Examining F test results to detect assumption violations

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All the following results are provided as part of an F test for variance.

  • Normality tests:
  • If the assumptions for the F test hold, the values from each sample should come from a normal distribution. Departures from normality can suggest the presence of outliers in the data, or of a nonnormal distribution in one or more of the samples. The normality test will give an indication of whether the populations from which the samples were drawn appear to be normally distributed, but will not indicate the cause(s) of the nonnormality. The smaller the sample size, the less likely the normality test will be able to detect nonnormality.
  • Histograms:
  • The histogram for each sample has a reference normal distribution curve for a normal distribution with the same mean and variance as the sample. This provides a reference for detecting gross nonnormality when the sample sizes are large.
  • Boxplots:
  • Suspected outliers appear in a boxplot as individual points o or x outside the box. If these appear on both sides of the box, they also suggest the possibility of a heavy-tailed distribution. If they appear on only one side, they also suggest the possibility of a skewed distribution. Skewness is also suggested if the mean (+) does not lie on or near the central line of the boxplot, or if the central line of the boxplot does not evenly divide the box. Examples of these plots will help illustrate the various situations.
  • Normal probability plot:
  • For values sampled from a normal distribution, the normal probability plot, (normal Q-Q plot) has the points all lying on or near the straight line drawn through the middle half of the points. Scattered points lying away from the line are suspected outliers. Examples of these plots will help illustrate the various situations.

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