Sampling Distribution

An important thing to know about a sampling distribution that will help many understand the process is that it is not the distribution of a solitary sample, it is actually the process of selecting all possible subsets from a population and calculating a selected statistic, such as the mean or proportion, and using that information to make inferences about the population.




Sampling is the act of pulling all possible samples from the population and calculating the selected statistic and then putting it back in the “bucket”, and pulling another sample and calculating the mean and again putting that sample back in the bucket. This is called sampling because it is a process that is repeated. When you take each statistic, for instance the mean, from each sampling, and plot it on graph, theoretically each mean of all samples pulled will be close, although not exact, to the observed parameter of the population. The plotting will resemble the bell curve (see left).





It is not realistic that researchers will be able to pull all possible combinations of samples, as this would be expensive and time intensive, but theoretically the information they gain from the samples of the population they do investigate will be similar to one another and cluster around a particular value, and this value can be interpreted as the same as the population value (see right).  These results are then considered to be generalizable to the population.





I think the below video is a good depiction of what the textbook attempts to represent in Figure 7.5 on page 223.  For some reason that graphic was hard for me to interpret-I think this video, and the graphics above add a little visual clarity to what the textbook tries to explain




The concept of a sampling distribution is often the most difficult concept in introductory statistics for students to grasp. Locate and present at least one internet resource that explains and illustrates the concept. What do you think it adds to the description in your textbook?


2 thoughts on “Sampling Distribution

  • October 27, 2015 at 11:08 am

    I think this video is very good about illustrating the normal distribution structure and the process of choosing multiple samples to create a sampling distribution. However, the presenter does not use the word “random” when beginning her discussion about how the sampling distribution is constructed. There’s no emphasis on the important fact that the Central Limit Theorem ONLY applies to samples that that are drawn RANDOMLY from a larger population. (Caps are not meant for shouting, but only for emphasis!) Technically speaking, estimation can based on the CLT only for data based on a random sample. More broadly, carefully drawn probability samples that have random components, but are not simple random samples may be used for estimation However, if a researcher uses inferential statistics on a nonprobability sample and seems unaware that this is a violation of an important assumption, take care with your interpretation of the results!

  • October 18, 2015 at 9:46 pm

    Dear Sam,
    I think you make an good point here. Thanks for adding the video in the blog. I think videos have more impact when you are learning any concept that has to do with practical application. Textbook has sufficient information to understand the concept but video adds more to it and makes it easy to understand the concept. I like the video and how it explains most of the points clearly.

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