Relative Frequency Two Way Table

Statistics Definitions >

What is a Ii Way Table?

A 2 way table is a manner to display frequencies or relative frequencies for two categorical variables. One category is represented by rows and a 2d category is represented by columns.

Example

Sixty people (30 men and 30 women) were asked what blazon of movie they would prefer to watch and the following responses were recorded:

6 men preferred rom-coms.
16 men preferred activity movies.
8 men preferred horror movies.
12 women preferred rom-coms.
14 women preferred activity movies.
four women preferred horror movies.

The information collected was used to build the post-obit two way table:

The entries in the table are counts; this type of table is chosen a two way frequency table. The table has several features:

Categories are labeled in the left column and top row.
The counts are placed in the heart of the table.
Totals appear at the end of each row and column.
A sum of all counts (a grand total) is placed at the bottom correct.
The totals in the right cavalcade and bottom row are chosen marginal distributions (excluding the grand total).
The entries in the centre of the table (everything except the marginal distributions) are called joint frequencies.

Two Fashion Relative Frequency Tabular array

Instead of displaying counts in the table, yous could testify relative frequencies. This is the same two way relative frequency table (decimals, percents, or ratios) displayed instead of counts:

To catechumen counts into relative frequencies, carve up the count by the total number of items. In the higher up tabular array, the starting time count is for men / Rom-com (count=6), and so 6/60 = 0.ane.
The totals in the right cavalcade and bottom row are, like the 2 way frequency table, called marginal distributions. However, the entries in the heart of the table are called conditional frequencies or conditional distributions.

Two fashion frequency tables are sometimes called contingency tables, just that term is commonly only used once you get into more avant-garde statistics that involves inquiry and hypothesis testing.

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References

Agresti A. (1990) Categorical Data Analysis. John Wiley and Sons, New York.
Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences, Wiley.
Levine, D. (2014). Even Yous Can Learn Statistics and Analytics: An Easy to Empathize Guide to Statistics and Analytics 3rd Edition. Pearson FT Printing

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