Simultaneous Bonferroni Confidence Intervals
/****************************************************************/
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: BONFER */
/* TITLE: Simultaneous Bonferroni Confidence Intervals */
/* PRODUCT: QC */
/* SYSTEM: ALL */
/* KEYS: Simultaneous Confidence Intervals, */
/* PROCS: MEANS PRINT SHEWHART */
/* DATA: */
/* */
/* REF: R.G. Miller (1980), Simultaneous Statistical */
/* Inference, New York: Springer-Verlag. */
/* */
/* Robert N. Rodriguez (1996), "Health Care */
/* Applications of Statistical Process Control: */
/* Examples Using the SAS System", Procedings of the */
/* Twenty-First Annual SAS Users Group International */
/* Conference, 1381-1396. */
/* */
/* NOTES: */
/* */
/****************************************************************/
options ls=64 nodate nonumber;
goptions htext= 3.5 pct htitle=4.0 pct
ftext='albany amt';
options ls=64 nodate nonumber;
* Simultaneous Bonferroni confidence intervals;
data csection;
length id $ 2 n94 n95 $4;
input id csect94 vag94 csect95 vag95;
total94 = csect94 + vag94;
total95 = csect95 + vag95;
n94 = left( put( total94, 4. ) );
n95 = left( put( total95, 4. ) );
label id = 'Medical Group Identification Number'
n94 = 'Number of Deliveries'
n95 = 'Number of Deliveries';
cards;
1A 163 907 150 773
1K 55 314 45 253
1B 52 179 34 136
1D 19 128 18 114
3I 21 98 20 86
3M 15 81 12 93
1E 15 52 10 67
1N 6 43 19 55
1Q 12 67 7 62
3H 7 65 11 54
1R 4 43 11 38
1H 5 32 9 39
3J 7 12 7 13
1C 13 42 8 35
3B 3 33 6 37
1M 6 8 4 25
3C 6 27 5 23
1O 8 26 4 23
1J 6 18 6 16
1T 1 3 3 19
3E 2 12 4 14
1G 1 7 4 11
3D 7 22 4 9
3G 2 5 1 10
1L 2 4 2 8
1I 1 3 1 7
1P 16 65 0 3
1F 0 1 0 3
1S 1 2 1 2
;
data csect95;
set csection end=eof;
if eof then call symput('ngroups', left( put( _n_, 4. )));
run;
proc means noprint data=csect95;
var total95;
output out=total sum=n;
data total;
set total end=eof;
if eof then call symput('n', left( put( n, 4. )));
put n;
run;
data csect95;
set csection;
keep id p95l p951 p95x p953 p95h p95n p95s p95m n95;
p95x = csect95 / total95;
p95n = total95;
alpha = 0.01;
g = probit( 1 - ( alpha / ( 2 * &ngroups ) ) );
p953 = p95x + g * sqrt( p95x * ( 1 - p95x ) / &n );
p951 = p95x - g * sqrt( p95x * ( 1 - p95x ) / &n );
z = probit( 1 - ( alpha / 2 * &ngroups ));
p95l = p95x - z * sqrt( p95x * ( 1 - p95x ) / p95n );
p953 = p95x + z * sqrt( p95x * ( 1 - p95x ) / p95n );
/* assign dummy variables */
p95h = p953;
p95l = p951;
p95s = 0.001;
p95m = p95x;
run;
proc print;
run;
title 'C-Sections as a Proportion of Total'
' Deliveries in 1995';
symbol v=none w=1;
proc shewhart history=csect95;
boxchart p95*id (n95) /
nolimitslegend
nolcl
noucl
xsymbol = 'Avg'
turnhlabels
blocklabtype = scaled
nolegend
npanel = &ngroups
cframe = ligr
cboxes = black
haxis = axis1
cboxfill = yellow;
axis1 value = ( h=2.2 pct ) ;
label p95x = 'Simultaneous 99% Intervals';
run;