Final answer:
The main difference between parametric and nonparametric procedures is that parametric procedures assume a specific distribution of the data, while nonparametric procedures do not and are more flexible, especially when data doesn't follow a normal distribution or when its distribution is unknown.
Step-by-step explanation:
The key difference between parametric and nonparametric procedures lies in the assumptions they make about the underlying distribution of the data. Parametric procedures assume that the data follows a certain distribution, typically a normal distribution, which allows for the estimation of parameters such as mean and variance. Consequently, these procedures utilize specific probability distributions and are equipped to infer population characteristics from sample data.
Nonparametric procedures, on the other hand, do not make such strict distributional assumptions. They are used when there is no suitable parametric test available or when the assumptions for parametric tests are violated. Nonparametric methods are more flexible and can be applied to data that does not conform to any particular distribution, making them especially useful with ordinal data or when the data's underlying distribution is unknown or non-normal.
The choice of mathematical model, whether parametric or nonparametric, can significantly impact the conclusions drawn from statistical analyses. While parametric models are built upon a null hypothesis and often involve setting thresholds for Type I errors to determine significance, nonparametric models are free from these constraints, providing a more subjective-free approach to statistical practice.