Sampling and Sampling Distributions

Sampling and Sampling Distributions

Sampling is one of the main concepts that are used in modern statistics. This process can be described as the selection of elements from a certain set in which elements have some common qualities. This activity is based on the assumption that it is possible to understand the properties of a certain population by examining a part of this population (Allen 51).

This is the main premise that statisticians rely on. One should bear in mind that in this context the term population is applied not only to a certain group of people. It is used to describe a collection of entities, for example, automotive parts, households, products, or any other elements (Allen 51). Thus, one can say that this concept is applicable to various fields. This is one of the main issues that should be considered. Overall, researchers should take several steps in order to ensure the validity of their studies.

In particular, they should identify the characteristics of the population and choose the elements that have these characteristics. For example, one can speak about age, gender, occupation, marital status, and so forth. This strategy is particularly applicable to various demographic studies. However, the choice of these characteristics normally depends on the research questions that should be addressed. These are some of the main aspects that should be discussed.

It should be kept in mind that sampling is one of the most widespread techniques that are used in various sciences. For example, one can mention psychology, sociology, biology, material science, and many other academic fields. This technique began to be used in the nineteenth century, especially in demographic studies.

Nevertheless, in the twentieth century, various statistical tools became more sophisticated (Stigler 5). At present, the notion of sampling is widely used in various studies. Moreover, this technique can be applied in non-academic fields. For example, it is widely applied in various manufacturers. This is one of the reasons why this concept attracts close attention of many professionals.

Researchers should take into account that there are sampling errors that can undermine the validity of a study. In other words, they should ensure that the results derived in the course do not deviate from the tendencies that can be observed in the entire population. Provided that this precaution is not taken, the study of a sample can give an inaccurate description of the entire population. Apart from that, one should speak about such a concept as sampling distribution.

This notion can be described as the quantitative value of some attribute that can be used to characterize a population. For example, it is possible to mention such attributes as age, income level, or even attitudes of people. One should bear in mind that this probability distribution is usually based the study of a random sample (Allen 51). In this way, a researcher can gain an idea about the properties of the population or its behavior.

One should remember that sampling distribution lays the foundation for the so-called statistical inference. As it has been said before, a scientist can deduce the properties of the entire set by looking at its different elements or subsets. Apart from that, researchers rely on various tests which can demonstrate whether the results of the study are valid. These confidence tests can help a researcher to strengthen the validity of a study. This is one of the main points that can be made.

There is another issue that should be taken into account by people who use statistical methods. In particular, one should mention the estimation of sample size. It has to be representative of the entire population; otherwise the sample distribution cannot be called accurate. Additionally, much attention should be paid to the sampling methods that can be used. For example, researchers can select a sample in a random or systemic way.

The choice of strategies is also dependent on the goals that a scholar intends to attain. Thus, it is possible to argue that a person, who examines statistical data, should consider a great number of factors in order to gain accurate data. These issues should be considered by researchers.

Admittedly, the use of sampling distribution can provide only an approximate description of different phenomena. They cannot be used to understand every aspect of a certain population. Sometimes, it is necessary to conduct longitudinal studies in order to detect the changes in the properties of a population. Nevertheless, these tools can still be used to scientists who may study social, economic, or psychological phenomena. This is one of the main arguments that can be put forward.

On the whole, this discussion indicates that sampling and sampling distribution play an important role in modern statistics. It is critical for understanding the properties of a specific population. This technique is applicable to various fields in which it is necessary to analyze different kinds of quantitative data. At present, such concepts as sampling and sampling distributions play an essential role in the design of the research methodology.

Confidence Interval Estimation

Although we work with samples, our goal is to describe and draw inferences regarding the underlying population. Values obtained from samples are referred to as ‘sample statistics’ which we have to use to garner idea of corresponding values in the underlying population, that are referred to as ‘population parameters’. But how do we do this? If we are doing ‘census’ type of studies, then the measured values are directly the population parameters since a census covers the entire population. However, if we are studying samples, then what we have in our hand at study end are the sample statistics. If we have a large enough and adequately representative sample, it is logical to presume that the sample statistics would be close to the ‘true values’, that is the population parameters, but they would probably not be identical to them. Strictly speaking, without doing a census it is not possible to get true population values. Practically speaking, it is possible to use a sample statistic and estimates of error in the sample to get a fair idea of the population parameter, not as a single value, but as a range of values. This range is the confidence interval (CI). How well the sample statistic estimates the underlying population value is always an issue. The CI addresses this issue because it provides a range of values which is likely to contain the population parameter of interest.

The CI is a descriptive statistics measure, but we can use it to draw inferences regarding the underlying population (1). In particular, they often offer a more dependable alternative to conclusions based on the P value (2). They also indicate the precision or reliability of our observations—the narrower the CI of a sample statistic, the more reliable is our estimation of the underlying population parameter. Wherever sampling is involved, we can calculate CI. Thus we can calculate CI of means, medians, proportions, odds ratios (ORs), relative risks, numbers needed to treat, and so on. The concept of the CI was introduced by Jerzy Neyman in a paper published in 1937 (3). It has now gained wide acceptance although many of us are not quite confident about it (4). To be fair it is not an intuitive concept but requires some reflection and effort to understand, calculate and interpret correctly. In this article we will look at these issues.