Applied Statistics Using SPSS, STATISTICA, MATLAB and R

52 2 Presenting and Summarising the Data
represent the probability density estimate for a given bin. We can list de densities
of PRT as follows:
> h$density
[1] 1.333333e-04 1.033333e-03 1.166667e-03
[4] 9.666667e-04 5.666667e-04 4.666667e-04
[7] 4.333333e-04 2.000000e-04 3.333333e-05
Thus, using the formula previously mentioned for the probability density
estimates, we compute the relative frequencies using the bin length (200 in our
case) as follows:
> h$density*200
[1] 0.026666661 0.206666667 0.233333333 0.193333333
[5] 0.113333333 0.093333333 0.086666667 0.040000000
[9] 0.006666667
2.2.3 Multivariate Tables, Scatter Plots and 3D Plots
Multivariate tables display the frequencies of multivariate data. Figure 2.19 shows
the format of a bivariate table displaying the counts nij corresponding to the several
combinations of categories of two random variables. Such a bivariate table is
called a cross table or contingency table.
When dealing with continuous variables, one can also build cross tables using
categories in accordance to the bins that would be assigned to a histogram
representation of the variables.
y 1
. . .
x 1
n 11
n 21
n 12
n 22
. . .
. . .
. . .
n 1c
n 2c
. . . . . . . . . . . .
nr1 nr2 . . . nrc rr c . . .
1 c2 cc Figure 2.19. An r×c contingency table with the observed absolute frequencies
(counts nij). The row and column totals are ri and cj, respectively.
Example 2.3
y 2
y r
x 2
Q: Consider the variables SEX and Q4 (4 th enquiry question) of the Freshmen
dataset (see Appendix E). Determine the cross table for these two categorical
variables.
x c
r 1
r 2
. . .