Re: What, exactly, is Z-score?

[TQuinn211@xxxxxxx]

In a message dated 98-08-24 22:25:09 EDT, rjb@xxxxxxxxxxxxxxxxxxx writes:

<< 
 >so... when somebody is talking about a value that is 3 standard deviations
 >from the average, the z-score would be 3
 >
 >Nothing magical about it at all.
 
 Nothing magical, but let's be precise.  If the value is ABOVE the average
 its z-score is 3. If the value is BELOW the average, then its z-score would
 be -3
  >>


Gee rjb,

Since I didn't indicate in my response if it was above or  below, nor left nor
to the right of the average score, I would have thought it would have been
intuitively obvious that the direction from the average must be taken into
consideration and that is the primary purpose of the + or - sign.

So if it makes you any happier and to clear up any confusion concerning
preciseness, if the observed value is 3 standard deviations to the LEFT of the
population average, then the the Z score is a minus 3. If it is 3 standard
deviations to the RIGHT of the population average then it would be a + 3.
Unless of course you are using the Y-axis as your scale then the reference
values would be rotated accordingly.

In addition, don't forget to do the appropriate tests for normality on the
data using the skewness and kurtosis testing methodologies, and if the tests
for normality fail, perform the appropriate adjustments to your z score
calculations to avoid false  probability assessments.


 Don't forget to take into consideration that the population average can never
be truly known for an infinite data set so it might be  more appropriate to
use a student's t distribution for your probability estimates correcting of
course for the apppropriate degrees of freedom based on the sample size
employed and the number of estimates derived from the sample data for the
population parameters. Additional adjustment will need to be made if it is
determined that the underlying distribution has failed the tests for normality
and the use of the  Gaussian distribution model is deemed inappropriate.


Is that precise enough?

Also is it safe to assume you DO know how to handle the necessary adjustments
when it is detemined the underlying distribution is NOT normal?


All the best,

Terry Quinn.


P.S. For the record. the x-bar indicator I previously supplied to this forum
does in fact take these issues into account in their construction.

In addition, Those of you who may be trying them on intraday charts where the
time interval is less than 10 minutes, are most likely seeing a whipsaw
effect.

That is because the underlying assessment for  statistical independence used
in their construction fails for price date plotted on an interval of less than
10 minutes.