Question

The data set “UCBAdmissions” in R contains admission decisions by gender at six departments of UC Berkeley. For this data set, carry out appropriate test for independence between the admission decision and gender for each of the departments.

What are your conclusions? Please submit your R script with the answer.

Answer 1

Install the package "vcd". You will find a function called assocstats().

install.package("vcd")

library(vcd)

> assocstats(UCBAdmissions)
$`Dept:A`
                    X^2 df   P(> X^2)
Likelihood Ratio 19.054  1 1.2707e-05
Pearson          17.248  1 3.2804e-05

Phi-Coefficient   : 0.136 
Contingency Coeff.: 0.135 
Cramer's V        : 0.136 

$`Dept:B`
                     X^2 df P(> X^2)
Likelihood Ratio 0.25864  1  0.61105
Pearson          0.25372  1  0.61447

Phi-Coefficient   : 0.021 
Contingency Coeff.: 0.021 
Cramer's V        : 0.021 

$`Dept:C`
                     X^2 df P(> X^2)
Likelihood Ratio 0.75098  1  0.38616
Pearson          0.75354  1  0.38536

Phi-Coefficient   : 0.029 
Contingency Coeff.: 0.029 
Cramer's V        : 0.029 

$`Dept:D`
                     X^2 df P(> X^2)
Likelihood Ratio 0.29787  1  0.58522
Pearson          0.29798  1  0.58515

Phi-Coefficient   : 0.019 
Contingency Coeff.: 0.019 
Cramer's V        : 0.019 

$`Dept:E`
                     X^2 df P(> X^2)
Likelihood Ratio 0.99039  1  0.31965
Pearson          1.00107  1  0.31705

Phi-Coefficient   : 0.041 
Contingency Coeff.: 0.041 
Cramer's V        : 0.041 

$`Dept:F`
                     X^2 df P(> X^2)
Likelihood Ratio 0.38362  1  0.53567
Pearson          0.38409  1  0.53542

Phi-Coefficient   : 0.023 
Contingency Coeff.: 0.023 
Cramer's V        : 0.0

Look at the p-values.Only department A has some dependence between admission decision and gender. For the rest, the conclusion is inconclusive as we cannot reject the null hypothesis of independence.