5
How well the new teaching method works
From the data, we are 95% confident that the new teaching method
is (1.73, 157) times effective than the old method.
> library(faraway)
> data(spector)
> help (spector)
A data frame with 32 observations on the following 4
variables.
grade 1 = exam grades improved, 0 = not improved
psi 1 = student exposed to PSI (a new teach method), 0 = not
exposed
tuce a measure of ability when entering the class
gpa grade point average
> head(spector)
grade psi tuce
1
0
0
20
2
0
0
22
3
0
0
24
4
0
0
12
5
1
0
21
6
0
0
17
gpa
2.66
2.89
3.28
2.92
4.00
2.86
> library(survival)
> cmod<-clogit(grade~tuce+gpa+strata(psi),spector)
> summary(cmod)
Call:
coxph(formula = Surv(rep(1, 32), grade) ~ tuce + gpa +
strata(psi),
data = spector, method = "exact")
n= 32
coef exp(coef) se(coef)
z
p
tuce 0.0883
1.09
0.136 0.651 0.51
gpa 2.5850
13.26
1.189 2.174 0.03
tuce
gpa
exp(coef) exp(-coef) lower .95 upper .95
1.09
0.9155
0.837
1.42
13.26
0.0754
1.290
136.37
Rsquare= 0.242
(max possible= 0.601 )
Likelihood ratio test= 8.85 on 2 df,
p=0.012
Wald test
= 6 on 2 df,
p=0.0499
Score (logrank) test = 8.31 on 2 df,
p=0.0157
Drop tuce as the p-value is large (0.51)
> cmod2<-clogit(grade~gpa+strata(psi),spector)
> summary(cmod2)
Call:
coxph(formula = Surv(rep(1, 32), grade) ~ gpa + strata(psi),
data = spector, method = "exact")
n= 32
coef exp(coef) se(coef)
z
p
gpa 2.80
16.5
1.15 2.44 0.015
gpa
exp(coef) exp(-coef) lower .95 upper .95
16.5
0.0606
1.73
157
Rsquare= 0.231
(max possible= 0.601 )
Likelihood ratio test= 8.4 on 1 df,
Wald test
= 5.94 on 1 df,
Score (logrank) test = 7.9 on 1 df,
p=0.00375
p=0.0148
p=0.00493
From the data, we are 95% confident that the new teaching method
is (1.73, 157) times effective than the old method.
halfnorm(residuals(cmod2))