5.05 Two-Way Frequency Tables
Making Two-Way Relative Frequency Tables
Converting the data to proportional values can make it easier to see and interpret relationships. When the data is shown as proportions, and sometimes percentages, the table is called a two-way relative frequency table. Each cell is shown as a ratio relative to all the data. The joint relative frequency is the proportional values in the interior of the table. The marginal relative frequency is shown in the column and row totals.
Joint Frequency
Each entry in a two-way table A joint frequency shows the data for each two-category response and occurs in the body of the table
Example 1: A survey of high-school students asked whether they prefer driving a pick-up truck or a car.
Male Students: 56 preferred a pick-up truck 62 preferred a car Female Students: 40 preferred a pick-up truck 68 preferred a car blob:chrome-untrusted://media-app/f7717cf6-d218-4717-ac51-0fc67c8d3f4a
Interpreting Data Using Conditional Relative Frequencies
Not all survey results fall into one category. You might like hip hop and rock, or you may not like either type of music. Two-way frequency tables such as the ones you have been exploring allow you to evaluate which parts of the survey responses fall into which categories. But what if you wanted to know the probability that a student likes hip hop out of all students who like rock? This is where a conditional relative frequency is useful.
Joint Relative Frequency
The proportional values found in the interior of a relative frequency table
The Statistical Process and Two-way Frequency Tables
A statistical process is a four-step problem-solving process: 1). Formulate a statistical question that anticipates variability and can be answered by data. 2). Design and implement a plan that collects good data. 3). Analyze the data by graphs and/or numerical methods. 4). Interpret the analysis based on the original question.
Two-Way Frequency Table
A table that displays the frequencies of data in two different categories
Sum It Up
The four-step statistical process might require data that has two categories. A two-way frequency table shows the frequencies for data that has two categories. A joint frequency is found by reading from the inner cells of a two-way frequency table. Look at the row title and the column title to find the two categories for each joint frequency. The sums for each row and column are shown as marginal frequencies. Marginal frequencies are found on the outside edges of the table (in the last row and the last column). A relative frequency table shows each frequency as a proportion of the whole data sample size. A joint relative frequency is found by dividing a joint frequency by the whole sample size. A marginal relative frequency is found by dividing a marginal frequency by the whole sample size. A conditional relative frequency shows a frequency proportion for a given condition or category. For example, if you are given a specific category (in a row or column), what do the other categories show? This is helpful when looking for trends or associations in the data. A conditional relative frequency is found by dividing a joint frequency by a marginal frequency. Two tables are needed to display the calculations for conditional relative frequencies: One table to show row categories Another table to show column categories
Marginal Relative Frequency
The values shown in the column and row totals of a relative frequency table
Conditional Relative Frequency
This value shows a frequency proportion for a given condition or category
Formulas
To find a relative frequency, divide the frequency by the total size of the sample. A conditional relative frequency is found by dividing the joint frequency by the marginal frequency for that row or column.
What Does It Mean?
When two factors have a higher percentage, they can be said to have a strong association, or correlation, with each other. This means they are strongly related. The higher the percentage, or the closer the decimal value is to one, the stronger the association