Differentiation between the terms parameter and statistic is important only in the use of inferential statistics. This is because the calculation of parameters is usually either impossible or infeasible because of the amount of time and money required to gather data about the whole population under study. In such case, the researcher can take a random sample of the population, calculate a statistic on the sample, and infer by estimation the value of the parameter.

Did You Know

We use descriptive statistics simply to describe what's going on in our data. With inferential statistics we want to draw inferences about populations from samples. We use inferential statistics to infer from the sample data what the population might think. With inferential statistics, we try to reach conclusions that extend beyond the immediate data alone. Descriptive statistics "describe" data that have been collected. Commonly used descriptive statistics include frequency counts, ranges, means, modes, median scores, and standard deviations.

 

Inferential statistics is mainly concerned with the rules or logic of how a relatively small sample from a large population could be tested, and the results of those tests can be inferred to be true for everyone in the population. For example, if we want to test whether Bayer aspirin is better than Tylenol at relieving pain, we could not give these drugs to everyone in the population. It’s not practical since the general population is so large. Instead we might give it to a couple of hundred people and see which one works better with them. With inferential statistics we can infer that what was true for a few hundred people is also true for a very large population of hundreds of thousands of people.[1]

 

Unless parameters are computed directly from the population, the statistician never knows with certainty whether the estimates or inferences made from samples are true.

The basis for inferential statistics then is the ability to make decisions about parameters without having to complete a census of the population.

Additional Resources: Notation

For a great introduction to parameter and statistic data is notated in statistics, see page 2 -4 of the following document: http://faculty.uncfsu.edu/dwallace/Lesson%201.pdf