I have given a data and I have to check the data if it's normally distributed and if not I have to transform the data into normality. the histogram of the data

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I had done shapiro-wilk normality test and p-value is clearly smaller than 0.05.

I had tried transforming to log, sqrt. But it is still not normally distributed.

Is there other ways to transfer to normality or is it impossible for some data? If that's impossible I have explain why.


As reply to the comments: that's the part of assignment. It says I either of transform to normal distribution. If it's not possible I have to say why is it not possible.

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    $\begingroup$ Why do you want to transform to normality? Did you try Box-Cox transform? $\endgroup$ – kjetil b halvorsen May 31 '16 at 8:26
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    $\begingroup$ "I have to transform the data into normality" I seriously doubt that you have to do that. $\endgroup$ – Roland May 31 '16 at 9:12
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    $\begingroup$ Age in completed years cannot be normal -- it's discrete. But why would you need a variable like Age to ever be normal? $\endgroup$ – Glen_b -Reinstate Monica May 31 '16 at 9:30
  • $\begingroup$ and positive ;-) $\endgroup$ – ocram May 31 '16 at 9:40
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    $\begingroup$ It might help to show us the exact text of the prompt for this assignment. $\endgroup$ – Kodiologist May 31 '16 at 12:12

You have a number of issues here.

  1. the Q-Q plot shows that your data are discrete -- they only take integer values (ages in completed years). So you know immediately that any transformation of the data will give a discrete result; this makes it impossible to actually transform to normality (though one could get reasonably close to normality).

  2. The Q-Q plot indicates that the distribution from which the data were drawn is light-tailed (in both tails) so transformations designed to reduce a heavy right tail (like log or square root) won't get you to normality anyway -- they'll make that light right tail even lighter. You might find a simple power-ladder transformation that makes the distribution a bit more symmetric looking, but it won't be normal. However ...

  3. Why would you need a variable like Age to be normal? (What purpose would that serve?)

This seems to be a strange thing to get you to do and I wonder whether the person who has asked for it has misunderstood something (e.g. about regression assumptions)


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