Using R for Introductory Statistics : John Verzani

Using R for introductory statistics 124A model formula of the type numeric ~ factor represents the statistical modelThat is, for each level i of the factor, there is a sample,with mean described by µ i .As this model says something about the means of the different samples, multipleboxplots are useful for viewing the data. A boxplot allows us to compare the medians,which are basically the mean if the data is not skewed. Consequently, it is the plot madewhen the plot () function encounters such a model formula. That is, if x is a numeric datavector and f a factor indicating which group the corresponding element of x belongs to,then the command plot (x ~ f) will create side-by-side boxplots of values of x split up bythe levels of f.For example, Figure 4.6 could also have been made with the commands> plot(gestation ~ factor(inc), data=babies,varwidth=TRUE,+ subset = gestation != 999 & inc !=98,+ xlab="income level", ylab="gestation (days)")The function factor() explicitly makes inc a factor and not a numeric data vector.Otherwise, the arguments are identical to those to the boxplot() function that createdFigure 4.6.4.3.3 Creating contingency tables with xtabs()We saw in Example 4.1 how to make a three-way contingency table using the table()function starting with raw data. What if we had only the count data? How could we enterit in to make a three-way contingency table? We can enter the data in as a data frame andthen use xtabs() to create contingency tables. The xtabs() function offers a formulainterface as an alternative to table().The function as.data.frame() inverts what xtabs() and table() do. It will create a dataframe with all possible combinations of the variable levels and a count of frequencieswhen called on a contingency table.■ Example 4.7: Seat-belt usage factors The three-way table in Table 4.5 showspercentages of seat-belt usage for two years, broken down by type of law enforcementand type of car. Law enforcement is primary if a driver can be pulled over and ticketedfor not wearing a seat belt, and secondary if a driver can be ticketed for this offense onlyif pulled over for another infraction. This data comes from a summary of the 2002Moving Traffic Study as part of NOPUS (http://www.nhtsa.gov/), which identified thesetwo factors as the primary factors in determining seat-belt usage.We show how to enter the data into R using a data frame, and from thereTable 4.5 Seat-belt data by type of law andvehicleEnforcement primary secondaryYear 2001 2002 2001 2002Car typepassenger 71 82 71 71