Log of Splus Data Analyses Related to HW 2 & 3
======================================= 3/9/03


#3.1
> round(unlist(ScorProfW(matrix(c(1601,510,162527,412368),ncol=2),.05,
      c(0,.03),npts=30)[2:4]),6)
 WaldInts1 WaldInts2 ScorInts1 ScorInts2  LRInts1  LRInts2 
  0.008032  0.009007  0.008043  0.009017 0.008458 0.009152

> round(unlist(ScorProfW(matrix(c(1601,510,162527,412368),ncol=2),.05,
      c(.5,10),npts=30,type="RR")[2:4]),4) 
 WaldInts1 WaldInts2 ScorInts1 ScorInts2 LRInts1 LRInts2 
    7.2082     8.801    7.1494    8.7232  7.1915  8.7312

> round(unlist(ScorProfW(matrix(c(1601,510,162527,412368),ncol=2),.05,
      c(.5,10),npts=50,type="OR")[2:4]),4)
 WaldInts1 WaldInts2 ScorInts1 ScorInts2 LRInts1 LRInts2 
    7.1491    8.7231    7.2084    8.8012  7.2233  8.8095

#3.15 
(b) 
> for(i in c(1:5,seq(10,80,10),seq(150,570,30))) cat("With theta=",i,
    ",  ExtHyp prob of 15=",1-pExtHyp(14,15,15,22,i),"\n")
With theta= 1 ,  ExtHyp prob of 15= 0.00109945027486269 
With theta= 2 ,  ExtHyp prob of 15= 0.0122567830877285 
With theta= 3 ,  ExtHyp prob of 15= 0.0363560434976881 
With theta= 4 ,  ExtHyp prob of 15= 0.0688177364213567 
With theta= 5 ,  ExtHyp prob of 15= 0.105241290372662 
With theta= 10 ,  ExtHyp prob of 15= 0.280886169031004 
With theta= 20 ,  ExtHyp prob of 15= 0.50439183188548 
With theta= 30 ,  ExtHyp prob of 15= 0.625402113035335 
With theta= 40 ,  ExtHyp prob of 15= 0.699557739175097 
With theta= 50 ,  ExtHyp prob of 15= 0.749393546536196 
With theta= 60 ,  ExtHyp prob of 15= 0.785119888953706 
With theta= 70 ,  ExtHyp prob of 15= 0.811962734679643 
With theta= 80 ,  ExtHyp prob of 15= 0.832859807904861 
With theta= 150 ,  ExtHyp prob of 15= 0.906048958475889 
With theta= 180 ,  ExtHyp prob of 15= 0.920903086231513 
With theta= 210 ,  ExtHyp prob of 15= 0.931702915022108 
With theta= 240 ,  ExtHyp prob of 15= 0.939908570308354 
With theta= 270 ,  ExtHyp prob of 15= 0.946354339115316 
With theta= 300 ,  ExtHyp prob of 15= 0.95155146463432 
With theta= 330 ,  ExtHyp prob of 15= 0.955830680132932 
With theta= 360 ,  ExtHyp prob of 15= 0.959415405308401 
With theta= 390 ,  ExtHyp prob of 15= 0.962462001227197 
With theta= 420 ,  ExtHyp prob of 15= 0.965083171233284 
With theta= 450 ,  ExtHyp prob of 15= 0.9673622027066 
With theta= 480 ,  ExtHyp prob of 15= 0.969361975633623 
With theta= 510 ,  ExtHyp prob of 15= 0.971130851829377 
With theta= 540 ,  ExtHyp prob of 15= 0.972706636123995 
With theta= 570 ,  ExtHyp prob of 15= 0.974119307783109 
### The Cornfield (1956) exact interval is = (2.58,590)

> 1-pExtHyp(14,15,15,22,2.58) ### = 0.02491509
> 1-pExtHyp(14,15,15,22,590)  ### = 0.9749826

> for(i in c(1:5,seq(300,570,30))) cat("With theta=",i,
  "  Score Stat is",round(NuisBinOR(matrix(c(15,7,0,8), ncol=2),
  thet=i)["Scorstat"],4),"\n")
With theta= 1   Score Stat is 3.3029 
With theta= 2   Score Stat is 2.3625 
With theta= 3   Score Stat is 1.961 
With theta= 4   Score Stat is 1.7241 
With theta= 5   Score Stat is 1.5626 
With theta= 300   Score Stat is 0.2372 
With theta= 330   Score Stat is 0.2263 
With theta= 360   Score Stat is 0.2168 
With theta= 390   Score Stat is 0.2084 
With theta= 420   Score Stat is 0.2009 
With theta= 450   Score Stat is 0.1941 
With theta= 480   Score Stat is 0.188 
With theta= 510   Score Stat is 0.1825 
With theta= 540   Score Stat is 0.1774 
With theta= 570   Score Stat is 0.1727 
### Score interval is (3,Inf)

### Recoded  NuisBinOR  to avoid  Inf loglik's
> for(i in c(1:7,seq(300,570,30))) cat("With theta=",i,
  "  LRstat is",round(NuisBinOR(matrix(c(15,7,0,8), ncol=2),
  thet=i)["LRstat"],4),"\n")
With theta= 1   LRstat is 14.0672 
With theta= 2   LRstat is 9.2209 
With theta= 3   LRstat is 7.0125 
With theta= 4   LRstat is 5.7053 
With theta= 5   LRstat is 4.8287
With theta= 6   LRstat is 4.1954 
With theta= 7   LRstat is 3.7143  
With theta= 300   LRstat is 0.1132 
With theta= 330   LRstat is 0.103 
With theta= 360   LRstat is 0.0945 
With theta= 390   LRstat is 0.0873 
With theta= 420   LRstat is 0.0811 
With theta= 450   LRstat is 0.0757 
With theta= 480   LRstat is 0.071 
With theta= 510   LRstat is 0.0669 
With theta= 540   LRstat is 0.0632 
With theta= 570   LRstat is 0.0599 
### LR profile interval is (6.71,Inf)