> #############################
> ### Berkeley admissions data 
> ### Lessons 4 & 5
> ### Uses dataset already in R
> ### See also berkeley1.R in Lesson 4 for a different code 
> ### See also related berkeleyLoglin.R in Lesson 5
> #############################
> 
> ### Dataset already exist in R library
> UCBAdmissions 
, , Dept = A

          Gender
Admit      Male Female
  Admitted  512     89
  Rejected  313     19

, , Dept = B

          Gender
Admit      Male Female
  Admitted  353     17
  Rejected  207      8

, , Dept = C

          Gender
Admit      Male Female
  Admitted  120    202
  Rejected  205    391

, , Dept = D

          Gender
Admit      Male Female
  Admitted  138    131
  Rejected  279    244

, , Dept = E

          Gender
Admit      Male Female
  Admitted   53     94
  Rejected  138    299

, , Dept = F

          Gender
Admit      Male Female
  Admitted   22     24
  Rejected  351    317

> 
> ### To test the odds-ratios in the marginal table and each of the subtables
> library(vcd)
> 
> ##marginal table Admit x Gender
> admit.gender=margin.table(UCBAdmissions, c(1,2))
> admit.gender
          Gender
Admit      Male Female
  Admitted 1198    557
  Rejected 1493   1278
> admit.gender/4526
          Gender
Admit           Male    Female
  Admitted 0.2646929 0.1230667
  Rejected 0.3298719 0.2823685
> 
> exp(oddsratio(admit.gender))
[1] 1.84108
> chisq.test(admit.gender)

	Pearson's Chi-squared test with Yates' continuity correction

data:  admit.gender 
X-squared = 91.6096, df = 1, p-value < 2.2e-16

> 
> ##Tests for partial tables AdmitxGender for each level of Dept.
> chisq.test(UCBAdmissions[,,1])

	Pearson's Chi-squared test with Yates' continuity correction

data:  UCBAdmissions[, , 1] 
X-squared = 16.3718, df = 1, p-value = 5.205e-05

> exp(oddsratio(UCBAdmissions[,,1]))
[1] 0.3492120
> 
> chisq.test(UCBAdmissions[,,2])

	Pearson's Chi-squared test with Yates' continuity correction

data:  UCBAdmissions[, , 2] 
X-squared = 0.0851, df = 1, p-value = 0.7705

> exp(oddsratio(UCBAdmissions[,,2]))
[1] 0.8025007
> 
> chisq.test(UCBAdmissions[,,3])

	Pearson's Chi-squared test with Yates' continuity correction

data:  UCBAdmissions[, , 3] 
X-squared = 0.6332, df = 1, p-value = 0.4262

> exp(oddsratio(UCBAdmissions[,,3]))
[1] 1.133060
> 
> chisq.test(UCBAdmissions[,,4])

	Pearson's Chi-squared test with Yates' continuity correction

data:  UCBAdmissions[, , 4] 
X-squared = 0.2216, df = 1, p-value = 0.6378

> exp(oddsratio(UCBAdmissions[,,4]))
[1] 0.9212838
> 
> chisq.test(UCBAdmissions[,,5])

	Pearson's Chi-squared test with Yates' continuity correction

data:  UCBAdmissions[, , 5] 
X-squared = 0.808, df = 1, p-value = 0.3687

> exp(oddsratio(UCBAdmissions[,,5])
+ 
+ chisq.test(UCBAdmissions[,,6])
Error: syntax error
> exp(oddsratio(UCBAdmissions[,,6]))
[1] 0.8278727
> 
> ### To visualize graphically these association explore fourfold() function in the vcd() package!
> 
> ### CMH test
> mantelhaen.test(UCBAdmissions)

	Mantel-Haenszel chi-squared test with continuity correction

data:  UCBAdmissions 
Mantel-Haenszel X-squared = 1.4269, df = 1, p-value = 0.2323
alternative hypothesis: true common odds ratio is not equal to 1 
95 percent confidence interval:
 0.7719074 1.0603298 
sample estimates:
common odds ratio 
        0.9046968