On this occasion, Ángel A. Gómez Degraves, agricultural engineer and expert in Statistics and research methodology in Social Sciences, will explain what a representative sample consists of and how this sample should be selected so that it faithfully represents the target variable of a research study.
A probability sample in its structure approaches a higher degree of what is called representativeness when the value of the distance between the sample estimate and the value of the population parameter becomes smaller, this is known as aquariety in Statistical Inference.
We can be in the presence of a sufficiently representative sample when the selection process assigns a probability of inclusion in advance to each element, if this probability is different from zero, if it is known, and not necessarily being equal for each element of the population and, in addition, if the sampling error is low, if aquaricity exists and if a random process is used in its selection.
Difference between sample and representative sample
In statistics, a sample is a subset of cases or individuals from a population. In various applications, it is of interest that a sample is representative, and for this purpose an appropriate sampling technique must be chosen that produces an adequate random sample. It is also a subset of the population, and to be representative, it must have the same characteristics as the population.
Samples are obtained with the intention of inferring properties of the whole population, for which they must be representative of the population (a representative sample is technically called a random sample). To fulfill this characteristic, the inclusion of subjects in the sample must follow a sampling technique. In such cases, information similar to that of an exhaustive study can be obtained more quickly and at lower cost (see advantages of choosing a sample, below)..
The sample space from which a particular sample is taken consists of the set of all possible samples that can be drawn from a population using a given sampling technique.
Non-representative sample examples
Unlike probability sampling, where every member of the population has a known chance of being selected, in non-probability sampling, not all members of the population have the opportunity to participate in the study.
Convenience sampling is a non-probability sampling technique where samples from the population are selected only because they are conveniently available to the researcher. These samples are selected only because they are easy to recruit and because the researcher did not consider selecting a sample that represents the entire population.
Ideally, in research, it is good to analyze samples that represent the population. But, in some research, the population is too large to evaluate and consider the entire population.
An example of convenience sampling would be to use student volunteers who are known to the researcher. The researcher can send the survey to the students and they would then act as the sample.
Sample and representative sample examples
To conduct market research we need a representative sample. Can you imagine having to interview all the people in a city or a country? It would definitely be very complicated and time-consuming.
If we don’t have representativeness, we will surely have data that will be of no use to us. It is important to ensure that the characteristics that matter to us and that we need to investigate are found in the sample to be studied.
We should bear in mind that we will always be prone to sampling bias because there will always be people who do not answer the survey because they are busy, or who answer it incompletely, so we will not be able to obtain the data we require.
If we are going to have a probabilistic or random sampling, we must make sure that we have updated information on the population from which we will draw the sample and survey the majority to ensure representativeness. The sample will be chosen randomly, which guarantees that each member of the population will have the same probability of selection and inclusion in the sample group.