# What does it mean by “The statistic is asymptotically distributed as N(0,1).”

I'm reading a paper Mardia (1974) about multivariate normal tests.

There is a line that says "The statistic is asymptotically distributed as N(0,1)."

Now, I have calculated this value for one of my data sets, and it is -5.8, and for another set it is 0.87.

I am guessing it is something to do with Z scores?

For example, if this value is between +/- 2, then I have a 0.954 chance of it being normal (replace proper null hypothesis terminology here).

If i'm correct that would mean my "statistic" is just like a sample std deviation?

• This is related to convergence in distribution. – StubbornAtom Jun 26 '18 at 5:03

## 1 Answer

Yes, the sample standard deviation is a statistic. If a statistic s(x) of some data x is asymptotically distributed as N(0,1), that generally just means that it is distributed as N(0,1) sample size(x) approaches infinity.

• so what i say about it being between -2 and 2 is correct? Basically I have this statistic, I need to know if it then means my test for normal has passed – CptLightning Jun 26 '18 at 22:41