What are parametric statistics? Give an example.

Question

Quizplus · Accepted Answer

The Answer is Parametric statistics refer to a branch of statistics that assumes that the data has a specific type of distribution, usually a normal distribution, and that the parameters of this distribution—such as the mean and the variance—are known or can be estimated from the data. These methods rely on certain assumptions about the underlying population from which the sample data are drawn.

The key feature of parametric statistics is the use of parameters (hence the name) to define the distribution of the data. These parameters are numbers that summarize the characteristics of the entire population from which the samples are taken. For example, in a normal distribution, the parameters are the mean (average) and the standard deviation (a measure of spread).

Parametric statistical methods are powerful because they allow for making inferences and predictions about the population, and they can be more efficient (requiring smaller sample sizes) than non-parametric methods when the assumptions hold true. However, if the assumptions are violated, the results can be misleading or incorrect.

An example of parametric statistics is the use of a t-test to determine whether there are significant differences between the means of two groups. For instance, researchers might want to test whether a new teaching method leads to better test scores than a traditional method. They would collect scores from a group of students taught with the new method and another group taught with the traditional method. The t-test would allow the researchers to determine if the difference in the average scores between the two groups is statistically significant, assuming that the scores are normally distributed and that other assumptions of the t-test are met.

Another example is linear regression, where the relationship between a dependent variable and one or more independent variables is modeled. The parameters in this case are the regression coefficients that represent the change in the dependent variable for a one-unit change in an independent variable, assuming that the relationship between the variables is linear.

In summary, parametric statistics are a set of statistical techniques based on assumptions about the distribution of the underlying population data. They are used to make inferences or predictions about population parameters, and they are most effective when the assumptions on which they are based are valid.

What Are Parametric Statistics? Give an Example