A cross table provides information about a bivariate distribution, that is, the distribution of two variables. To obtain a cross table, we just need to add a second variable in the table() function: Here, we display a cross table between satisfaction with democracy and gender:
table(
pss$stfdem,
pss$gndr
)##
## female male
## 0 117 109
## 1 133 135
## 2 211 225
## 3 287 331
## 4 377 377
## 5 466 384
## 6 311 320
## 7 251 271
## 8 164 174
## 9 82 97
## 10 41 42As with everything in R, we can also save this table as an object:
mytable <- table(
pss$stfdem,
pss$gndr
)To display percentages instead of frequencies, the prop.table() function is used. This function can output column, row, or total percentages. We can either call a table object or use the table() function within the function. Here, we call the row percentage by specifying the value \(1\) in the last argument.
# Zeilenprozentuierung
prop.table(
mytable,
1
) ##
## female male
## 0 0.5176991 0.4823009
## 1 0.4962687 0.5037313
## 2 0.4839450 0.5160550
## 3 0.4644013 0.5355987
## 4 0.5000000 0.5000000
## 5 0.5482353 0.4517647
## 6 0.4928685 0.5071315
## 7 0.4808429 0.5191571
## 8 0.4852071 0.5147929
## 9 0.4581006 0.5418994
## 10 0.4939759 0.5060241# alternativer Weg mit table()-Funktion
prop.table(
table(
pss$stfdem,
pss$gndr
),
1
)The column percentages can be displayed by changing the second argument to the value \(2\):
prop.table(
mytable,
2
)##
## female male
## 0 0.04795082 0.04421907
## 1 0.05450820 0.05476673
## 2 0.08647541 0.09127789
## 3 0.11762295 0.13427992
## 4 0.15450820 0.15294118
## 5 0.19098361 0.15578093
## 6 0.12745902 0.12981744
## 7 0.10286885 0.10993915
## 8 0.06721311 0.07058824
## 9 0.03360656 0.03935091
## 10 0.01680328 0.01703854If no second argument is provided, the total percentages will be automatically displayed:
prop.table(mytable)##
## female male
## 0 0.023853211 0.022222222
## 1 0.027115189 0.027522936
## 2 0.043017329 0.045871560
## 3 0.058511723 0.067482161
## 4 0.076860347 0.076860347
## 5 0.095005097 0.078287462
## 6 0.063404689 0.065239551
## 7 0.051172273 0.055249745
## 8 0.033435270 0.035474006
## 9 0.016717635 0.019775739
## 10 0.008358818 0.008562691The marginal frequencies can be displayed using the margin.table() function. Again, the value \(1\) in the second argument represents row marginal frequencies, and the value \(2\) displays the column marginal frequencies:
# Zeilenrandhäufigkeiten
margin.table(
mytable,
1
)##
## 0 1 2 3 4 5 6 7 8 9 10
## 226 268 436 618 754 850 631 522 338 179 83# Spaltenrandhäufigkeiten
margin.table(
mytable,
2
)##
## female male
## 2440 2465There are various libraries that allow for a more aesthetically pleasing representation of relative frequencies. One of them is the library gmodels:
if(!require("gmodels")) install.packages("gmodels")
library("gmodels")From the library, we use the CrossTable() function. This function outputs all the information mentioned above at once:
CrossTable(
pss$stfdem,
pss$gndr
)##
##
## Cell Contents
## |-------------------------|
## | N |
## | Chi-square contribution |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 4905
##
##
## | pss$gndr
## pss$stfdem | female | male | Row Total |
## -------------|-----------|-----------|-----------|
## 0 | 117 | 109 | 226 |
## | 0.186 | 0.184 | |
## | 0.518 | 0.482 | 0.046 |
## | 0.048 | 0.044 | |
## | 0.024 | 0.022 | |
## -------------|-----------|-----------|-----------|
## 1 | 133 | 135 | 268 |
## | 0.001 | 0.001 | |
## | 0.496 | 0.504 | 0.055 |
## | 0.055 | 0.055 | |
## | 0.027 | 0.028 | |
## -------------|-----------|-----------|-----------|
## 2 | 211 | 225 | 436 |
## | 0.160 | 0.158 | |
## | 0.484 | 0.516 | 0.089 |
## | 0.086 | 0.091 | |
## | 0.043 | 0.046 | |
## -------------|-----------|-----------|-----------|
## 3 | 287 | 331 | 618 |
## | 1.357 | 1.343 | |
## | 0.464 | 0.536 | 0.126 |
## | 0.118 | 0.134 | |
## | 0.059 | 0.067 | |
## -------------|-----------|-----------|-----------|
## 4 | 377 | 377 | 754 |
## | 0.010 | 0.010 | |
## | 0.500 | 0.500 | 0.154 |
## | 0.155 | 0.153 | |
## | 0.077 | 0.077 | |
## -------------|-----------|-----------|-----------|
## 5 | 466 | 384 | 850 |
## | 4.407 | 4.362 | |
## | 0.548 | 0.452 | 0.173 |
## | 0.191 | 0.156 | |
## | 0.095 | 0.078 | |
## -------------|-----------|-----------|-----------|
## 6 | 311 | 320 | 631 |
## | 0.027 | 0.026 | |
## | 0.493 | 0.507 | 0.129 |
## | 0.127 | 0.130 | |
## | 0.063 | 0.065 | |
## -------------|-----------|-----------|-----------|
## 7 | 251 | 271 | 522 |
## | 0.289 | 0.287 | |
## | 0.481 | 0.519 | 0.106 |
## | 0.103 | 0.110 | |
## | 0.051 | 0.055 | |
## -------------|-----------|-----------|-----------|
## 8 | 164 | 174 | 338 |
## | 0.102 | 0.101 | |
## | 0.485 | 0.515 | 0.069 |
## | 0.067 | 0.071 | |
## | 0.033 | 0.035 | |
## -------------|-----------|-----------|-----------|
## 9 | 82 | 97 | 179 |
## | 0.557 | 0.552 | |
## | 0.458 | 0.542 | 0.036 |
## | 0.034 | 0.039 | |
## | 0.017 | 0.020 | |
## -------------|-----------|-----------|-----------|
## 10 | 41 | 42 | 83 |
## | 0.002 | 0.002 | |
## | 0.494 | 0.506 | 0.017 |
## | 0.017 | 0.017 | |
## | 0.008 | 0.009 | |
## -------------|-----------|-----------|-----------|
## Column Total | 2440 | 2465 | 4905 |
## | 0.497 | 0.503 | |
## -------------|-----------|-----------|-----------|
##
##