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Under what circumstances might the assumption of the underlying population being normally distributed be inappropriate when...

Under what circumstances might the assumption of the underlying population being normally distributed be inappropriate when considering a single sample of a continuous variable?

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Answer #1
  • When considering a single sample of a continuous variable, it would be inappropriate to assume that the data is normal if the data strongly rejects the null hypothesis that the data is from a normal distribution.
  • A normal Q-Q plot can be drawn and if most of the points on the plot are close to the line passing though the 25th and the 75th quantile, then the data is said to follow a normal distribution, otherwise there isn't sufficient evidence to assume the normality of the data.
  • Decision regarding normality of data can also be made via statistical tests like, Chi-squared test for goodness of fit, Shapiro's test, Ryan-Joner test, Anderson-Darling test, etc.

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