Also do I need to test the normality for the categorical data?


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    $\begingroup$ This question has been answered before. See also: stats.stackexchange.com/questions/2492/… and stats.stackexchange.com/questions/3514/…. You should make sure your question has not already been asked and answered before posting it as a new question. $\endgroup$ – Marquis de Carabas Jul 4 '15 at 10:01
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    $\begingroup$ If it's categorical data, it can't be normal.... Only variables that are least approximately continuous could possibly be (close to) normal. If this is unclear, please explain what you mean by "categorical" and/or give examples of categorical variables. $\endgroup$ – Nick Cox Jul 4 '15 at 10:12
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    $\begingroup$ Why do you feel you need to test normality? $\endgroup$ – Glen_b Jul 4 '15 at 12:14
  • $\begingroup$ The very best test is easy to compute, has an extremely low false positive rate in most settings, and a fabulous false negative rate of zero: without even looking at the data, conclude that the underlying distribution is non-normal. $\endgroup$ – whuber Jul 4 '15 at 14:52