# skew and kurtosis using std error

#### kalbright36

##### New Member
Im using "frequencies" on SPSS Student version. We are supposed to determine skewness and curtosis by dividing each by respective std error, then looking up that number in the z-score table.
i. e. the value for skewness is 6.887. The z-score table does not go that high, so this means the distribution is skewed to the right, positive skew.
If this were the value for kurtosis, would this mean leptokurtosis since it is a large, positive number?
But having a negative value for skew or kurtosis doesn't necessarily mean negative skew or platykurtosis, right?
What would numbers look like for negative skew? For platykurtosis? I'm assuming they would not be found in the z-score table either. THANKS!

#### JohnM

##### TS Contributor
Without having access to SPSS, it's pretty difficult to answer software questions, but here's some general info on skewness indices:

skewness

a perfectly symmetrical distribution will have a skewness of 0 - a negative number indicates a distribution skewed to the left (the more negative, the more skewed it is), a positive number indicates that it's skewed to the right (the more positive, the more skewed it is)

kurtosis

a perfect normal distribution will have a kurtosis of 3.0
if it's less than 3, it's platykurtic (flatter) - the lower it is, the flatter it will be
if it's more than 3, it's leptokurtoc (more peaked) - the higher it is, the "pointier" it will be

#### monu_anupam23

##### New Member
Dear Bright,
I would also second John on this problem. The skewness in the normal distribution is 0. any no. less than 1 would mean that the data is skewed to the left and anything positive would mean that data is skewed to the right.
On the other hand the kurtosis of a normally distributed curve is 3. any no. more than this means that the data would become more pointed that is leptokurtic and platykurtic if kurtosis is less than 3, i.e platykurtic, and that data would take a flater curve. So in your case it is leptokurtic.

#### kalbright36

##### New Member
Dear friends,
The numbers that you are talking about--are they the z-scores or the initial values for skewness (or kutosis)?
If the initilal value is negative and it is divided by its std error (still negative). Once I look up a z-score for it, is that also negative?
Thanks so much for your help!

#### JohnM

##### TS Contributor
They're initial values.

Since a standard error must be positive, then dividing something by it will not change the sign, so yes, a negative number divided by the standard error will always be negative.