alpha and z value

Posts: 59

alpha and z value

how alpha and z value is related ?

If alpha is 0.05 then what will be the value of z?

Grand Advisor
Posts: 17,329

Re: alpha and z value

In what context?

Also, is it a one sided or two sided test?


Check the basic definitions. 


Z Score:


Alpha :


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...




Posts: 3,406

Re: alpha and z value

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); 

proc print; run;
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