Diff for "FAQ/power/propsn" - CBU statistics Wiki

Differences between revisions 1 and 25 (spanning 24 versions)

This program uses the difference in proportions [http://en.wikipedia.org/wiki/Effect_size#Cohen.27s_d (or equivalently the odds ratio)] as the effect size.

p1 and p2 are the proportions in groups 1 and 2 respectively being compared, delta is the ratio: size of group 2 / size of group 1, alpha is the (two-tailed) type I error. The program then outputs the sample sizes required for the specified power. A power calculator is also available in a [attachment:prop2wok.xls spreadsheet] or using a web calculator [http://statpages.org/proppowr.html here.] and [:FAQ/rpropspow in R].

An [:FAQ/capacityeg: example] uses marginal probabilities to compute cell probabilities in a 2x2 table to give inputs for a power analysis.

[ADJUST THE EXAMPLE INPUT AS DESIRED; THEN COPY AND PASTE INTO A SPSS SYNTAX WINDOW AND RUN; OUTPUT BOTH TO SPREADSHEET AND OUTPUT WINDOW].

DATA LIST free
/alpha p1 p2 delta power. 
BEGIN DATA. 
.05 0.19 0.09 2 0.87
.05 0.40 0.35 2 0.80
END DATA. 

set errors=none.
define propn (!pos !tokens(1)
                   / !pos !tokens(1)
                   / !pos !tokens(1)
                   / !pos !tokens(1)
                   / !pos !tokens(1)).
COMPUTE #POW = !5.
compute #conf = 1-!1.
compute #lc3 = 1.
compute #ind=0.
compute n1=3.
compute n2=!4*n1.
compute #pbar= (n1*!2 + n2*!3) / (n1+n2).
compute #z2= ( (!2-!3) /sqrt( #pbar*(1-#pbar)*( (1/n1) + (1/n2) ) ) )**2.
compute oddsr = ( n1*!2*n2*(1-!3) ) / ( n1*(1-!2)*n2*!3 ).
compute #CUMF2=1-ncdf.chisq(idf.chisq(1-!1,1),1,#z2).
compute #diff=1.
SET MXLOOPS=40000.
LOOP IF (#DIFF GT .00005) .
+       DO IF (#CUMF2 LT #pow) .
+               COMPUTE #LC3 = n1.
+               COMPUTE n1 = (n1 + 1).
+                      compute n2=!4*n1.
+                      compute #pbar= (n1*!2 + n2*!3) / (n1+n2).
+                      compute #z2= ( (!2-!3) /sqrt( #pbar*(1-#pbar)*( (1/n1) + (1/n2) ) ) )**2.
+                      compute #CUMF2=1-ncdf.chisq(idf.chisq(1-!1,1),1,#z2).
+       ELSE .
+               COMPUTE #LC1 = n1 .
+               COMPUTE n1 = (n1 + #LC3)/2 .
+                      compute n2=!4*n1.
+                      compute #pbar= (n1*!2 + n2*!3) / (n1+n2).
+                      compute #z2= ( (!2-!3) /sqrt( #pbar*(1-#pbar)*( (1/n1) + (1/n2) ) ) )**2.
+                      compute #CUMF2=1-ncdf.chisq(idf.chisq(1-!1,1),1,#z2).
+       END IF .
+       COMPUTE #DIFF = ABS(#CUMF2 - #pow) .
END LOOP .
if (n1-trunc(n1) gt 0.5) #ind=1.
if (#ind eq 0) n1=trunc(n1)+1.
if (#ind eq 1) n1=rnd(n1).
EXECUTE .
compute alpha=!1.
compute p1=!2.
compute p2=!3.
compute n2=!4*n1.
compute power=!5.
formats n1 (f7.0) n2 (f7.0) alpha (f5.2) p1 (f5.2) p2 (f5.2) power (f5.2).
variable labels n1 'Sample Size 1' /n2 'Sample Size 2' /alpha 'Alpha' /p1 'Proportion 1' /p2 'Proportion 2' /power 'Power'.
report format=list automatic align(center)
  /variables=n1 n2 alpha p1 p2 power 
  /title "Sample Size required for a two sample, two-tailed binomial test" .
!enddefine.
define propncc (!pos !tokens(1)
                   / !pos !tokens(1)
                   / !pos !tokens(1)
                   / !pos !tokens(1)
                   / !pos !tokens(1)).
COMPUTE #POW = !5.
compute #conf = 1-!1.
compute #lc3 = 1.
compute #ind=0.
compute n1=3.
compute n2=!4*n1.
compute #contc= 0.5*((1/n1)+(1/n2)).
compute #pbar= (n1*p1 + n2*p2) / (n1+n2).
compute #z21= ( ( abs(p1-p2)-#contc ) /sqrt( #pbar*(1-#pbar)*( (1/n1) + (1/n2) ) ) )**2.
compute #CUMF2=1-ncdf.chisq(idf.chisq(1-alpha,1),1,#z21).
compute #diff=1.
SET MXLOOPS=40000.
LOOP IF (#DIFF GT .00005) .
+       DO IF (#CUMF2 LT #pow) .
+               COMPUTE #LC3 = n1.
+               COMPUTE n1 = (n1 + 1).
+                      compute n2=!4*n1.
+                      compute #contc= 0.5*((1/n1)+(1/n2)).
+                      compute #pbar= (n1*p1 + n2*p2) / (n1+n2).
+                      compute #z21= ( ( abs(p1-p2)-#contc ) /sqrt( #pbar*(1-#pbar)*( (1/n1) + (1/n2) ) ) )**2.
+                      compute #CUMF2=1-ncdf.chisq(idf.chisq(1-alpha,1),1,#z21).
+       ELSE .
+               COMPUTE #LC1 = n1 .
+               COMPUTE n1 = (n1 + #LC3)/2 .
+                      compute n2=!4*n1.
+                      compute #contc= 0.5*((1/n1)+(1/n2)).
+                      compute #pbar= (n1*p1 + n2*p2) / (n1+n2).
+                      compute #z21= ( ( abs(p1-p2)-#contc ) /sqrt( #pbar*(1-#pbar)*( (1/n1) + (1/n2) ) ) )**2.
+                      compute #CUMF2=1-ncdf.chisq(idf.chisq(1-alpha,1),1,#z21).
+       END IF .
+       COMPUTE #DIFF = ABS(#CUMF2 - #pow) .
END LOOP .
if (n1-trunc(n1) gt 0.5) #ind=1.
if (#ind eq 0) n1=trunc(n1)+1.
if (#ind eq 1) n1=rnd(n1).
EXECUTE .
compute alpha=!1.
compute p1=!2.
compute p2=!3.
compute n2=!4*n1.
compute power=!5.
formats n1 (f7.0) n2 (f7.0) alpha (f5.2) p1 (f5.2) p2 (f5.2) power (f5.2).
variable labels n1 'Sample Size 1' /n2 'Sample Size 2' /alpha 'Alpha' /p1 'Proportion 1' /p2 'Proportion 2' /power 'Power'.
report format=list automatic align(center)
  /variables=n1 n2 alpha p1 p2 power 
  /title "Sample Sizes for a two sample, two-tailed binomial test (continuity corrected)" .
!enddefine.
matrix.
get m /variables=alpha p1 p2 delta power  /missing=omit.
compute alpha=make(1,1,0).
compute p1=make(1,1,0).
compute p2=make(1,1,0).
compute delta=make(1,1,0).
compute power=make(1,1,0).
compute alpha=m(:,1).
compute p1=m(:,2).
compute p2=m(:,3).
compute delta=m(:,4).
compute power=m(:,5).  
end matrix.
propn alpha p1 p2 delta power.
propncc alpha p1 p2 delta power.

-  ⇤ ← Revision 1 as of 2006-09-15 10:48:25 → 
  Size: 2496
  Editor: PeterWatson
  Comment:
+   ← Revision 25 as of 2012-05-03 13:12:09 → ⇥
  Size: 5472
  Editor: PeterWatson
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 1:
+This program uses the difference in proportions [http://en.wikipedia.org/wiki/Effect_size#Cohen.27s_d (or equivalently the odds ratio)] as the effect size.
-Line 2:
+Line 3:
+p1 and p2 are the proportions in groups 1 and 2 respectively being compared, delta is the ratio: size of group 2 / size of group 1, alpha is the (two-tailed) type I error. The program then outputs the sample sizes required for the specified power. A power calculator is also available in a [attachment:prop2wok.xls spreadsheet] or using a web calculator [http://statpages.org/proppowr.html here.] and [:FAQ/rpropspow in R].

An [:FAQ/capacityeg: example] uses marginal probabilities to compute cell probabilities in a 2x2 table to give inputs for a power analysis. 

[ADJUST THE EXAMPLE INPUT AS DESIRED; THEN COPY AND PASTE INTO A SPSS SYNTAX WINDOW AND RUN; OUTPUT BOTH TO SPREADSHEET AND OUTPUT WINDOW].
-Line 5:
+Line 11:
-/p1 p2 ratio alpha power.
BEGIN DATA.
0.19 0.09 1 0.05 0.80
0.19 0.09 4 0.05 0.80
0.19 0.09 10 0.05 0.80
END DATA.

compute p11= (p1*ratio)/(1+ratio).
compute p12=((1-p1)*ratio)/(1+ratio).
compute p21=p2/(1+ratio).
compute p22=(1-p2)/(1+ratio).
+/alpha p1 p2 delta power. 
BEGIN DATA. 
.05 0.19 0.09 2 0.87
.05 0.40 0.35 2 0.80
END DATA.
 Line 18:
-define orpow ( !pos !tokens(1)
                    / !pos !tokens(1)
                    / !pos !tokens(1)
                    / !pos !tokens(1)
                    / !pos !tokens(1)
                    / !pos !tokens(1)).


compute oddsr = (!1*!4)/(!3*!2).
exe.


COMPUTE #POW = !6.
COMPUTE #chisq1 = ( LN(oddsr) / sqrt((1/!1)+(1/!2)+(1/!3)+(1/!4))  )**2.
compute #df=1.
compute #conf = 1-!5.
+define propn (!pos !tokens(1)
                   / !pos !tokens(1)
                   / !pos !tokens(1)
                   / !pos !tokens(1)
                   / !pos !tokens(1)).
COMPUTE #POW = !5.
compute #conf = 1-!1.
-Line 36:
+Line 27:
-compute #chisq = 3.000.
comment COMPUTE #LC1 = 2.000.
COMPUTE #CUMF2 = 1 - NCDF.CHISQ(IDF.CHISQ(#conf,#DF),#DF,#CHISQ).
COMPUTE #DIFF = 1 .
SET MXLOOPS=10000.
+compute n1=3.
compute n2=!4*n1.
compute #pbar= (n1*!2 + n2*!3) / (n1+n2).
compute #z2= ( (!2-!3) /sqrt( #pbar*(1-#pbar)*( (1/n1) + (1/n2) ) ) )**2.
compute oddsr = ( n1*!2*n2*(1-!3) ) / ( n1*(1-!2)*n2*!3 ).
compute #CUMF2=1-ncdf.chisq(idf.chisq(1-!1,1),1,#z2).
compute #diff=1.
SET MXLOOPS=40000.
-Line 43:
+Line 37:
-+		COMPUTE #LC3 = #CHISQ.
+		COMPUTE #CHISQ = (#chisq + rnd(#chisq/3)).
+		COMPUTE #CUMF2 =  1 - NCDF.CHISQ(IDF.CHISQ(#conf,#DF),#DF,#CHISQ).
++		COMPUTE #LC3 = n1.
+		COMPUTE n1 = (n1 + 1).
+                      compute n2=!4*n1.
+                      compute #pbar= (n1*!2 + n2*!3) / (n1+n2).
+                      compute #z2= ( (!2-!3) /sqrt( #pbar*(1-#pbar)*( (1/n1) + (1/n2) ) ) )**2.
+                      compute #CUMF2=1-ncdf.chisq(idf.chisq(1-!1,1),1,#z2).
-Line 47:
+Line 44:
-+		COMPUTE #LC1 = #chisq .
+		COMPUTE #chisq = (#chisq + #LC3)/2 .
+		COMPUTE #CUMF2 = 1 - NCDF.CHISQ(IDF.CHISQ(#conf,#DF),#DF,#CHISQ).
++		COMPUTE #LC1 = n1 .
+		COMPUTE n1 = (n1 + #LC3)/2 .
+                      compute n2=!4*n1.
+                      compute #pbar= (n1*!2 + n2*!3) / (n1+n2).
+                      compute #z2= ( (!2-!3) /sqrt( #pbar*(1-#pbar)*( (1/n1) + (1/n2) ) ) )**2.
+                      compute #CUMF2=1-ncdf.chisq(idf.chisq(1-!1,1),1,#z2).
 Line 53:
-compute ntot = #chisq/#chisq1.
exe.
if (ntot-trunc(ntot) gt 0.5) #ind=1.
if (#ind eq 0) ntot=trunc(ntot)+1.
if (#ind eq 1) ntot=rnd(ntot).
+if (n1-trunc(n1) gt 0.5) #ind=1.
if (#ind eq 0) n1=trunc(n1)+1.
if (#ind eq 1) n1=rnd(n1).
-Line 59:
+Line 57:
-compute p11=!1.
compute p12=!2.
compute p21=!3.
compute p22=!4.
compute alpha=!5.
compute power=!6.
compute p1=p11/(p11+p12).
compute p2=p21/(p21+p22).
formats ntot (f7.0) alpha (f5.2) p1 (f5.2) p2 (f5.2) ratio (f5.2) oddsr power (f5.2).
variable labels ntot 'Total Sample Size Required' /alpha 'Alpha' /p1 'Proportion 1' /p2 'Proportion 2' /ratio 'Ratio Gp1:Gp2' /oddsr 'Odds Ratio' /power 'Power'.
+compute alpha=!1.
compute p1=!2.
compute p2=!3.
compute n2=!4*n1.
compute power=!5.
formats n1 (f7.0) n2 (f7.0) alpha (f5.2) p1 (f5.2) p2 (f5.2) power (f5.2).
variable labels n1 'Sample Size 1' /n2 'Sample Size 2' /alpha 'Alpha' /p1 'Proportion 1' /p2 'Proportion 2' /power 'Power'.
-Line 70:
+Line 65:
-  /variables=ntot alpha p1 p2 ratio oddsr power 
  /title "Sample Size for comparing two independent proportions given power" .
+  /variables=n1 n2 alpha p1 p2 power 
  /title "Sample Size required for a two sample, two-tailed binomial test" .
-Line 73:
+Line 68:
+define propncc (!pos !tokens(1)
                   / !pos !tokens(1)
                   / !pos !tokens(1)
                   / !pos !tokens(1)
                   / !pos !tokens(1)).
COMPUTE #POW = !5.
compute #conf = 1-!1.
compute #lc3 = 1.
compute #ind=0.
compute n1=3.
compute n2=!4*n1.
compute #contc= 0.5*((1/n1)+(1/n2)).
compute #pbar= (n1*p1 + n2*p2) / (n1+n2).
compute #z21= ( ( abs(p1-p2)-#contc ) /sqrt( #pbar*(1-#pbar)*( (1/n1) + (1/n2) ) ) )**2.
compute #CUMF2=1-ncdf.chisq(idf.chisq(1-alpha,1),1,#z21).
compute #diff=1.
SET MXLOOPS=40000.
LOOP IF (#DIFF GT .00005) .
+	DO IF (#CUMF2 LT #pow) .
+		COMPUTE #LC3 = n1.
+		COMPUTE n1 = (n1 + 1).
+                      compute n2=!4*n1.
+                      compute #contc= 0.5*((1/n1)+(1/n2)).
+                      compute #pbar= (n1*p1 + n2*p2) / (n1+n2).
+                      compute #z21= ( ( abs(p1-p2)-#contc ) /sqrt( #pbar*(1-#pbar)*( (1/n1) + (1/n2) ) ) )**2.
+                      compute #CUMF2=1-ncdf.chisq(idf.chisq(1-alpha,1),1,#z21).
+	ELSE .
+		COMPUTE #LC1 = n1 .
+		COMPUTE n1 = (n1 + #LC3)/2 .
+                      compute n2=!4*n1.
+                      compute #contc= 0.5*((1/n1)+(1/n2)).
+                      compute #pbar= (n1*p1 + n2*p2) / (n1+n2).
+                      compute #z21= ( ( abs(p1-p2)-#contc ) /sqrt( #pbar*(1-#pbar)*( (1/n1) + (1/n2) ) ) )**2.
+                      compute #CUMF2=1-ncdf.chisq(idf.chisq(1-alpha,1),1,#z21).
+	END IF .
+	COMPUTE #DIFF = ABS(#CUMF2 - #pow) .
END LOOP .
if (n1-trunc(n1) gt 0.5) #ind=1.
if (#ind eq 0) n1=trunc(n1)+1.
if (#ind eq 1) n1=rnd(n1).
EXECUTE .
compute alpha=!1.
compute p1=!2.
compute p2=!3.
compute n2=!4*n1.
compute power=!5.
formats n1 (f7.0) n2 (f7.0) alpha (f5.2) p1 (f5.2) p2 (f5.2) power (f5.2).
variable labels n1 'Sample Size 1' /n2 'Sample Size 2' /alpha 'Alpha' /p1 'Proportion 1' /p2 'Proportion 2' /power 'Power'.
report format=list automatic align(center)
  /variables=n1 n2 alpha p1 p2 power 
  /title "Sample Sizes for a two sample, two-tailed binomial test (continuity corrected)" .
!enddefine.
-Line 75:
+Line 121:
-get m /variables=p11 p12 p21 p22 alpha power /missing=omit.
compute p11=make(1,1,0).
compute p12=make(1,1,0).
compute p21=make(1,1,0).
compute p22=make(1,1,0).
+get m /variables=alpha p1 p2 delta power  /missing=omit.
-Line 81:
+Line 123:
+compute p1=make(1,1,0).
compute p2=make(1,1,0).
compute delta=make(1,1,0).
-Line 82:
+Line 127:
-compute p11=m(:,1).
compute p12=m(:,2).
compute p21=m(:,3).
compute p22=m(:,4).  
compute alpha=m(:,5).
compute power=m(:,6).
+compute alpha=m(:,1).
compute p1=m(:,2).
compute p2=m(:,3).
compute delta=m(:,4).
compute power=m(:,5).
-Line 89:
+Line 133:
-orpow p11 p12 p21 p22 alpha power.
+propn alpha p1 p2 delta power.
propncc alpha p1 p2 delta power.

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