Kurtosis and Skewness

[Sigma888@aol.com]

Okay ... I just came out of a rather lively debate in a management meeting 
about the validity / usefulness of Kurtosis and Skewness as indicators of change 
from one time sample to another.

Here is the situation ... in the manufacturing environment in which I work, 
the run length (number of units ordered per job) is a critical factor.  In 
fact, our quotes, contracts, estimates, etc., allow for different waste allowances 
and throughput assumptions for smaller [versus larger] units ordered.

Recently, we have experienced a significant change in work mix, e.g.; smaller 
versus larger units ordered.  This is consistent with "just in time" and 
"supply chain management" direction that we have seen in many markets attempting 
to manage their their inventory levels as low as possible to reduce costs but 
not too low as to meet customer demand and satisfaction levels.

We have typically measured our work mix by "average run length".  This would 
be the number of units produced per job.  However, in a recent analysis we 
used the median run length per job as a potential indicator for radical change in 
work mix (which affects schedule, customer satisfaction and certainly net 
income in our industry).  Using the median, our year over year results show 
virtually no difference (11,516 versus 11,419 per job).  The average (or mean) is 
higher (31,748 versus 35,162 per job),

However, the standard deviation is noticeably higher (60.27 versus 68.26) 
this year versus last.  

I interpret this to be insignificant change in median, somewhat in mean, but 
significant change in variation (which would drive the mean higher).

However, some argue that although there are more extreme average job sizes 
year over year (a few much higher and a few a little lower), the majority of 
jobs are centered around the median and have the same higher as they do lower.  
The argument is; kurtosis and skewness ... the two indicators that Shewart 
proclaimed as superfluous.

For my data on the above;

Kurtosis = 35.5 versus 27.1
Skewness = 5.2 versus 4.6

Are the differences here significant?

This is not a test ... it is a question of theory and practice.  What makes 
sense?

Interested in any input you may have.

Thanks,

Vince Vaughn