What is the main difference between parametric and nonparametric statistics?
The main difference between parametric and nonparametric statistics lies in the assumptions they make about the underlying population distribution.
Parametric statistics assume that the data being analyzed comes from a specific, known probability distribution (such as the normal distribution). This allows for specific mathematical models to be applied to the data and inferences to be made about population parameters (e.g., mean or variance) based on sample statistics. Parametric methods typically require a large enough sample size and satisfy assumptions of normality, independence, and homogeneity of variance.
On the other hand, nonparametric statistics do not make explicit assumptions about the population distribution. Instead, they focus on analyzing data based on their ranks or orderings. Nonparametric methods are often used when the assumptions of parametric methods cannot be met or when the data are measured on an ordinal or categorical scale. Nonparametric tests are generally considered to be more flexible and robust to violations of assumptions, but they may have less statistical power.
To determine which type of statistical analysis is appropriate, you need to consider the nature of your data and the assumptions that can be reasonably assumed to be met. If your data satisfy the assumptions of parametric methods, such as normality and homogeneity of variance, these methods can provide more powerful inference. If the assumptions are not met, or if you are working with categorical or ranked data, nonparametric methods may be more appropriate.