Unit 3 Family Materials

Two-variable Statistics

Two-variable Statistics

In this unit, students learn about two-way tables and use them to determine if two categories have an association. For example, would you predict that a forecast of rain over a school is associated with the number of students wearing rain boots? What association do you think the rain has with students’ eye colors?

It is possible for two things to have no association, as you may have guessed for rain and students’ eye colors. With your student, make predictions about associations found in daily life. For example, do these pairs share an association?

  • length of time a plant spends in sunlight and its growth

  • the size of a car and the amount of gas it takes to be full

  • number of open apps on your mobile phone and battery percentage

What other associations can you think of together?

Students can use tables and collected data to determine if two things are associated. One type of table is a two-way table, which organizes two categorical variables. A categorical variable is a variable that takes on values which can be divided into groups or categories. For example, color is a categorical variable which can take on values like red, blue, or green. In the table, you may notice that it has a total of four categories, but only two categorical variables (hand dominance and fruit preference).

With your student, examine the data collected from 1,914 other students.

   prefer mangoes   prefer pineapples   total 
 left-handed  50 66  
 right-handed  826 972  
 total     1,914
  1. Predict if there is an association between hand dominance and fruit preference.

  2. Complete the table with the totals for each column and row.

  3. Among the students who are left-handed, the proportion who prefer pineapples is about 0.57, since \(66 \div 116=0.57\). This means that about 57% of students in this group who are left-handed prefer pineapples over mangoes. What proportion of those who are left-handed prefer mangoes?

  4. What proportion of those who are right-handed prefer mangoes?

  5. Is there a significant difference between the proportion of left-handed students who prefer mangoes and the proportion of right-handed students who prefer mangoes?

  6. Was your prediction accurate? Is there an association between hand dominance and fruit preference?

Solution

  1. Sample response: I think there shouldn’t be any association between hand dominance and fruit preference, since neither should influence the other.

  2.    prefer mangoes   prefer pineapples   total 
     left-handed  50 66 116
     right-handed  826 972 1,798
     total 876 1,038 1,914
  3. 0.43, because \(50 \div 116=0.43\) or \(1 - 0.57 = 0.43\)
  4. 0.46, because  \(826 \div1,798=0.46\)
  5. No, there is no significant difference between left-handed students who prefer mangoes and right-handed students who prefer mangoes, because 0.43 and 0.46 are close in value.
  6. Sample response: I predicted there would be no association, and I think that the math supports my prediction. No, there is no association between hand dominance and fruit preference.