In statistics, a parameter is a number that describes some characteristic of a population.
Examples of parameters include:
- Population mean (e.g. mean height of all U.S. citizens)
- Population proportion (e.g. proportion of U.S. citizens that support a law)
- Population variance (e.g. variance of annual income among U.S. households)
Since it’s often too time-consuming and costly to collect data on every individual element in a population, researchers will collect a random sample from the population and use a sample statistic to estimate the population parameter.
For example, instead of collecting data on the annual income of every household in a certain state, researchers may instead collect data for 2,000 households and use the mean income of the households in the sample to estimate the mean income for households in the entire state.
A parameter of interest is the specific parameter that we’re interested in estimating during a data collection process.
The following examples illustrate different parameters of interest in real-world scenarios.
Example 1: Estimating a Population Mean
Suppose a biologist is interested in finding the mean weight of a certain population of 800 turtles.
Since it would be too time-consuming to go around and weigh every individual turtle, she may instead collect a random sample of 30 turtles and use the sample mean weight to estimate the population mean weight.
In this example, the parameter of interest is the population mean.
In order to estimate the value of this parameter, the biologist will use the sample mean.
For example, if the mean weight of turtles in the sample is 190.4 pounds, then the best estimate for the mean weight among turtles in the population will also be 190.4 pounds.
Example 2: Estimating a Population Proportion
Suppose a politician is interested in finding out the proportion of residents in a certain city with a population of 5,0000 that support a certain law.
Since it would be too costly to go around and survey every individual resident, he may instead collect a random sample of 1,000 residents and use the sample proportion to estimate the population proportion.
In this example, the parameter of interest is the population proportion.
In order to estimate the value of this parameter, the politician will use the sample proportion.
For example, if 25% of residents in the sample support the law, then the best estimate for the proportion of residents in the population that support the law will also be 25%.
The following tutorials provide additional information about parameters of interest in statistics:
Introduction to Hypothesis Testing
Statistic vs. Parameter: What’s the Difference?
What is a Representative Sample and Why is it Important?