2022 Introduction to Statistics in Research Mitchell 2nd ed

I N T R O T O R E S E A R C H : D A T A V I S U A L I Z A T I O N & C O M M O N S T A T T E S T S

The importance of a representative sample size

To understand the power of sample size, let's look at a population Vs varying sample sizes. In this image of the population and varying sample sizes using SPSS with a variety of sample sizes. As you can see, even a sample size of 50 is still representative of the population.

Population Size : 5,000 arrests in 2020 Data collected: prior drug/alcohol arrests

But the important point is that the sample is selected without bias. Consider the 5,000 arrests. If we chose a sample based on convenience we allow selection bias. As an example, if we pick the month of December for the arrest record, that may not be a representative sample. Even voluntary responses can be a type of convenience sampling. Remember, people who are motivated to volunteer often hold strong opinions. It is extremely unlikely that they are representative of the population. One of the easiest ways to sample without bias is to use a simple random sample. The sections below list some of the sampling techniques with information about each. Read what you need to gain understanding.

Self-Assessment - Does the sample represent the population?

Table 39: Various Sample sizes showing bell curve

Question 1 : A sample is a subset of a population.

True or False

Question 2 : Suppose your professor asked you to gather a sample of 20 students from your college. You survey 20 students in your next class (which happens to be an equestrian class). This sample will be representative of all students at your college. True or False

More on Samples…. Simple Random Sample

A sample size "n" is selected from the population in a way that ensures that every different possible sample of the desired size has the same chance of being selected. You can use random number tables, or easily use the =Rand() function in Excel. Here is a three-minute video on how to do this:

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