# Cross Tabulation with Xtabs exercises

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The `xtabs()`

function creates contingency tables in frequency-weighted format. Use `xtabs()`

when you want to numerically study the distribution of one categorical variable, or the relationship between two categorical variables. Categorical variables are also called “factor” variables in R.

Using a formula interface, `xtabs()`

can create a contingency table, (also a “sparse matrix”), from cross-classifying factors, usually contained in a data frame.

Answers to the exercises are available here.

**Exercise 1**

`xtabs()`

with One Categorical Variable

Input the following required Data Frame:

```
Data1 <- data.frame(Reference = c("KRXH", "KRPT", "FHRA", "CZKK", "CQTN", "PZXW", "SZRZ", "RMZE", "STNX", "TMDW"), Status = c("Accepted", "Accepted", "Rejected", "Accepted", "Rejected", "Accepted", "Rejected", "Rejected", "Accepted", "Accepted"), Gender = c("Female", "Male", "Male", "Female", "Female", "Female", "Male", "Female", "Female", "Female"), Test = c("Test1", "Test1", "Test2", "Test3", "Test1", "Test4", "Test4", "Test2", "Test3", "Test1"), NewOrFollowUp = c("New", "New", "New", "New", "New", "Follow-up", "New", "New", "New", "New"))
```

The `xtabs()`

function can display the frequency, or count, of the levels of categorical variables. For the first exercise, use the `xtabs()`

function to find the count of levels in the variable, “`Status`

“, within the above dataframe, “`Data1`

“.

**Exercise 2**

Two Categorical Variables – Discoving relationships within a dataset

Next, using the `xtabs()`

function, apply two variables from “`Data1`

“, to create a table delineating the relationship between the “`Reference`

” category, and the “`Status`

” category.

**Exercise 3**

Three Categorical Variables – Creating a Multi-Dimensional Table

Apply three variables from “`Data1`

” to create a Multi-Dimensional Cross-Tabulation of “`Status`

“, “`Gender`

“, and “`Test`

“.

**Exercise 4**

Creating Two Dimensional Tables from Multi-Dimensional

Cross-Tabulations

Enclose the `xtabs()`

formula from Exercise 3 within the “`ftable()`

” function, to display a Multi-Dimensional Cross-Tabulation in two dimensions.

**Exercise 5**

Row Percentages

The R package “`tigerstats`

” is required for the next two exercises.

```
if(!require(tigerstats)) {install.packages("tigerstats"); require(tigerstats)}
library(tigerstats)
```

1) Create an `xtabs()`

formula that cross-tabulates “`Status`

“, and “`Test`

“.

2) Enclose the `xtabs()`

formula in the tigerstats function, “`rowPerc()`

” to display row percentages for “`Status`

” by “`Test`

“.

**Exercise 6**

Column Percentages

1) Create an `xtab()`

formula that cross-tabulates “`Reference`

“, and “`Status`

“.

2) Use “`colPerc()`

” to display column percentages for “`Reference`

” by “`Status`

“.

**Exercise 7**

Plotting Cross-Tabulations

Use the “`plot()`

” function, and the “`xtabs()`

” function to plot “`Status`

” by “`Gender`

“.

**Exercise 8**

`xtabs()`

– Explanatory and Response Variables

In order to examine whether the explanatory variable “`Gender`

” affects the response variable “` Status`

“, create a two factor `xtabs()`

formula with the Response variable as the first condition, and the Explanatory variable as the second condition.

**Exercise 9**

Using `cbind()`

with `xtabs()`

Using the “`cbind()`

” function within an `xtabs()`

formula can define the last two columns of a flat table of your dataset. The variable after ~ (tilde) will display as the row data. For example, `ftable(xtabs(cbind(variable1, variable2) ~ variable3, data=" "))`

.

For this exercise, create a flat table with columns for “`Gender`

” and “`Test`

“. The row variables are “`Reference`

“.

**Exercise 10**

Testing Correlation with `xtabs()`

When processed through the “`summary()`

” function, an `xtabs()`

formula can test for independence of variables. Therefore, use `summary()`

and `xtabs()`

to test for a “`Reference`

” affecting “`Status`

” correlation.

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