03-02-2016 09:08 PM
In what context?
Also, is it a one sided or two sided test?
Check the basic definitions.
Back in the day you'd have the read the Z cut off value from the table:
So if alpha was 0.05 and it was a two sided score, divide alpha in half for 0.025. Look up that value (or 1-0.025=0.0975) in the table and the corresponding Z critical value is 1.96 (or -1.96). You can use this number to compare to the Z score you calculate in your data, if the Z-Score is less than the cutoff you accept your null hypothesis, otherwise you reject your null hypothesis.
In the inverse manner, you can calculate your Z-Score, find the area under the curve and that is your p-value, which is compared to your cutoff level.
The one vs two sides is important here, if it was a one sided test, you would look up 0.05 in the table which would give you a critical value of ~1.645
I think I'm mangling this but hopefully it helps to clear up things.
This is more of a stats than SAS question...
03-03-2016 11:12 AM
Perhaps you mean "In SAS, how can I compute the z-score from the alpha value?
The answer is to use the QUANTILE function. Reeza already gave the explanation of a two-sided critical value,
so here is the SAS code.
ZLeft (=-1.96) is the value such that the area under the normal density curve to the left of ZLeft is 0.025.
ZRightt (= 1.96) is the value such that the area under the normal density curve to the right of ZRight is 0.025.
The area under the curve between ZLeft and ZRight is 0.95.
For a probability distribution such as the normal distribution "area under the curve on an interval" is equivalent to "probability that a random variable will take a value in that interval."
data A; alpha = 0.05; zLeft = quantile("Normal", alpha/2); zRight = quantile("Normal", 1-alpha/2); run; proc print; run;