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My scale's data is normally distributed, except for one dimension of the scale... The overall data has a normal distribution along with several dimensions in the scale.

First, suppose that all data are normally distributed, can I use non-parametric test? Is there a rule which requires the use of parametric tests when data is normally distributed. I know parametric is more powerful but is it a problem to insist on non-parametric test?

Second, while deciding for the types of tests, should I check total scale's k-s values for deciding whether data is normally distributed or... first total, then dimensions one by one... what should one do if all dimensions are normally distributed except for one dimension?

Thanks

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    $\begingroup$ 1. None of your scales are actually normal. It's pointless to test it (but if you must test, why use one with such low power in the tails?). 2. you can have parametric non-normal methods. 3. non-parametric is not the same as non-normal; you can use non-parametric methods on anything for which the assumptions would be reasonable. However, all of these questions are answered on site already. $\endgroup$ – Glen_b -Reinstate Monica Nov 2 '17 at 0:21
  • $\begingroup$ See for example -- stats.stackexchange.com/questions/41764/… and stats.stackexchange.com/questions/266586/… which relate to several of the issues here $\endgroup$ – Glen_b -Reinstate Monica Nov 2 '17 at 0:51
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First, yes, you can use a non-parametric test on normally distributed data.

Second, it is not the data which matters, usually. E.g. in ordinary least squares regression, what matters is the distribution of the errors. And some parametric tests don't require normality of anything.

Third, parametric tests are more powerful for the purpose for which they are intended if their assumptions are met. Often, a non-parametric test has slightly different purposes.

Finally, it would help if you told us the actual problem you are trying to solve. Your first paragraph about dimensions of a scale is unclear.

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  • $\begingroup$ Hi Peter, many thanks for your answer, what I a mean is that I have one scale with the dimensions of love and happiness. My sample is below 20. Should I check normality ? or even if the data is normally distributed, is it good to turn to non-parametric as Gosling (2004) tells the group of more than 30 require normality test and parametric tests... What do you suggest? $\endgroup$ – Xaxen Nov 5 '17 at 18:30
  • $\begingroup$ With a small N, tests of normality will be useless - they will only be significant if the nonnormality is blatantly obvious. What you should depends on what you are trying to find out. $\endgroup$ – Peter Flom - Reinstate Monica Nov 5 '17 at 18:33

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