## 95% Confidence Intervals (Correlation) w/o Fisher Z

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# 95% Confidence Intervals (Correlation) w/o Fisher Z

I am trying to determine confidence intervals for a correlation, but without using Fisher's Z as the Ho=0 and Ha(do not) equal 0.  So no Fisher Z required.

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## Re: 95% Confidence Intervals (Correlation) w/o Fisher Z

[ Edited ]
Posted in reply to AsthmaticRunner

Why you wouldn't accept the probability under H0: rho=0 produced by PROC CORR, I have no idea.  Even if it uses the z transform, wouldn't it produce the correct probability?

However, if you must.  Using the "testing rho=0" section of Estimation and Confidence Intervals in notes for Introduction to Statistics at Andrews.edu, it looks like you can calculate t=r•sqrt((n-2)/(1-r2)), where r is your sample correlation.  You can compare your value ot t against the critical values for n-2 degrees of freedom and alpha level of your choice.

Assuming you know your N and r in, say, dataset mycorrs, you can do this:

data want;
set mycorrs;
df=n-2;
alpha=0.05;
sample_t=r*sqrt(df)/(1-r**2);

prob_abs_t=probt(abs(sample_t),df);
prob_abs_r_eq_0=2*(1-prob_abs_t);

lower_critval=tinv(alpha/2,df);
upper_critval=-1*lower_critval;

put 'Sample stats: ' r= n= sample_t=  ' Prob >|r| under H0: ' prob_abs_r_eq_0;

if lower_critval <= sample_t <= upper_critval then put "H0: rho=0 is not rejected at " alpha=;
else put "H0: rho=0 is rejected at " alpha=;
run;

Lots of extra stuff in this program, but it is not clear what precisely you want.

Added two minutes later: you really might want to put this question in the Analytics section, sub-section IML.

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