# sample size calcs - why do these produce different results

#### msecic

##### New Member
What are the interpretations for each of these?

data a;
input z p q e;
cards;
1.96 0.95 0.05 0.05
;
data b;
set a;
n=(z*z*p*q)/(e*e);
run;
proc print; run;

****************************;

proc power;
onesamplefreq test=z method=normal
sides = 2
alpha = 0.05
nullproportion = 0.90
proportion = 0.95
ntotal = .
power = 0.9;
run;

#### hlsmith

##### Less is more. Stay pure. Stay poor.
I think it would help to better describe what you are trying to do. Are you just trying to recreate the one-sample z-test sample size formula?

If so, where is your power value in the first equation? Can you reference or send a link to the formula you are trying to use?

#### hlsmith

##### Less is more. Stay pure. Stay poor.
I believe this is what you are trying to do:

Code:
[SIZE=2][FONT=Courier New][COLOR=#000080][SIZE=2][FONT=Courier New][COLOR=#000080][B][SIZE=2][FONT=Courier New][COLOR=#000080]proc[/COLOR][/FONT][/SIZE][/B][/COLOR][/FONT][/SIZE][/COLOR][/FONT][/SIZE][B][FONT=Courier New][SIZE=2][COLOR=#000080][FONT=Courier New][SIZE=2][COLOR=#000080][FONT=Courier New][SIZE=2][COLOR=#000080]power[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/B][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2];[/SIZE][/FONT]
[/SIZE][/FONT][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff]onesamplefreq[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff]test[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2]=z [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff]method[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2]=normal[/SIZE][/FONT]
[/SIZE][/FONT][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff]sides[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2] = [/SIZE][/FONT][/SIZE][/FONT][B][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080]2[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/B]
[FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff]alpha[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2] = [/SIZE][/FONT][/SIZE][/FONT][B][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080]0.05[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/B]
[FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff]nullproportion[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2] = [/SIZE][/FONT][/SIZE][/FONT][B][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080]0.90[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/B]
[FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2]proportion = [/SIZE][/FONT][/SIZE][/FONT][B][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080]0.95[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/B]
[FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff]ntotal[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2] = [/SIZE][/FONT][/SIZE][/FONT][B][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080].[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/B]
[FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff]power[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2] = [/SIZE][/FONT][/SIZE][/FONT][B][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080]0.9[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/B][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2];[/SIZE][/FONT]
[/SIZE][/FONT][B][FONT=Courier New][SIZE=2][COLOR=#000080][FONT=Courier New][SIZE=2][COLOR=#000080][FONT=Courier New][SIZE=2][COLOR=#000080]run[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/B][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2];[/SIZE][/FONT]
[SIZE=2][FONT=Courier New]　[/FONT][/SIZE]
[/SIZE][/FONT][B][FONT=Courier New][SIZE=2][COLOR=#000080][FONT=Courier New][SIZE=2][COLOR=#000080][FONT=Courier New][SIZE=2][COLOR=#000080]data[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/B][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2] sample_size_calc;[/SIZE][/FONT]
[/SIZE][/FONT][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff]input[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2] z_alpha z_power pop_p sample_p;[/SIZE][/FONT]
[SIZE=2][FONT=Courier New]sample_size=(((z_alpha*(sqrt(pop_p*([/FONT][/SIZE][/SIZE][/FONT][B][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080]1[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/B][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2]-pop_p)))) + (z_power*(sqrt(sample_p *[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2]([/SIZE][/FONT][/SIZE][/FONT][B][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080]1[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/B][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2]- [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2]sample_p))))) / (pop_p - sample_p) )**[/SIZE][/FONT][/SIZE][/FONT][B][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080][FONT=Courier New][SIZE=2][COLOR=#008080]2[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/B][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2];[/SIZE][/FONT]
[/SIZE][/FONT][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff]datalines[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2];[/SIZE][/FONT]
[SIZE=2][FONT=Courier New]1.96 1.28 0.90 0.95[/FONT][/SIZE]
[SIZE=2][FONT=Courier New];[/FONT][/SIZE]
[/SIZE][/FONT][B][FONT=Courier New][SIZE=2][COLOR=#000080][FONT=Courier New][SIZE=2][COLOR=#000080][FONT=Courier New][SIZE=2][COLOR=#000080]run[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/B][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2];[/SIZE][/FONT]
[/SIZE][/FONT]
[SIZE=2][FONT=Courier New][COLOR=#000080][SIZE=2][FONT=Courier New][COLOR=#000080][B][SIZE=2][FONT=Courier New][COLOR=#000080]proc [/COLOR][/FONT][/SIZE][/B][/COLOR][/FONT][/SIZE][/COLOR][/FONT][/SIZE][B][FONT=Courier New][SIZE=2][COLOR=#000080][FONT=Courier New][SIZE=2][COLOR=#000080][FONT=Courier New][SIZE=2][COLOR=#000080]print [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/B][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff]data[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2]=sample_size_calc [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff][FONT=Courier New][SIZE=2][COLOR=#0000ff]noobs[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2];[/SIZE][/FONT]
[/SIZE][/FONT][B][FONT=Courier New][SIZE=2][COLOR=#000080][FONT=Courier New][SIZE=2][COLOR=#000080][FONT=Courier New][SIZE=2][COLOR=#000080]run[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/B][FONT=Courier New][SIZE=2][FONT=Courier New][SIZE=2];[/SIZE][/FONT]
[/SIZE][/FONT]
301 versus 300.654