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Great discussion! Nice explanation of the parametric and nonparametric tests, the importance of meeting the assumptions for those tests, and you provided a great explanation of parametric and nonparametric assumptions. Nonparametric tests don’t have the same assumption requirements as you point out. I know that even if you have a randomly gathered sample of adequate size you can still have data that is not normally distributed- this happened in my research! What preliminary tests would you recommend to determine if the data you collected is normally distributed?
Thank you,
Dr. Mary
reply two
DINA SHARBINI
Discussion: Module 10
COLLAPSE
Discussion: Module 10
In the realm of statistical analysis, researchers often encounter the need to make informed decisions regarding selecting appropriate tests to analyze their data. This decision-making process involves careful consideration of the assumptions underlying parametric and nonparametric statistical tests (Vrbin, 2022). Parametric tests, such as t-tests and ANOVA, rely on assumptions of normality, homogeneity of variance, and interval or ratio scale measurement. In contrast, nonparametric tests, like the Wilcoxon rank-sum test and the Kruskal-Wallis test, operate under fewer distributional assumptions and are more robust to violations of normality. Exploring the assumptions of parametric and nonparametric tests, the circumstances under which researchers might choose one approach over the other, and the impact of variable types on test selection. By understanding these considerations, researchers can make informed choices to ensure the validity and reliability of their statistical analyses.
Parametric tests, such as t-tests, ANOVA, and linear regression, rely on several key assumptions. Normality is a central assumption, as these tests are sensitive to deviations from a normal distribution. Violations of normality can lead to inaccurate results and inflated Type I error rates. Additionally, parametric tests assume homogeneity of variance, meaning that the variability within groups is consistent across all groups being compared. This assumption is particularly critical for ANOVA and regression analyses. Finally, parametric tests require data to be measured on interval or ratio scales, ensuring meaningful interpretation of numerical differences.
Nonparametric tests, exemplified by the Wilcoxon rank-sum test, Kruskal-Wallis test, and Spearman’s rank correlation, are characterized by fewer underlying assumptions when compared to parametric tests. They do not assume a specific distribution for the data and are robust to violations of normality. Instead of analysing the raw data values, nonparametric tests focus on the ranks or orders of observations, making them suitable for ordinal, interval, or ratio scale data. Furthermore, nonparametric tests do not require homogeneity of variance, making them particularly useful for datasets with unequal variances between groups or conditions.
The decision to use parametric or nonparametric tests depends on various factors, including the nature of the data and the assumptions underlying each test. Researchers may opt for nonparametric tests when their data do not meet the stringent assumptions of parametric tests. This is often the case with skewed or non-normally distributed data, small sample sizes (Zhou et al., 2023), or datasets with heterogeneous variances. Nonparametric tests provide reliable results even in the presence of such violations. Alternatively, when data meet the assumptions of normality, and homogeneity of variance, and are measured on interval or ratio scales, parametric tests are preferred. Under these circumstances, parametric tests typically exhibit greater statistical power than nonparametric tests, enabling a more precise identification of genuine effects. Moreover, parametric tests often provide more precise estimates of population parameters (Hopkins et al., 2018), enhancing the interpretability of results.
The type of variables collected in the dataset influences the choice between parametric and nonparametric tests. Continuous variables are typically analyzed using parametric tests, provided that the assumptions of normality and homogeneity of variance are met. Nonparametric tests may be used as an alternative for continuous variables when these assumptions are violated or when dealing with small sample sizes. Categorical or ordinal variables are often analyzed using nonparametric tests, as they do not require distributional assumptions. However, parametric tests can be applied to categorical variables if they can be transformed into numerical scores and meet the assumptions of normality and homogeneity of variance (Lee, 2020).
In conclusion, researchers should carefully evaluate the assumptions of parametric and nonparametric tests and consider the characteristics of their data when selecting an appropriate statistical approach. Both parametric and nonparametric tests have their advantages and limitations, and the choice between them ultimately depends on the specific research context and data properties.
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