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I am studying a variable on 50000 observations, I have applied a cox box transformation to make it normal, but even with transformation the kolmogorov smirnof and the anderson darling test tells that my distribution is not normal, given the qqplot that I have, and the number of observations can I say that my variable is approximately normal? I want to use parametric test but all the test rely on the normality assumption

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  • $\begingroup$ Since it is a statistics related question, I think it would be better if you ask it on www.stats.stackexchange.com or www.math.stackexchange.com. $\endgroup$
    – Ankit Seth
    Commented Mar 27, 2018 at 9:20

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Your data is already binned. You should do a Chi-Squared test to see if the hypothesis that your data is normally distributed is correct. You can refer to this question to see how you can go about this.

You will set your baseline as the Normal distribution with the mean and variance from your dataset. Then you will test the difference in expected value between the Normal distribution and yours.

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Many will tell you that normality tests are overly sensitive, especially given that most statistical tests are robust to even gross departures from normality. If you are very concerned, conduct a parametric test anyway along with a nonparametric, and if the end results agree, stick with the parametric.

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  • $\begingroup$ I have used a box-cox transformation to get a normal distribution $\endgroup$
    – youngam
    Commented Mar 27, 2018 at 22:12
  • $\begingroup$ Yes, and that's fine. I just wouldn't worry too much if that transform fails a normality test. Normality tests are overly sensitive. $\endgroup$
    – HEITZ
    Commented Mar 27, 2018 at 22:16

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