One-Way vs. Two-Way Tables (and Where Crosstab Software Fits)

When it comes to analyzing statistics, the playing field is wide open with various methods that produce various insights and results. Tables typically provide a straightforward view of you data, and even they have variations you can use. Two of the more common are one-way tables and two-way tables, with the latter a component in crosstab software.

One-Way Tables 

One-way tables are those that present data for a single, categorical variable. Categorical variables refer to variables described by labels or names, such as hat color, shoe style or a dog breed. The one-way table below showcases data on three hat color choices of 10 men surveyed.

Hat Color Choices Red Blue Yellow
5 3 2

 

The data that appears in one-way tables can easily be represented in bar chart, since the table is the bar chart’s tabular equivalent. Both bar charts and one-way tables showcase categorical data in the form of frequency counts or relative frequencies.

  • Frequency counts refer to the number of times a specific event occurs.
  • Relative frequencies refer to the number of times a specific event occurs in relation to the total population.

The relative frequency of a man preferring a red hat, for example, would be 5/10, or 50 percent.

Two-Way Tables

Anyone familiar with crosstab software is already familiar with two-way tables. Also known as contingency tables or cross-tabulations, two-way tables are ideal for analyzing relationships between categorical variables. Like one-way tables, crosstab software tables can double as frequency counts or relative frequencies.

The two-way table below shows data on the preferred leisure activity of 50 adults, with preferences broken down by gender. 

Leisure Activity Dance Sports TV Total
Men 2 10 8 20
Women 16 6 8 30
Total 18 16 16 50

 

Not only could the above table be described as a two-way table, contingency table or cross-tabulation, but it could also be called a frequency table since the table entries are frequency counts.

Finding the relative frequency of any of the data simply involves looking at the number of times a certain event occurs in relation to the overall population. Because relative frequencies are indicated by percentages, you or your crosstab software would need to do some quick math to determine relative frequencies.

Relative Frequency Examples

Relative frequency of men preferring dance: 2/50 = .04 = 4 percent

Relative frequency of men preferring sports: 10/50 = .20 = 20 percent

Relative frequency of women preferring dance: 16/50 = .32 = 32 percent

Relative frequency of women preferring sports: 6/50 = .12 = 12 percent

Relative frequency of men preferring TV: 8/50 = .16 = 16 percent

Relative frequency of women preferring TV: 8/50 = .16 = 16 percent

Transforming numbers from the crosstab software table into relative frequency percentages can give you a better idea of the meaningful weight of each response. Additional relative frequencies could also be calculated, giving you additional insights into your data.

Whether you use one-way tables and bar charts or two-way tables and crosstab software, your data analysis can become much more intricate and intriguing using the right tools for the job.

 

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