The Role of Sampling Distributions in Inferential Statistics- Practical Examples and Insights

A sampling distribution is the probability distribution of a measurement arising from selecting random samples from a designated population. It includes the sampling distribution of proportion, mean, and t-distribution (Lacort, 2014). In the mean sampling distribution, the mean of each sample group from the selected population is calculated, and all data points are plotted. A graph is then prepared to indicate a normal distribution and the sampling distribution mean at the center.

In proportion sampling distribution, information about the proportions in the selected population is obtained (Härdle et al., 2015). The mean from all the sample proportions is determined to get the sample proportion which is the mean of all the sample proportions calculated from every sample group distribution. It is considered when the sample size is too small, or there is less information about the population. It mainly estimates the confidence intervals, mean of the population, linear regression, and statistical differences (Bagla, 2018). A sampling distribution is essential in inferential statistics because it helps eliminate variability when gathering statistical data and doing research. It also makes it easier to understand the distribution of frequencies in statistical data and the different outcomes that may exist in a dataset.

A good example of a sampling distribution is accessing employee turnover in different departments in an organization. The sampling would include determining the number of employees who quit in every department. Every department would have one sample mean differing from each other. More data is then gathered from other departments that were not considered in the initial sampling. The final distribution of employees leaving each department will be the sampling distribution of the sample means. It can determine how far the mean from the initial sample is from the second mean and use the information to decide the departments with the highest employee turnover rate.

References

Bagla, V. (2018). Inferential statistics. Createspace Independent Publishing Platform.

Härdle, W. K., Klinke, S., & Rönz, B. (2015). Introduction to statistics: Using interactive MM*Stat elements. Springer.

Lacort, M. O. (2014). Descriptive and inferential statistics – Summaries of theory and exercises solved. Lulu.com.