3.1 The Histogram
3.1: The Histogram
3.1.1: Cross Tabulation
Cross tabulation (or crosstabs for short) is a statistical process that summarizes categorical data to create a contingency table.
Learning Objective
Demonstrate how cross tabulation provides a basic picture of the interrelation between two variables and helps to find interactions between them.
Key Takeaways
Key Points
- Crosstabs are heavily used in survey research, business intelligence, engineering, and scientific research.
- Crosstabs provide a basic picture of the interrelation between two variables and can help find interactions between them.
- Most general-purpose statistical software programs are able to produce simple crosstabs.
Key Term
- cross tabulation
- a presentation of data in a tabular form to aid in identifying a relationship between variables
Cross tabulation (or crosstabs for short) is a statistical process that summarizes categorical data to create a contingency table. It is used heavily in survey research, business intelligence, engineering, and scientific research. Moreover, it provides a basic picture of the interrelation between two variables and can help find interactions between them.
In survey research (e.g., polling, market research), a “crosstab” is any table showing summary statistics. Commonly, crosstabs in survey research are combinations of multiple different tables. For example, combines multiple contingency tables and tables of averages.
Crosstab of Cola Preference by Age and Gender
A crosstab is a combination of various tables showing summary statistics.
Contingency Tables
A contingency table is a type of table in a matrix format that displays the (multivariate) frequency distribution of the variables. A crucial problem of multivariate statistics is finding the direct dependence structure underlying the variables contained in high dimensional contingency tables. If some of the conditional independences are revealed, then even the storage of the data can be done in a smarter way. In order to do this, one can use information theory concepts, which gain the information only from the distribution of probability. Probability can be expressed easily from the contingency table by the relative frequencies.
As an example, suppose that we have two variables, sex (male or female) and handedness (right- or left-handed). Further suppose that 100 individuals are randomly sampled from a very large population as part of a study of sex differences in handedness. A contingency table can be created to display the numbers of individuals who are male and right-handed, male and left-handed, female and right-handed, and female and left-handed .
The numbers of the males, females, and right-and-left-handed individuals are called marginal totals. The grand total–i.e., the total number of individuals represented in the contingency table– is the number in the bottom right corner.
The table allows us to see at a glance that the proportion of men who are right-handed is about the