Critical values vs p-values

[AlexeyS]

Hello, i don't know where is my error.

Suppose i have a normal distribution, and to calculate critical values :

data criticalvalue;
alpha=0.05;
normal_left = round(quantile('NORMAL', alpha), .001);
normal_right = round(quantile('NORMAL', 1-alpha), .001);
normal_two = round(quantile('NORMAL', 1-alpha/2), .001);
run;

Now, i wan to calculate p-values, based on critical values :

data p_values;
zstat = -1.645;
normal_left = probnorm(zstat);
normal_right = probnorm(abs(zstat));
normal_two = 2*(1 - probnorm(abs(zstat)));
run;

My question is : why p-value normal_two is not equal to probability for two_sided when i calculated critical value(1-alpha/2)? In p-value i got 0.1, and probability for critical value i got 0.975. So, what's wrong?

Thank you

[PaigeMiller]

It's not a linear translation, you have the wrong value of zstat.

data p_values;
zstat = -1.645;
normal_left = probnorm(zstat);
normal_right = probnorm(abs(zstat));
normal_two = 1-probnorm(1.96);
run;

[AlexeyS]

Thank you

[PaigeMiller]

Or another solution

data p_values;
zstat = -1.645;
normal_left = probnorm(zstat);
normal_right = probnorm(abs(zstat));
normal_two = 1-probnorm(quantile('NORMAL', 1-alpha/2));
run;

[PGStats · Accepted solution]

Or to show the symmetry:

 71         data _null_;
 72         alpha=0.05;
 73         q_left = round(quantile('NORMAL', alpha), .001);
 74         q_right = round(quantile('NORMAL', 1-alpha), .001);
 75         q_two = round(quantile('NORMAL', 1-alpha/2), .001);
 76         p_left = probnorm(q_left);
 77         p_right = 1 - probnorm(q_right);
 78         p_two =  2 * (1 - probnorm(q_two));
 79         put (_all_) (=/);
 80         run;
 
 alpha=0.05
 q_left=-1.645
 q_right=1.645
 q_two=1.96
 p_left=0.0499849055
 p_right=0.0499849055
 p_two=0.0499957903