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Checking for normality, transforming non-normal data, sample variability

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STAT 301
Brett Hunter

14 September Checking for Normality Check histogram We can check a normal distribution assumption with the use of a normal probability plot (Q-Q plot) What is it? A scatterplot of the (normal score, observation) pairs A normal score is what we expect the value of the observation to be if it truly came from a normal distribution. What are we looking for? A substantial linear pattern suggests that population normality is plausible Curvature casts doubt on a normal assumption Points falling outside the “bands” are warnings of possible non-normality (when bands are used) Transforming non-normal data If we have non-normal data, we can try to transform the data so that it is approximately normal. Then we can apply statistical methods used for normal data to the transformed data. The common transformations are 1 x Log (x) (base 10 or base e, usually base e unless otherwise stated) √ x So if the data is not normal, try a transformation to see if the transformed data is normal. If it is, we can then use the normal tables to find probabilities involvi
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