students, every geographic area, etc.), researchers typically rely on
sampling to acquire a section of the population to perform an experiment or observational study. It is important that the group selected be representative of the population, and not biased in a systematic manner. For example, a group comprised of the wealthiest individuals in a given area probably would not
accurately reflect the opinions of the entire population in that area. For this reason, randomization is typically employed to achieve an unbiased sample. The most common sampling designs are
simple random sampling,
stratified random sampling, and
multistage random sampling.
Simple Random Sampling
Simple random sampling is
the basic sampling technique where we select a group of subjects (a sample) for study from a larger group (a population). Each individual is chosen entirely by chance and each member of the population has an equal chance of being included in the sample. Every possible sample of a given size has the same chance of selection.
(Definition taken from Valerie J. Easton and John H. McColl's Statistics Glossary
v1.1)
Stratified Random Sampling
There may often be factors which divide up the population into sub-populations (groups / strata) and we may expect the measurement of interest to vary among the different sub-populations. This has to be accounted for when we select a sample from the population in order that we obtain a sample that is representative of the population. This is achieved by
stratified sampling.
A stratified sample is obtained by taking samples from
each stratum or sub-group of a population.
When we sample a population with several strata, we generally require that the proportion of each stratum in the sample should be the same as in the population.
Stratified sampling techniques are generally used when the population is heterogeneous, or dissimilar, where certain homogeneous, or similar, sub-populations can be isolated (strata). Simple random sampling is most appropriate when the entire population from which the sample is
taken is homogeneous. Some reasons for using stratified sampling over simple random sampling are:
a) the cost per observation in the survey may be reduced;
b) estimates of the population parameters may be wanted for each sub-population;
c) increased accuracy at given cost.
Example
Suppose a farmer wishes to work out the average milk yield of each cow type in his herd which consists of Ayrshire, Friesian, Galloway and Jersey cows. He could divide up his herd
into the four sub-groups and take samples from these.
(Definition and example taken from Valerie J. Easton and John H. McColl's Statistics Glossary v1.1)
Multistage Random Sampling
A
multistage random sample is constructed by taking a series of simple random samples in stages. This type of sampling is often more practical than simple random sampling for studies requiring "on
location" analysis, such as door-to-door surveys. In a multistage random sample, a large area, such as a country, is first divided into smaller regions (such as states), and a random sample of these regions is collected. In the second stage, a random sample of smaller areas (such as counties) is taken from within each of the regions chosen in the first stage. Then, in the third stage, a random sample of even smaller areas (such as neighborhoods) is taken from within each of the areas chosen in
the second stage. If these areas are sufficiently small for the purposes of the study, then the researcher might stop at the third stage. If not, he or she may continue to sample from the areas chosen in the third stage, etc., until appropriately small areas have been chosen.
| Glossary
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| | Chapter 1
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| | biased sampling method
| A sampling method that produces data that systematically differ from the sampled population. Repeated sampling will not correct the bias.
| | cluster sample
| A sample obtained by stratifying the population, or sampling frame, and then selecting some or all of the items from some, but not all, of the strata.
| | continuous variable
| A quantitative variable that can assume an uncountable number of values.
| | data
| The set of values collected from the variable from each of the elements that belong to the sample or population.
| | data value
| The value of the variable associated with one element of a population or sample. This value may be a number, a word, or a symbol.
| | discrete variable
| A quantitative variable that can assume a countable number of values.
| | experiment
| A planned activity whose results yield a set of data.
| | experiments
| A planned activity that results in data.
| | finite population
| A population whose membership can or could be physically listed.
| | infinite population
| A population whose membership is unlimited.
| | judgment samples
| Kind of samples that are selected on the basis of being judged ?typical.?
| | multistage random sampling
| A sample design in which the elements of the sampling frame are subdivided and the sample is chosen in more than one stage.
| | nominal variable
| A qualitative variable that characterizes (or describes, or names) an element of a population.
| | observational studies
| A method of data collection that does not modify the environment and does not control the process.
| | ordinal variable
| A qualitative variable that incorporates an ordered position, or ranking.
| | parameter
| A numerical value summarizing all the data of an entire population.
| | population
| A collection, or set, of individuals, objects, or events whose properties are to be analyzed.
| | probability samples
| Samples in which the elements are selected on the basis of probability. Each element in a population has a certain probability of being selected as part of the sample.
| | proportional stratified sampling
| A sample obtained by stratifying the population, or sampling frame, and then selecting a number of items in proportion to the size of the strata from each strata by means of a simple random sampling technique.
| | qualitative (or attribute or categorical) variable
| A variable that describes or categorizes an element of a population.
| | quantitative (or numerical) variable
| A variable that quantifies an element of a population.
| | sample
| A subset of a population that will be used to produce data.
| | sampling frame
| A list, or set, of the elements belonging to the population from which the sample will be drawn.
| | sampling method
| The process of selecting items or events that will become the sample.
| | simple random sample
| A sample selected in such a way that every element in the population or sampling frame has an equal probability of being chosen. Equivalently, all samples of size n have an equal chance of being selected.
| | single-stage sampling
| A sample design in which the elements of the sampling frame are treated equally and there is no subdividing or partitioning of the frame.
| | statistic
| A numerical value summarizing the sample data.
| | statistics
| The science of collecting, describing, and interpreting data.
| | stratified random sample
| A sample obtained by stratifying the population, or sampling frame, and then selecting a number of items from each of the strata by means of a simple random sampling technique.
| | systematic sampling method
| A sample in which every kth item of the sampling frame is selected, starting from a first element, which is randomly selected from the first k elements.
| | unbiased sampling method
| A sampling method that is not biased and produces data that are representative of the sampled population.
| | variability
| The extent to which data values for a particular variable differ from each other.
| | variable
| A characteristic of interest about each individual element of a population or sample.
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Is a method by which every element of a population has a chance of being included in sample?
Simple random sampling. In simple random sampling (SRS), each sampling unit of a population has an equal chance of being included in the sample. Consequently, each possible sample also has an equal chance of being selected.
Which of the following is a sampling method in which every element of the population?
Random sampling simply describes when every element in a population has an equal chance of being chosen for the sample.
Which element in the population has an equal chance of occurring?
Random sampling is analogous to putting everyone's name into a hat and drawing out several names. Each element in the population has an equal chance of occuring. While this is the preferred way of sampling, it is often difficult to do. It requires that a complete list of every element in the population be obtained.
What is probability sampling method?
Revised on September 6, 2022. Probability sampling is a sampling method that involves randomly selecting a sample, or a part of the population that you want to research. It is also sometimes called random sampling.