<div dir="ltr">There was some offline back and forth on this question.<div><br></div><div>--------</div><div>[1]</div><div><span style="font-family:arial,sans-serif;font-size:13px">Commonly, the letter Z refers to standardized normal distribution: </span></div>
<div><span style="font-family:arial,sans-serif;font-size:13px">mean=0.0, stdev=1.0 </span><span style="font-family:arial,sans-serif;font-size:13px">If you have</span><span style="font-family:arial,sans-serif;font-size:13px"> </span></div>
<br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px"> x[*] and derive xAvg and xStd</span><br style="font-family:arial,sans-serif;font-size:13px"><br style="font-family:arial,sans-serif;font-size:13px">
<span style="font-family:arial,sans-serif;font-size:13px">then</span><br style="font-family:arial,sans-serif;font-size:13px"><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px"> x0 = x-xAvg ; x0 ia 0.0 centered</span><br style="font-family:arial,sans-serif;font-size:13px">
<span style="font-family:arial,sans-serif;font-size:13px"> x0 = x0/xStd ; normalize by stdev</span><br style="font-family:arial,sans-serif;font-size:13px"><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">So, x0 has 0.0 mean and std. dev. of 1.0</span><br style="font-family:arial,sans-serif;font-size:13px">
<br style="font-family:arial,sans-serif;font-size:13px"><div style="font-family:arial,sans-serif;font-size:13px">EG: Any x0 > 3.0 is significant at the 99.9% level<br></div><span style="font-family:arial,sans-serif;font-size:13px"> > 1.96 95% </span><div>
<span style="font-family:arial,sans-serif;font-size:13px"><br></span></div><div><span style="font-family:arial,sans-serif;font-size:13px">-------</span></div><div><span style="font-family:arial,sans-serif;font-size:13px">[2] </span></div>
<div><span style="font-family:arial,sans-serif;font-size:13px">It turns out the context of the question was (edited):</span></div><span style="font-family:arial,sans-serif;font-size:13px">I'm doing a correlation analysis of 2 fields and need to know 'which</span><br style="font-family:arial,sans-serif;font-size:13px">
<span style="font-family:arial,sans-serif;font-size:13px">correlation coefficients are statistically different between the two</span><br style="font-family:arial,sans-serif;font-size:13px"><div><span style="font-family:arial,sans-serif;font-size:13px">experiments.'</span><span style="font-family:arial,sans-serif;font-size:13px"> </span></div>
<div><span style="font-family:arial,sans-serif;font-size:13px"><br></span></div><div><span style="font-family:arial,sans-serif;font-size:13px">The user subsequently sent:</span></div><div><br></div><span style="font-family:arial,sans-serif;font-size:13px">It appears a z-test is very similar to a t-test. </span><span style="font-family:arial,sans-serif;font-size:13px">The only difference that I can glean is:</span><br style="font-family:arial,sans-serif;font-size:13px">
<span style="font-family:arial,sans-serif;font-size:13px">the denominator of the t-test has the standard deviations of the two samples,</span><br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">while the denominator of the z-test has the standard deviations of the two populations.</span><br style="font-family:arial,sans-serif;font-size:13px">
<br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">I found a surprisingly helpful webpage here:</span><br style="font-family:arial,sans-serif;font-size:13px">
<a href="http://www.cliffsnotes.com/math/statistics/univariate-inferential-tests/two-sample-t-test-for-comparing-two-means" target="_blank" style="font-family:arial,sans-serif;font-size:13px">http://www.cliffsnotes.com/<u></u>math/statistics/univariate-<u></u>inferential-tests/two-sample-<u></u>t-test-for-comparing-two-means</a><br style="font-family:arial,sans-serif;font-size:13px">
<br style="font-family:arial,sans-serif;font-size:13px"><span style="font-family:arial,sans-serif;font-size:13px">and here:</span><br style="font-family:arial,sans-serif;font-size:13px"><a href="http://www.cliffsnotes.com/math/statistics/univariate-inferential-tests/two-sample-z-test-for-comparing-two-means" target="_blank" style="font-family:arial,sans-serif;font-size:13px">http://www.cliffsnotes.com/<u></u>math/statistics/univariate-<u></u>inferential-tests/two-sample-<u></u>z-test-for-comparing-two-means</a><br style="font-family:arial,sans-serif;font-size:13px">
<div><span style="font-family:arial,sans-serif;font-size:13px"> </span><br style="font-family:arial,sans-serif;font-size:13px"><div class="gmail_extra"><br><br><div class="gmail_quote">On Tue, Aug 5, 2014 at 9:02 AM, <span dir="ltr"><<a href="mailto:lsmith@ucar.edu" target="_blank">lsmith@ucar.edu</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">Hi gang,<br>
Has anyone ever used NCL to do a Z-test? It is a statistical test<br>
involving the null hypothesis and a normal distribution (?).<br>
If so, any tips would be most appreciated!<br>
Thanks!<br>
-Lesley<br>
<br>
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