Module 5: Descriptive Statistics for Two Variables
Module 5: Descriptive Statistics for Two Variables
5.01 Learning Objectives
Module 5: Learning Objectives
After completing this module, you should be able to:
1. Classify a data analysis situation according to the role-type classification
2. Identify the appropriate graphical display for a given classification in different contexts
3. Identify the appropriate numerical measures for a given classification in different contexts
4. Compare conditional percentages in a two-way table
5. Summarize distributions of two variables
6. Determine the relationship between two quantitative variables, when given a graph
7. Describe the overall pattern and the striking deviations in a graph of two variables
5.02 Explanatory and Response Variables
Explanatory and Response Variables
Career Connections
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Explanatory and Response Variables
Whenever you need to dig deeper to analyze data, you will likely need to measure units of something that
might be the cause and units of something that might be the effect.
For example, suppose you are managing a security company that patrols warehouses at night, and you
suspect that the higher absenteeism in winter is due to the lower temperatures. You can test your theory by
gathering two types of data. You can chart how cold a given night is and how many people came to work. If
your theory is correct, the data will show that as temperatures get colder, more employees will call in sick.
Or in a manufacturing situation, you might suspect that a recent spate of defective merchandise might be due to faulty goods
from a particular supplier. You might track the number of items returned that had that supplier's component to the number of
items returned that had the same component from another supplier. With enough data, comparing these numbers will shed light
on whether the supplier is the cause.
When one variable causes change in another, we call the first variable the explanatory variable (or independent variable). The
affected variable is called the response variable (or dependent variable). In a randomized experiment, the researcher
manipulates values of the explanatory variable and measures the resulting changes in the response variable. The different
values of the explanatory variable are called
treatments
. An
experimental unit
is a single object or individual to be measured.
Exercise
Identifying the Explanatory and Response Variables
Example
An insurance company wants to investigate whether taking a National Safety Council course in workplace safety reduces the
risk of on the job injuries. Four-hundred employees in both the manufacturing and operations departments were recruited as
participants. The employees were divided randomly into two groups: one group will take the National Safety Council course,
and the other group will not receive additional safety training beyond the standard company training. Each employee is then
tracked over the course of the next two years and any employee that suffers an on the job injury is recorded. At the end of the