Statistics for laboratory scientists II

Solutions for the homework problems for lecture 3

1. Here is the R code for creating the observed table.

       mydata <- rbind( c(26, 63), c(29, 26))

   1. It's best to use the built-in function chisq.test() to perform the chi-square test, and to use the results of this test to perform the likelihood ratio test.

          chi <- chisq.test(mydata)
          chi                                           # stat=7.00; P-value = 0.008

   2. For calculating the LRT statistic and corresponding P-value, we can use the expected counts given within the results of chisq.test().

          ex <- chi$expected                            # expected counts
          lrt <- 2 * sum( mydata * log(mydata/ex) )     # value = 7.92
          1 - pchisq(lrt, 1)                            # P-value = 0.005

   3. Perform Fisher's exact test using the built-in function, fisher.test().

          fisher.test(mydata)                           # P-value = 0.008

   4. We reject the null hypothesis and conclude that the presence of maples is not independent of the presence of hickories.

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Last modified: Fri Mar 31 09:24:53 EST 2006