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I have one dependent variable and am trying to see if any of my 12 independent variables correlate with it, however I need to check everything for normality.

I understand I need to look at skewness and kurtosis. Does the formula look like the following: skewness score subtracted by mean of condition divided by the standard error of skewness (likewise for kurtosis).

Also are there absolute values that determine whether you should use a parametric/nonparametric test? E.g., skewness number above 2 = non parametric?

I am using SPSS.

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  • $\begingroup$ I think SPSS deducts 3 from the result of the kurtosis calculation, so a normal distribution will have a kurtosis of 0 rather than 3. It's a little trap to watch out for, for e.g. it appears Stata doesn't subtract the 3. $\endgroup$
    – Michelle
    Commented Feb 9, 2012 at 4:30
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    $\begingroup$ Why do you need to check the distributions of the independent variables? Furthermore, because you have separated your 13 variables this way into one dependent one and the rest dependent, one would think that you need to regress the DV on the IVs and check the normality of the residuals. $\endgroup$
    – whuber ♦
    Commented Feb 9, 2012 at 14:17

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The advantage of using Pearson's r is that it can take into account more finely-grained information than the nonparametric methods can. But r is vulnerable to the influence of outliers (which "spoil" a normal distribution) and to other non-normal shapes, which often cause one to underestimate the strength of association if one uses r. But rather than having strict decision rules for the choice of method, what we have are rules of thumb. Normality tests such as the Kolmogorov-Smirnov Test are notoriously unreliable. Yes, it is reasonable, or maybe I should say defensible, to set a criterion of +/-2 for skewness or kurtosis. Then again, with 12*2 such tests, you're fairly liable to get false positives, and so you may want to take steps to deal with the multiple comparison problem.

If I were in your shoes I would instead visually check each variable's histogram, and possibly its Q-Q plot (each is readily available via SPSS's Graphs menu), for marked departures from normality. And I'd make those plots available as an appendix to the assignment you hand in. It will be a useful exercise to see to what degree your instructor agrees with you on what I think comes down to a subjective decision.

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    $\begingroup$ This reply starts out really well, but I am concerned that the remarks about normality tests being "unreliable" could be misinterpreted as meaning those tests do not achieve the confidence and power claimed of them, which is not true. Going further, why then do you then propose a truly ad hoc unreliable normality test (comparing skewness and kurtosis to the interval $[-2,2]$)? Could you indicate why and how this does not contradict your earlier remarks? $\endgroup$
    – whuber ♦
    Commented Feb 9, 2012 at 14:21
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    $\begingroup$ Maybe I did contradict myself. Bottom line is that formal tests of normality are widely found to be unsatisfactory and that we all have to do the best we can with subjective determinations not so much about whether but about the degree to which distributions veer off from normality and how serious are the consequences for a particular procedure. $\endgroup$
    – rolando2
    Commented Feb 10, 2012 at 1:40
  • $\begingroup$ @whuber - I'll add that I didn't "propose" the skewness/kurtosis tests; I was reacting to what user9065 proposed. Maybe my response was not so sound on that point, but I see my larger point on the subjective factor in normality testing is being echoed by the consensus argument forming at stats.stackexchange.com/questions/2492/…. $\endgroup$
    – rolando2
    Commented May 4, 2012 at 21:45
  • $\begingroup$ I probably share many of your opinions, rolando2, but your use of "unreliable" seems infelicitous. AFAIK, the K-S test is extremely reliable: it does exactly what it claims to and does it very well when correctly applied. Perhaps you intended to use a different word, maybe one (if it exists) meaning something like "the interpretation depends on many circumstantial elements including sample size and analytical objectives"? $\endgroup$
    – whuber ♦
    Commented May 4, 2012 at 21:59
  • $\begingroup$ Sounds about right to me. $\endgroup$
    – rolando2
    Commented May 5, 2012 at 18:25
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Suggest you first start by determining the distribution of the independent variables. You can deduce this using t or F statistics with the null hypothesis that if all the independents are of the same distribution then the dependent variable has a given distribution.

Once you are happy with the estimate of the distribution then you start to filter out know distributions using their moments, as you have mentioned, skewness, kurtosis, mean standard deviation etc.

For example we can assume the sum of random variables with normal distribution will almost surely be equal in distribution to the sums ... etc.

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    $\begingroup$ How, specifically, do you propose to test distributions using "t or F statistics"? $\endgroup$
    – whuber ♦
    Commented Feb 9, 2012 at 14:22

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