Test for normality with values between 0 and 1

[Larissa Nederland]

Hi all,

I am relatively new to stata and statistics in general.
To start off my analysis I want to test for normal distribution. However, my observations are mostly ranging between 0 and 1 (as it tests for the accuracy of a certain other number) There are no negative values. What should I do to test if this data is normally distributed? If I run a normal test for normality, it seems as if it treats all variables between 0 and 1 as equal. Is there a way to adjust this?

Thanks for your help!

[Friedrich Huebler]

Which "normal test for normality" did you try? Stata offers several tests for normality.

help sktest
help swilk
help sfrancia

[Clyde Schechter]

If the values of your variable are actually restricted to lie between 0 and 1, then, in principle, it cannot be a normally distributed variable. The normal distribution with any mean and any positive variance has unbounded support.

Now, depending on the combination of sample size being small enough and the mean being located in the 0-1 interval and the sd being small enough, it may be that everything in your sample happens to lie between 0 and 1.

There are several different tests for normality in Stata. One of them is part of the output of the -ladder- command (which also looks at selected transforms of the variable). Another is the -swilk- command. You can also use -ksmirnoff-. There is also the graphical approach with -qnorm-.

So you have many options. But I can't resist asking why you want to do this in the first place. The circumstances where it really matters whether a variable has a normal distribution is pretty rare. And these statistical tests for normality are generally not helpful in those circumstances.

[Marcos Almeida]

Hello Larissa,

Friedrich and Clyde gave very clever recommendations. Apart from these excellent suggestions, and considering you said you're "relatively new to Stata and statistics in general", I wish to add that having the histogram of this particular variable ( . histogram name_variable) could be a nice start to check its pattern of distribution. Also, comparing the mean and the median, as well as checking skewness and kurtosis (. summarize name_variable, detail). Finally, you didn't inform the number of observations, neither presented a hint over the decimals... Both have a potential role in the distribution. If the number of observations is too low, you may eschew the normality assumption "tout court".

Hopefully that helps.

Best,

Marcos

[Carlo Lazzaro]

Larissa.
just echoing Others' skillful insights, without more details concerning your sample size, I would recommend you a visual inspection of the distribution of your data before reying on the result of one of the abovementioned normality test.
As an aside, as Clyde pointed out, i would first ask myself whether the normality of my variable is so relevant for carrying out any furtehr statistical analysis.
Normality is something we heard about during statistcs classes, but it is really hard to find in the real world.