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Discuss the assumptions of parametric statistical testing versus the assumptions of nonparametric tests. Discuss why a researcher would select a nonparametric approach based on the data and when they would select parametric tests for their data set. Does it matter what type of variables have been collected in the dataset?
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SEU Parametric and Nonparametric Tests Discussion
Introduction:
Parametric and nonparametric statistical tests are two different approaches used in data analysis. Parametric tests make certain assumptions about the population from which the data is derived, while nonparametric tests do not rely on these assumptions. In this response, we will discuss the assumptions of parametric and nonparametric tests and explore reasons why a researcher might choose one approach over the other based on their data. We will also discuss whether the type of variables collected in the dataset affects the choice of test.
Assumptions of Parametric Statistical Testing:
Parametric tests assume that the data is normally distributed in the population, the sample is randomly selected from the population, and the variances in different groups being compared are equal. These assumptions are often fundamental in parametric tests, such as t-tests and analysis of variance (ANOVA). Additionally, parametric tests assume that the variables being analyzed are measured on an interval or ratio scale.
Assumptions of Nonparametric Tests:
Nonparametric tests do not assume any specific distribution of the data in the population. These tests are often used when the data is not normally distributed or when the population assumptions necessary for parametric tests cannot be met. Nonparametric tests, such as the Mann-Whitney U test and the Kruskal-Wallis test, are based on ranks or other distribution-free methods. They focus on the order or ranking of the data rather than the magnitude or specific values.
Selection of Nonparametric or Parametric Tests:
Researchers may choose a nonparametric approach when their data does not meet the assumptions of parametric tests. If the data is clearly not normally distributed, skewed, or has outliers, nonparametric tests can provide a more robust analysis. Additionally, nonparametric tests are often used when the variables being analyzed are measured on an ordinal or nominal scale, as they do not rely on the assumption of interval/ratio scale variables.
On the other hand, parametric tests are generally more powerful (i.e., can detect small differences with higher precision) when the assumptions are met. If the data is normally distributed, the variances among groups are equal, and the variables are measured on an interval or ratio scale, researchers might opt for parametric tests. These tests provide more precise estimates and smaller confidence intervals, assuming the assumptions are valid.
Does the Type of Variables Collected Matter?
Yes, the type of variables collected in the dataset can influence the choice of statistical test. If the variables collected are measured on an interval or ratio scale and follow a normal distribution, parametric tests can be employed. However, if the variables are measured on an ordinal or nominal scale, nonparametric tests are more appropriate. It is essential to choose the right test to ensure accurate and reliable data analysis.
In conclusion, parametric and nonparametric tests differ in terms of assumptions and statistical procedures. Researchers select nonparametric tests when the data does not meet the assumptions of parametric tests or when variables are measured on an ordinal or nominal scale. Parametric tests are chosen when the assumptions are met and the variables are measured on an interval or ratio scale. The type of variables collected in the dataset does matter and should be taken into consideration when deciding on the appropriate statistical test.
