Lesson 17: Interpreting Two-Way Tables

Objective

You will calculate conditional, marginal, and joint frequencies and explain what they mean in the context of the data.

Vocabulary

marginal (relative) frequency, joint (relative) frequency, conditional relative frequency

Essential Concepts

Lesson 17 Essential Concepts

Marginal (relative) frequencies tell us about the distribution of a single variable. Conditional relative frequencies tell us about the distribution of one variable when "subsetting" the other.

Lesson

Time Use Campaign Data Collection Responses:
1. Today is the last day to collect data for the Time Use campaign. You will be using the Campaigns Tool to view your survey responses. Click on Campaigns on your IDS Homepage, found at https://tools.idsucla.org and sign in if prompted. Find the Time Use campaign and click on Responses.
Watch this video to learn how to use the Campaigns Tool.
1. Click on the blue plus sign (+) to expand the surveys you have submitted.
  1. For which days have you collected data?
  2. Do the total number of minutes for each day add up to approximately 1440?
  3. What patterns are you noticing?
  Note: If you forgot to include an activity for one of the days, simply submit another survey, making sure to select the correct day and include the activity.
In Lesson 16, you created 2 questions and a two-way table that would help you organize the data generated by your questions. You also collected data by surveying at least 20 people.
You will come back to your frequency table at the end of this lesson.
You also learned in Lesson 16 how to calculate relative frequencies. Now it’s time to look at other ways of understanding a two-way frequency table.
Here are the Cat Ownership and Instruments tables from Lesson 16:
Suppose that we want to know the following information:
1. How many students own a cat? 16
2. What is the proportion of students who own a cat? 16/35 ≈ 0.46 ≈ 46%
3. What is the proportion of students who do not play an instrument? 18/35 ≈ 0.51 ≈ 51%
Notice that the answers to the questions were located in the margins of the table and therefore are called marginal frequencies. The margins are the row and the column that show the total. Questions 6b and 6c are marginal relative frequencies because they are calculated from a subtotal that is divided by the grand total.
Now suppose that we want to know the following information:
1. How many students own a cat and play an instrument? 7
2. What is the proportion of students that own a cat and play and instrument? 7/35=0.2=20%
3. What is the proportion of students who neither own a cat nor play an instrument? 10/35 ≈ 0.286 ≈ 29%
Notice that the answers to the questions were located in the cells in the body of the table and therefore are called joint frequencies. Questions 8b and 8c are joint relative frequencies since they are being expressed out of a total number of occurrences.
Finally, suppose that we wanted to answer this question: Do a greater proportion of students in Rosa’s art class who do not own cats prefer to play an instrument than those who do own cats?
In this case, the total for the “No cats” row is important because we are only concerned with that subset of the group. Compare the values that show the conditional relative frequency for the row. Slightly more non-cat owners than cat owners play an instrument (53% vs 44%).

Note: This is a conditional relative frequency by row. We can also calculate conditional relative frequencies by column if we were interested in knowing the difference in cat ownership for those students who play instruments.
The two-way frequency table below shows which emotion males and females associate with the color red.

Gender and the Color Red

Love Anger Fear Total

Male 7 11 5 23

Female 12 15 10 37

Total 19 26 15 60
In your IDS Journal, write down four questions about the data in the table above that must be answered by the following:
1. a marginal frequency
2. a marginal relative frequency
3. a joint relative frequency
4. a conditional relative frequency (either by row or column)

Reflection

What are the essential learnings you are taking away from this lesson?

Homework & Next Day

Refer back to the two-way frequency table you created in Lesson 16 and:
1. Create a two-way relative frequency table.
2. Ask 4 questions about the data in your table that must be answered by a:
  1. marginal frequency
  2. marginal relative frequency
  3. joint relative frequency
  4. conditional relative frequency (either by row or column)
Complete Lab 1G prior to the Practicum.

	Love	Anger	Fear	Total
Male	7	11	5	23
Female	12	15	10	37
Total	19	26	15	60