[ncl-talk] Z-test?

Dennis Shea shea at ucar.edu
Thu Aug 7 11:24:44 MDT 2014

```There was some offline back and forth on this question.

--------
[1]
Commonly, the letter Z refers to standardized normal distribution:
mean=0.0, stdev=1.0   If you have

x[*] and derive xAvg and xStd

then

x0 = x-xAvg     ; x0 ia 0.0  centered
x0 = x0/xStd    ; normalize by stdev

So, x0 has 0.0 mean and std. dev. of 1.0

EG: Any x0 > 3.0    is significant at the 99.9% level
> 1.96       95%

-------
[2]
It turns out the context of the question was (edited):
I'm doing a correlation analysis of 2 fields and need to know 'which
correlation coefficients are statistically different between the two
experiments.'

The user subsequently sent:

It appears a z-test is very similar to a t-test. The only difference that I
can glean is:
the denominator of the t-test has the standard deviations of the two
samples,
while the denominator of the z-test has the standard deviations of the two
populations.

I found a surprisingly helpful webpage here:
http://www.cliffsnotes.com/math/statistics/univariate-
inferential-tests/two-sample-t-test-for-comparing-two-means

and here:
http://www.cliffsnotes.com/math/statistics/univariate-
inferential-tests/two-sample-z-test-for-comparing-two-means

On Tue, Aug 5, 2014 at 9:02 AM, <lsmith at ucar.edu> wrote:

> Hi gang,
> Has anyone ever used NCL to do a Z-test?  It is a statistical test
> involving the null hypothesis and a normal distribution (?).
> If so, any tips would be most appreciated!
> Thanks!
> -Lesley
>
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