Sampling and Sampling Distributions

Understanding sampling and sampling distributions (sampling methods, the central limit theorem, margin, and Standard errors)

When conducting statistical analysis, we refer to sampling as the process by which one selects a certain number of data observations for a larger population. These selected observations are used for data analysis and serve as a representation of the entire population being examined. Depending on the type of study being undertaken, the methods used to sample the proportions vary. It can be simple random sampling, systematic sampling or other sampling methods that suits the type of research being conducted. There are four major types of sampling, these are;

Simple random sampling is a process by which, a predetermined number of observations are selected from the population with every member of the population having an equal chance of being selected. The process does not have any set of inclusion criteria and the selection ends up being completely at random. The sample selected is usually representative of the entire populations.

In many ways, systematic sampling is similar to random sampling. In systematic sampling, the members of the population are assigned a number, these numbers are assigned at regular intervals and the selection also happens at regular intervals

In stratified sampling the population is segmented into different subgroups. Each subgroup varies in characteristics from the next subgroups. It ensures that the subgroups in the population are well represented and therefore an accurate representation of a certain characteristics that cannot be observed in the other subgroups.

In cluster sampling the population is segmented into different subgroups. Each of these subgroups shares the same characteristics as the rest of the subgroups and in clustered sampling, one chooses entire subgroups at random, rather than individual members from the population.

Sampling distributions

A sampling distribution is the probability distribution of a statistic derived from a greater number of samples taken from a particular population. The sampling distribution of a population is the frequency distribution of a number of different outcomes that may occur for a population statistic. A population can be defined as the entire pool from which a sample is taken. It can refer to a group of people, objects, items, products or any other measurements being done to study a certain phenomenon. The sampling distribution usually has the following characteristics;

1. Sampling distribution can be used to measure more than the mean. These might include, ranges, standard deviations, variances, proportions can also be calculated from a sampling distribution.
2. A sampling distribution is a statistic derived from several samples taken from a wider population. This can be the mean/ average, standard deviation, variance, range or other measures used in descriptive statistics.
3. It describes the set of potential outcomes of a statistic, such as the mean or mode of a variable, in the same way that it describes a population.
4. The vast majority of data analyzed by researchers comes from samples rather than populations. This is because, in many cases, it is difficult to have the data from entire populations. For instance, if your wanted to study the weight of all Americans, it would be impossible to acquire the data of each and every American, however, a sample can be used to measure the average weight of Americans that could represents the entire American population.

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