# Z-score for Skewness and Kurtosis

#### Bruno

##### New Member
Hi, I have a sample of data (about a hundred numbers) and I would like to roughly estimate whether they follow a normal distribution or not. From what I understand, two useful parameters are the z-scores for skewness and kurtosis. According to this site, for example, they are defined as

Z_skew = skew / Standard_Error(skew)
Z_kurtosis = kurtosis / Standard_Error(kurtosis)

I'm just a bit confused about this: how do I calculate the standard error of the skewness, or kurtosis?
Thanks

Bruno

#### lilithlacuna

##### New Member
skewness: b1=sum(xi-mean)^3/(N-1)*s^3 for ND b1=0

tested by normal deviate z = sqrt(b1(N+1)(N+3)/6(N-2))

kurtosis: b2=sum(xi-mean)^4/(N-1)*s^4 for ND b2=3

tested by normal deviate z =
(b2-3+6/(N+1))sqrt((N+1)(N+1)(N+3)(N+5)/24N(N-2)(N-3))

(ref:http://www.math.yorku.ca/Who/Faculty/Monette/Ed-stat/0277.html)

If you have access to SPSS, the 'explore' option will automatically calculate both skewness/kurtosis and corresponding errors for you

#### lilithlacuna

##### New Member
P.S. The best method of checking normality is to plot a histogram: if the distribution is relatively bell shaped (i.e. graph lumped high in the middle and tailing at either end) and doesn't extend to a greater extent on one side than on the other, proceed with parametric stats. Also, check if mean and median are roughly the same: if skewing is a concern, they will differ appreciably as the mean will be drawn out to the side of the skewing.

E

#### elnaz

##### Guest
Hello

if you want survey on your data that are your data normal ?
you can do normality test that there is in every statistical software
ofcaurse dear Lilithacuna said true that you can compute skewness and kurtosis in every statistical software, too.
if you dont have statistical sotware , tell me and send your data i will do for you.

i hope you will be succeed.
Best regards
Elnaz