Sample size for proportions

* (I) SAMPLE SIZE FOR CONFIDENCE INTERVAL ESTIMATION *.

DEFINE ciprop(p=!DEFAULT(0.5) !TOKENS(1) /eps=!TOKENS(1) /ci=!DEFAULT(95) !TOKENS(1) ). 
* Sample size required for the CI for one proportion *.
MATRIX.
PRINT  /TITLE '       SAMPLE SIZE: CONFIDENCE INTERVAL PRECISION: ONE PROPORTION'.
compute p=!p.
compute eps=!eps.
compute ci=!ci.
do if ci=95.
compute zalfa=1.96.
end if.
do if ci=99.
compute zalfa=2.576.
end if.
do if ci=99.9.
compute zalfa=3.09.
end if.
print ci
 /format="f8.1"
 /title='Confidence level (%)'.
print eps
 /format="f8.2"
 /title="Precision desired".
print p
 /format="f8.2"
 /title="Estimated proportion".
compute n=TRUNC(p*(1-p)*((zalfa/eps)**2))+1.
print n
 /format="f8.0"
 /title="Sample size required".
END MATRIX.
!ENDDEFINE.

* MACRO call: give values for estimated proportion, precision desired and confidence level
  If there is no info about the estimated proportion, assume the most conservative (p=0.5)
  default values for p & ci are 0.5 and 95 *.
 
ciprop eps=0.02.  
ciprop p=0.3 eps=0.04 ci=99.
ciprop p=0.2 eps=0.03 ci=99.9.

********************************************************************************

(II) SAMPLE SIZE FOR HIPOTHESIS TESTING *.

* Usual conditions for alfa and power (auxiliary file).
* This file covers the most used conditions for
  sample size determination (add your own if required):
  - alfa=5% and 1% with one or two tailed tests
  - power=80%, 90%, 95% and 99%.
* This file must be active in order to make the MACROS work.

DATA LIST LIST /id(F2.0) alfa(f8.3) tails(F2.0) power(F8.3).
BEGIN DATA
 1 0.05 1 0.80
 2 0.05 2 0.80
 3 0.05 1 0.90
 4 0.05 2 0.90
 5 0.05 1 0.95
 6 0.05 2 0.95
 7 0.05 1 0.99
 8 0.05 2 0.99
 9 0.01 1 0.80
10 0.01 2 0.80
11 0.01 1 0.90
12 0.01 2 0.90
13 0.01 1 0.95
14 0.01 2 0.95
15 0.01 1 0.99
16 0.01 2 0.99
END DATA.
COMPUTE zalfa = IDF.NORMAL(1-(alfa/tails),0,1) .
COMPUTE zbeta = IDF.NORMAL(1-power,0,1) .
EXEC.

*********************************************
* ONE SAMPLE, BINARY OUTCOMES (PROPORTIONS) *
*********************************************.

DEFINE oneprop(p0=!TOKENS(1) /p1=!TOKENS(1)). 
* Comparison of one sample proportion with a population proportion 
  p0: null hypothesis value for p
  p1: alternative hypothesis value for p
  (auxiliary file needed) *.
MATRIX.
PRINT  /TITLE '       SAMPLE SIZE: ONE PROPORTION '.
get id /var=id.
get alfa /var=alfa.
get tails/ var=tails.
get power /var=power.
get zalfa /var=zalfa.
get zbeta /var=zbeta.
compute p0=!p0.
compute p1=!p1.
compute diff=abs(p0-p1).
print {p0,p1,diff}
 /format="f8.2"
 /clabels="Null p","Alt. p", "Diff."
 /title="Difference worth detecting".
compute n=TRUNC(((zalfa*sqrt(p0*(1-p0))-zbeta*sqrt(p1*(1-p1)))&**2)/(diff&**2))+1.
print {id,100*alfa,tails,100*power,n}
 /format="f8.0"
 /clabels="Id","Alfa(%)","N. tails","Power(%)","N"
 /title="Sample size required".
END MATRIX.
!ENDDEFINE.

* MACRO call: give values for p0 & p1 *.
oneprop p0=0.5 p1=0.8.


DEFINE poneprop(p0=!TOKENS(1) /p1=!TOKENS(1) /n=!TOKENS(1)
 /alfa=!DEFAULT(0.05) !TOKENS(1) /tails=!DEFAULT(2) !TOKENS(1)). 
* Power of a test, given a sample size and values for p0 and p1
  (auxiliary file NOT needed) *.
MATRIX.
PRINT  /TITLE '       SAMPLE SIZE: POWER OF A TEST (ONE PROPORTION)'.
compute p0=!p0.
compute p1=!p1.
compute diff=abs(p0-p1).
compute n=!n.
compute alfa=!alfa.
compute tails=!tails.
compute pval=alfa/tails.
do if pval=0.05.
compute zalfa=1.645.
end if.
do if pval=0.025.
compute zalfa=1.96.
end if.
do if pval=0.01.
compute zalfa=2.326.
end if.
do if pval=0.005.
compute zalfa=2.576.
end if.
print {p0,p1,diff}
 /format="f8.2"
 /clabels="Null p","Alt. p", "Diff."
 /title="Difference worth detecting".
print {100*alfa,tails,n}
 /format="f8.0"
 /clabels="Alfa(%)","Tails","N"
 /title="Input data".
compute beta=100*(1-cdfnorm((zalfa*sqrt(p0*(1-p0))-diff*sqrt(n))/sqrt(p1*(1-p1)))).
print beta
 /format="f8.1"
 /title="Power of the test (%)".
END MATRIX.
!ENDDEFINE.

* MACRO call: give values for p0, p1, sample size used, alfa level and tails *.
poneprop p0=0.5 p1=0.8 n=30 alfa=0.05 tails=2. 
poneprop p0=0.5 p1=0.8 n=20 alfa=0.05 tails=2. 
poneprop p0=0.5 p1=0.8 n=15 alfa=0.05 tails=1. 

* alfa levels & tails have default values of 0.05 & 2.

********************************************
* TWO INDEPENDENT SAMPLES, BINARY OUTCOMES *
********************************************.

DEFINE twoprop(p1=!TOKENS(1)/ p2=!TOKENS(1)/ r=!DEFAULT(1)!TOKENS(1)). 
* Comparison of 2 independent proportions (auxiliary file needed) *.
MATRIX.
PRINT  /TITLE '       SAMPLE SIZE: TWO INDEPENDENT PROPORTIONS'.
get id /var=id.
get alfa /var=alfa.
get tails/ var=tails.
get power /var=power.
get zalfa /var=zalfa.
get zbeta /var=zbeta.
compute k=!r.
compute p1=!p1.
compute q1=1-p1.
compute p2=!p2.
compute q2=1-p2.
compute p=(p1+k*p2)/(1+k).
compute q=1-p.
compute diff=abs(p1-p2).
print {p1,p2,diff}
 /format="f8.2"
 /clabels="p1","p2","Diff."
 /title="Difference worth detecting".
print k
 /format="f8.0"
 /title="Ratio (N2/N1)".
* Ni *.
COMPUTE n1=TRUNC(((zalfa*sqrt(p*q*(1+k)/k)-zbeta*sqrt(p1*q1+(p2*q2/k)))&**2)/(diff**2))+1.
COMPUTE n2=TRUNC(((zalfa*sqrt(p*q*(1+k))-zbeta*sqrt(k*p1*q1+(p2*q2)))&**2)/(diff**2))+1.
print {id,100*alfa,tails,100*power,n1,n2,n1+n2}
 /format="f8.0"
 /clabels="Id","Alfa(%)","N. tails","Power(%)","N1","N2","Total N"
 /title="Sample size required".
END MATRIX.
!ENDDEFINE.

* MACRO call: indicate values for p1, p2 and ratio *.
twoprop p1=0.5 p2=0.3 r=1.
twoprop p1=0.5 p2=0.3 r=2.
twoprop p1=0.5 p2=0.3 r=3.

* If you want to get the output for just one condition,
  for example alfa=5%, one tail and 90% power (row Nr. 3).
TEMPORARY.
SELECT IF ID=3.
twoprop p1=0.5 p2=0.3 r=2.


DEFINE ptwoprop(p1=!TOKENS(1) /p2=!TOKENS(1) /n1=!TOKENS(1) /n2=!TOKENS(1)
 /alfa=!DEFAULT(0.05) !TOKENS(1) /tails=!DEFAULT(2) !TOKENS(1)). 
* Power of a test, given sample sizes and observed p1 & p2
  (auxiliary file NOT needed) *.
MATRIX.
PRINT  /TITLE '       SAMPLE SIZE: POWER OF A TEST (TWO PROPORTIONS)'.
compute p1=!p1.
compute p2=!p2.
compute n1=!n1.
compute n2=!n2.
compute q1=1-p1.
compute q2=1-p2.
compute p=(n1*p1+n2*p2)/(n1+n2).
compute q=1-p.
compute diff=abs(p1-p2).
compute n=2*n1*n2/(n1+n2).
compute alfa=!alfa.
compute tails=!tails.
compute pval=alfa/tails.
do if pval=0.05.
compute zalfa=1.645.
end if.
do if pval=0.025.
compute zalfa=1.96.
end if.
do if pval=0.01.
compute zalfa=2.326.
end if.
do if pval=0.005.
compute zalfa=2.576.
end if.
compute diff=abs(p1-p2).
print {p1,p2,diff}
 /format="f8.2"
 /clabels="p1","p2","Diff."
 /title="Difference worth detecting".
print {100*alfa,tails,n1,n2}
 /format="f8.0"
 /clabels="Alfa(%)","Tails","N1","N2"
 /title="Input data".
compute beta=100*(1-cdfnorm((zalfa*sqrt(2*p*q)-diff*sqrt(n))/sqrt(p1*q1+p2*q2))).
print beta
 /format="f8.1"
 /title="Power of the test (%)".
END MATRIX.
!ENDDEFINE.

* MACRO call: give values for both sample sizes & proportions, alfa level and tails *.
ptwoprop p1=0.5 p2=0.3 n1=124 n2=124 alfa=0.05 tails=2. 
ptwoprop p1=0.5 p2=0.3 n1=82 n2=245 alfa=0.05 tails=2. 
ptwoprop p1=0.5 p2=0.3 n1=115 n2=229 alfa=0.01 tails=1. 
ptwoprop p1=0.5 p2=0.4 n1=50 n2=80 alfa=0.05 tails=1. 

* alfa levels & tails have default values of 0.05 & 2.