Unit 3 Family Materials
Twovariable Statistics
Twovariable Statistics
In this unit, students learn about twoway 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 twoway 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  

lefthanded  50  66  
righthanded  826  972  
total  1,914 

Predict if there is an association between hand dominance and fruit preference.

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

Among the students who are lefthanded, 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 lefthanded prefer pineapples over mangoes. What proportion of those who are lefthanded prefer mangoes?

What proportion of those who are righthanded prefer mangoes?

Is there a significant difference between the proportion of lefthanded students who prefer mangoes and the proportion of righthanded students who prefer mangoes?

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

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

prefer mangoes prefer pineapples total lefthanded 50 66 116 righthanded 826 972 1,798 total 876 1,038 1,914  0.43, because \(50 \div 116=0.43\) or \(1  0.57 = 0.43\)
 0.46, because \(826 \div1,798=0.46\)
 No, there is no significant difference between lefthanded students who prefer mangoes and righthanded students who prefer mangoes, because 0.43 and 0.46 are close in value.
 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.