## 25.1 Introduction: Odds ratios

A study (Mann and Blotnicky 2017) examined the eating habits of university students. One issue studied was the relationship between eating on-campus, and where the student lived.

The researchers cross-classified the \(n=183\) students
into groups:
each student (the unit of analysis)
was observed on two *qualitative* variables:

- Where they lived: With their parents, or
*not*with their parents; - Whether they ate most meals
*off-campus*, or most meals*on-campus*.

Since both variables are *qualitative*,
**means are not appropriate** for summarising the data.
However,
the students can be classified into a two-way table of counts
(Table 25.1),
called a *contingency table*.
Both qualitative variables have two levels,
so the table is a \(2\times 2\) table.

Lives with parents | Doesn’t live with parents | Total | |
---|---|---|---|

Most meals off-campus | 52 | 105 | 157 |

Most meals on-campus | 2 | 24 | 26 |

Total | 54 | 129 | 183 |

The purpose of the research is to study
the odds (or proportion) of students
who eat most meals off-campus,
comparing those who live with their parents
and those who do *not* live with their parents?

The parameter of interest could be
the difference between the **proportions** (or **percentages**) in each group,
a comparison between the **odds** in each group,
or the **odds ratio**.

For reasons that we can’t delve into,
usually the **odds ratio** (OR) is used as the parameter.
One important reason is that software
produces output related to the sample OR.

To compare two groups with regard to another qualitative variable,
software usually works with **odds** rather than percentages or proportions.

Using the OR, the RQ could be written as

Among university students, what is the odds ratio of students eating most meals off-campus, comparing those who

doanddo notlive with their parents?

The parameter is the population OR,
comparing the odds of eating most meals *off*-campus
for students living with their parents to students *not* living with their parents.

Take care in defining the odds ratios in the parameter!

Recall (Sect. 14.2 that software usually compares Row 1 to Row 2, and Columnn 1 to Column 2**Think 25.1 (POCI)**What is P, O, C and I for this RQs?