Defining normality: what is it, and how do you know if you are normal?

A normal distribution is not a naturally occurring phenomenon, but the assumption of normality is a basic premise for many statistical analyses. If your data is not normal, or approximately normal, certain statistical tests cannot be performed because the results obtained may not be valid. Researchers often go to great lengths to perform tests on their data to determine if their data approximates a normal distribution within certain parameters and reasonable limits. 

So, what is normality and how would you define normality? 

  1. First, do some research on your own and look up three different reputable sources that define normality from a statistical perspective and combine those definitions into one, reasonable, comprehensive definition of normality. You can use your textbook as one source, so you will need to find two additional sources that define normality from a statistical perspective. 
  2. Second, justify your definition by using the sources of information you’ve identified to support your definition of normality. Why is your definition better and more comprehensive than what is currently used in many textbooks?
  3. Finally, find an aviation-related research article that uses the assumption of normality, describe and summarize that study and the analyses used, and explain why the analyses may not be valid if the distribution was not assumed to be normal.
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