Sample size for means

(I) SAMPLE SIZE FOR CONFIDENCE INTERVAL ESTIMATION *.

DEFINE cimean(s=!TOKENS(1) /eps=!TOKENS(1) /ci=!DEFAULT(95) !TOKENS(1) ). 
* Sample size required for the CI for one mean *.
MATRIX.
PRINT  /TITLE '       SAMPLE SIZE: CONFIDENCE INTERVAL PRECISION: ONE MEAN'.
compute sd=!s.
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 sd
 /format="f8.3"
 /title="Estimated Std deviation".
compute n=TRUNC((zalfa**2)*(sd**2)/(eps**2))+1.
print {n}
 /format="f8.0"
 /title="Sample size required".
END MATRIX.
!ENDDEFINE.

* MACRO call: give values for Std deviation, precision desired and confidence level *.
cimean s=8.7 eps=2.
cimean s=8.7 eps=2 ci=99.
cimean s=8.7 eps=2 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 for 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, CONTINUOUS OUTCOMES *
***********************************.

DEFINE onemeand(d=!TOKENS(1)). 
* Comparison of one sample mean with a population mean
  with Cohen's d as input (auxiliary file needed) *.
MATRIX.
PRINT  /TITLE '       SAMPLE SIZE: ONE MEAN OR PAIRED MEANS (COHEN`S D)'.
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 cohend=!d.
print cohend
 /format="f8.2"
 /title="Difference worth detecting (Cohen's d)".
compute n=TRUNC(((zalfa-zbeta)/cohend)&**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 value for d *.
onemeand d=0.76.

DEFINE onemeanx(m=!TOKENS(1) /s=!TOKENS(1) ). 
* Comparison of one sample mean with a population
  mean with mean diff and Std deviation as input
  (auxiliary file needed) *.
MATRIX.
PRINT  /TITLE '       SAMPLE SIZE: ONE MEAN OR PAIRED MEANS (MEAN AND SD)'.
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 mean=!m.
compute sd=!s.
compute cohend=mean/sd.
print {mean,sd,cohend}
 /format="f8.2"
 /clabels="Mean","Std.dev","Cohen's d"
 /title="Data for difference worth detecting".
compute n=TRUNC(((zalfa-zbeta)/cohend)&**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 mean dif (sample-population) and Std deviation *.
onemeanx m=10 s=13.1.

DEFINE onemeanp(d=!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 an observed mean diff (Cohen's d)
  (auxiliary file NOT needed) *.
MATRIX.
PRINT  /TITLE '       SAMPLE SIZE: POWER OF A TEST (ONE MEAN WITH COHEN`S D)'.
compute cohend=!d.
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 cohend
 /format="f8.2"
 /title="Difference worth detecting (Cohen's d)".
print {100*alfa,tails,n}
 /format="f8.0"
 /clabels="Alfa(%)","Tails","N"
 /title="Input data".
compute beta=100*(1-cdfnorm(zalfa-abs(cohend*sqrt(n)))).
print beta
 /format="f8.1"
 /title="Power of the test (%)".
END MATRIX.
!ENDDEFINE.

* MACRO call: give values  Cohen's d, sample size used, alfa level and tails *.
onemeanp d=0.76 n=14 alfa=0.05 tails=2. 

************************************************
* TWO INDEPENDENT SAMPLES, CONTINUOUS OUTCOMES *
************************************************.

DEFINE twomeand(d=!TOKENS(1)/ r=!DEFAULT(1)!TOKENS(1)). 
* Comparison of 2 independent means with Cohen's d as input
  (auxiliary file needed) *.
MATRIX.
PRINT  /TITLE '       SAMPLE SIZE: TWO INDEPENDENT MEANS (STANDARDIZED MEAN DIFF.)'.
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 cohend=!d.
print cohend
 /format="f8.2"
 /title="Difference worth detecting (Cohen's d)".
print k
 /format="f8.0"
 /title="Ratio (N2/N1)".
* Harmonic N *.
compute n=TRUNC(2*((zalfa-zbeta)/cohend)&**2)+1.
* Sample Ni *.
COMPUTE n1=n*(k+1)/(2*k).
COMPUTE n2=n*(1+k)/2.
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 d and ratio *.
twomeand d=0.5 r=1.
twomeand d=0.5 r=2.
twomeand d=0.5 r=3.
twomeand d=0.3 r=1.
twomeand d=0.3 r=2.
twomeand d=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.
twomeand d=0.5 r=2.

DEFINE twomeanx(m1=!TOKENS(1)/ m2=!TOKENS(1)/ s=!TOKENS(1)/ r=!DEFAULT(1)!TOKENS(1)). 
* Comparison of 2 independent means with means and sd as input
  (auxiliary file needed) *.
MATRIX.
PRINT  /TITLE '       SAMPLE SIZE: TWO INDEPENDENT MEANS (UNSTANDARDIZED MEANS DIFF.)'.
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 mean1=!m1.
compute mean2=!m2.
compute sd=!s.
compute cohend=(mean1-mean2)/sd.
print {mean1,mean2,sd,cohend}
 /format="f8.2"
 /clabels="Mean1","Mean2","Std.dev","Cohen's d"
 /title="Data for difference worth detecting".
print k
 /format="f8.0"
 /title="Ratio (N2/N1)".
* Harmonic N *.
compute n=TRUNC(2*((zalfa-zbeta)/cohend)&**2)+1.
* Sample Ni *.
COMPUTE n1=n*(k+1)/(2*k).
COMPUTE n2=n*(1+k)/2.
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: give values for both means, common Std deviation and ratio *.
twomeanx m1=4.5 m2=4 s=1 r=1.
twomeanx m1=4.5 m2=4 s=1 r=2.
twomeanx m1=4.5 m2=4 s=1 r=3.
twomeanx m1=4.5 m2=4 s=0.9 r=1.
twomeanx m1=4.5 m2=4 s=0.9 r=2.
twomeanx m1=4.5 m2=4 s=0.9 r=3.

DEFINE twomeanp(d=!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 an observed mean diff (Cohen's d)
  (auxiliary file NOT needed) *.
MATRIX.
PRINT  /TITLE '       SAMPLE SIZE: POWER OF A TEST (TWO MEANS WITH COHEN`S D)'.
compute cohend=!d.
compute n1=!n1.
compute n2=!n2.
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.
print cohend
 /format="f8.2"
 /title="Difference worth detecting (Cohen's d)".
print {100*alfa,tails,n1,n2}
 /format="f8.0"
 /clabels="Alfa(%)","Tails","N1","N2"
 /title="Input data".
compute beta=100*(1-cdfnorm(zalfa-abs(cohend*sqrt(n/2)))).
print beta
 /format="f8.1"
 /title="Power of the test (%)".
END MATRIX.
!ENDDEFINE.

* MACRO call: give values for both sample sizes, Cohen's d, alfa level and tails *.
twomeanp d=0.94 n1=7 n2=14 alfa=0.05 tails=2.