Two Way Table Basics
What is a two-way table used for?
To display data that shows the relationship between two categorical variables.
What is a “bivariate categorical variable”?
Data that compares two categories, like “Grade Level” and “Favorite Sport.”
You survey 10 students. 4 like pizza and play soccer, 2 like pizza and don’t play, 3 don’t like pizza and play, 1 doesn’t like pizza and doesn’t play. Make a 2x2 table.
Pizza and Soccer: 4
Pizza and No Soccer: 2
No Pizza and Soccer: 3
No Pizza and No Soccer: 1
How do you find the relative frequency of students who like pizza and play soccer? (from 10 total students)
4/10 = 0.4 or 40%
If 80% of dog owners like to hike and only 30% of cat owners do, is there an association?
Yes, likely association between pet ownership and hiking.
What do we call the values in a two-way table that show how many times something occurs?
Frequencies
What is a “marginal total”?
The total in the rows or columns outside the main part of the table.
What is the row total for students who like pizza? (based on above)
4 + 2 = 6
Find the row relative frequency for students who like pizza and play soccer. (from pizza row total of 6)
4/6 ≈ 0.67 or 67%
If both boys and girls prefer soccer 50% of the time, is there an association between gender and sport preference?
No, no association.
What does each cell in a two-way table represent?
The frequency of subjects that fall into both categories.
What is a “joint frequency”?
The count of subjects that fall into both categories (an inner cell).
What is the column total for students who play soccer? (based on above)
4 + 3 = 7
Find the column relative frequency for students who play soccer and like pizza. (from soccer column total of 7)
4/7 ≈ 0.57 or 57%
If the percent of pizza lovers who play soccer is higher than the percent of non-pizza lovers who do, what might that suggest?
A possible association between pizza preference and playing soccer.
What is the difference between a frequency and a relative frequency?
Frequency is a count; relative frequency is a proportion or percent.
What is a “conditional relative frequency”?
A percentage based on a row or column total, not the overall total.
What is the total number of students surveyed?
10
What does it mean if row relative frequencies vary a lot?
It suggests a possible association between the variables.
If data shows no big difference in column percentages, what should you conclude?
That the two variables are likely not associated.
How do you find the total number of subjects in a two-way table?
Add all the frequencies in the table.
What does it mean when there's “no association” between two variables?
The variables do not seem to affect each other; the percentages are similar across groups.
What are the marginal totals for each row and column?
Pizza: 6, No Pizza: 4; Soccer: 7, No Soccer: 3
What does it mean if the relative frequencies are close in all rows/columns?
It suggests no strong association between the variables.
True or False: Two variables being associated means one causes the other.
False. Association does not mean causation.