Sampling theory entails developing a sample set. Samples extracted from a population are studied to establish how the sample relates to the population. Randomization should be done before sample selection, and this helps to bring out accurate statistical findings. In this context, a population refers to a group with desirable traits from which information can be sought (Upadhyay, 2020). The population can be categorized as infinite, finite, hypothetical, or existent (Upadhyay, 2020). As used in this theory, the word sample refers to a portion of the population that is chosen for investigative purposes.
Sampling theory is designed to fulfill three main objectives. They include hypothesis testing, estimating statistical measures, and inference of statistics (Upadhyay, 2020). For instance, out of a population of 1500 Alzheimer’s patients, 800 can be selected randomly. These are the samples. The desired attribute in this sample is a history of falls. Therefore, if only 200 patients report a history of falls, then 600 patients have never had a fall history. This can indicate that in a sample of 800 patients, 200 are successes and 600 are failures. Furthermore, the probability of success can be reported as 200/800 (0.25) while that of failure as 600/800 (0.75). This example shows the population, sample, and findings from the theory.
According to Carminati (2018), generalizability refers to the application of findings and conclusions made from a study on a representative sample to the whole population. This application is statistically possible. Dependable generalizability utilizes a large sample size. The larger the sample size, the more statistically accurate the generalizability (Carminati, 2018). Generalizability helps to save resources, both money and time, that would be used to study the entire population. Therefore, by applying the right statistical procedures, sample size, and sampling method, generalizability can be achieved