Test Notes,    4/9/03 evening

(1) > tstp1 <- array(c(90,100,210,90,40,170,20,160,120), dim=c(3,3))
> tstp1
     [,1] [,2] [,3]
[1,]   90   90   20
[2,]  100   40  160
[3,]  210  170  120
> tstp1eb <- matrix(c(80,320*c(100,210)/310, 60,
   240*c(40,170)/210, 60, 240*c(160,120)/280), ncol=3)
  tstp1ea <- tstp1eb; tstp1ea[2:3,1] <- 320*c(3/8,5/8)
  tstp1e0 <- outer(c(.2,.3,.5),c(400,300,300),"*")
> sum((tstp1-tstp1eb)^2/tstp1eb)   
[1] 53.6458					### X^2 for  Hb
> sum((tstp1-tstp1ea)^2/tstp1ea)
[1] 57.16667	   ### so 57.1667-53.6458 = 3.5209 = X^2  for Ha vs Hb
> sum((tstp1-tstp1e0)^2/tstp1e0)
[1] 137.6389   ### so 137.6389-57.1667= 80.472 = X^2  for H0 vs Ha
### Respectively compare these test statistics with 
> pchisq(.95, c(2,1,1))
[1] 5.991465 3.841459 3.841459

### Corresponding G^2 statistics: 
> 2*diff(c(0, sum(tstp1*log(tstp1/tstp1eb)),
   sum(tstp1*log(tstp1/tstp1ea)),
   sum(tstp1*log(tstp1/tstp1e0))))
[1]  60.7972  3.7118  78.0019
### So only the 1st and third are significant. Dividing all counts by
### 5 also divides EACH of X^2 and G^2 by 5:
> .Last.value/5
[1] 12.1594354  0.7423501 15.6003859  ### 1st & 2rd STILL significant

(3) > nv <- sample(5:10, 60, replace=T)
> Xv <- rexp(60)
> Yv <- rbinom(60, nv, plogis(-1 + .2*Xv))
> sum(Yv)
[1] 132
> sum(nv)
[1] 458
> summary(summary(tmpglm)$deviance.resid)
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-2.25100 -0.72460 -0.10640 -0.05093  0.62530  2.72200 
> summary(sqrt(nv/(tmpglm$fit*(1-tmpglm$fit)))*(
+    tmpglm$y-tmpglm$fit))
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-1.87700 -0.68330 -0.10580  0.01181  0.64330  2.86800