Week III DQ 1
Due Thursday (Extended from previous assignment)
Review the histograms you developed in Week 2. Keeping these in mind, discuss the following items using your own words to convey your understanding. Include examples when necessary.
Write a 250- to 300-word response to the following:
What is the difference between a normal distribution and a skewed distribution?
What causes a skew and how might a researcher deal with skewed data?
Under what conditions would it be acceptable to allow skewed variables in a research study?
Include your own experience as well as 2 citations that align with or contradict your comments as sourced from peer-reviewed academic journals, industry publications, books, and/or other sources. Cite your sources according to APA guidelines. If you found information that contradicts your experience, explain why you agree or disagree with the information.
Due Monday
Review your classmates’ initial post and provide additional information and/or insights related to the examples they offered. You should respond to at least one classmate in a minimum of 150 words.
Respond to Derrick
Employee Performance Ratings (Normal) vs. Annual Bonuses (Positively Skewed)
A normal distribution is symmetric and bell-shaped, with the mean, median, and mode all equal and located at the center. It is symmetric and bell-shaped, with most data clustered around the mean. For instance, adult IQ scores typically follow a normal distribution, with an average score of 100 and less frequent deviations.
In contrast, Skewed distributions are asymmetrical and stretched more to one side. Positively skewed distributions have a tail extending to the right, indicating a few higher values pull the mean above the median. Conversely, negatively skewed distributions have a tail extending to the left, indicating lower scores affect the mean. Examples include annual income.
Several data skew can be caused by natural limits in measurement scales, outliers, or underlying population characteristics. For example, a researcher collecting test scores in a class with high performance, but low performance may have a negative skew, as most students perform well but a few perform poorly.
Dealing with Skewed data can be normalized using transformations like log, square root, or inverse, making it suitable for parametric statistical tests. Non-parametric methods, such as log transformation, do not assume a normal distribution. For example, in a study on employee tenure, a right-skewed histogram was stabilized using a log transformation. However, it is not always necessary to transform or exclude skewed data. Under certain conditions, such as when the skew reflects a meaningful aspect of the phenomenon or when using robust statistical techniques, it may be appropriate to retain skewed variables. For instance, in behavioral economics, income distribution is often left skewed and transforming it would obscure real-world disparities. Skewness should not be automatically corrected unless it threatens the validity of assumptions behind specific statistical techniques.
Generalized linear models (GLMs) allow for skewness in assumptions, which can affect hypothesis testing. Researchers must assess the distribution's impact on the model and if acceptable, skewness might be acceptable, especially in large samples. In a histogram assignment week 2, skewed variables like income and performance ratings were identified. The natural skew in the data was preserved for authenticity, highlighting meaningful disparities in performance-based bonuses. The Central Limit Theorem helps stabilize results.
In summary, Normal distributions are ideal for statistical procedures due to their symmetry and predictable properties, but skewed distributions are common in real-world data. Understanding their causes helps researchers decide on the most appropriate transformation, alternative methods, or acceptance of skew.
References
Gravetter, F. J., & Wallnau, L. B. (2016). Statistics for the Behavioral Sciences (10th ed.). Cengage Learning.
Osborne, J. W. (2010). Improving your data transformations: Applying the Box-Cox transformation. Practical Assessment, Research, and Evaluation, 15(12), 1–9. https://doi.org/10.7275/QVMC-8Y08
