# 1.1 - Cases & Variables

1.1 - Cases & Variables

Throughout the course, we will be using many of the terms introduced in this lesson. Let's start by defining some of the most frequently used terms: case, variable, and constant.

case is an experimental unit. These are the individuals from which data are collected. When data are collected from humans, we sometimes call them participants. When data are collected from animals, the term subjects is often used. Another synonym is experimental unit

variable is a characteristic that is measured and can take on different values. In other words, something that varies between cases. This is in contrast to a constant which is the same for all cases in a research study.

Case
An experimental unit from which data are collected
Variable
Characteristic of cases that can take on different values (in other words, something that can vary)
Constant
Characteristic that is the same for all cases in a study

Let's look at a few examples.

## Example: Study Time & Grades

A teacher wants to know if third grade students who spend more time reading at home get higher homework and exam grades.

The students are the cases. There are three variables: amount of time spent reading at home, homework grades, and exam grades. The grade-level of the students is a constant because all students are in the third grade.

## Example: Dog Food

A researcher wants to know if dogs who are fed only canned food have different body mass indexes (BMI) than dogs who are fed only hard food. They collect BMI data from 50 dogs who eat only canned food and 50 dogs who eat only hard food.

The cases are the dogs. There are two variables: type of food and BMI. A constant would be subspecies, because all cases are domestic dogs.

## Example: Age & Weight of Sea Otters

Researchers are studying the relationship between age and weight in a sample of 100 male sea otters (Enhydra lutris).

The 100 otters are the cases. There are two variables: age and weight. Biological sex is a constant because all subjects are male. Species is also a constant

# 1.1.1 - Categorical & Quantitative Variables

1.1.1 - Categorical & Quantitative Variables

Variables can be classified as categorical or quantitative. Categorical variables are those that provide groupings that may have no logical order, or a logical order with inconsistent differences between groups (e.g., the difference between 1st place and 2 second place in a race is not equivalent to the difference between 3rd place and 4th place). Quantitative variables have numerical values with consistent intervals.

Categorical variable
Names or labels (i.e., categories) with no logical order or with a logical order but inconsistent differences between groups (e.g., rankings), also known as qualitative.
Quantitative variable
Numerical values with magnitudes that can be placed in a meaningful order with consistent intervals, also known as numerical.

## Example: Weight

A team of medical researchers weigh participants in kilograms. Weight in kilograms is a quantitative variable because it takes on numerical values with meaningful magnitudes and equal intervals.

## Example: Favorite Ice Cream Flavor

A teacher conducts a poll in her class. She asks her students if they would prefer chocolate, vanilla, or strawberry ice cream at their class party. Preferred ice cream flavor is a categorical variable because the different flavors are categories with no meaningful order of magnitudes.

## Example: Birth Location

A survey asks “On which continent were you born?” This is a categorical variable because the different continents represent categories without a meaningful order of magnitudes.

## Example: Children per Household

A census asks every household in a city how many children under the age of 18 reside there. Number of children in a household is a quantitative variable because it has a numerical value with a meaningful order and equal intervals.

## Example: Highway Mile Markers

When a car breaks down on the highway, the emergency dispatcher may ask for the nearest mile marker. Highway mile marker value is a quantitative variable because it is numeric with a meaningful order of magnitudes and equal intervals.

## Example: Running Distance

A runner records the distance he runs each day in miles. Distance in miles is a quantitative variable because it takes on numerical values with meaningful magnitudes and equal intervals.

## Example: Highest Level of Education

A census asks residents for the highest level of education they have obtained: less than high school, high school, 2-year degree, 4-year degree, master's degree, doctoral/professional degree. This is a categorical variable. While there is a meaningful order of educational attainment, the differences between each category are not consistent. For example, the difference between high school and 2-year degree is not the same as the difference between a master's degree and a doctoral/professional degree. Because there are not equal intervals, this variable cannot be classified as quantitative.

## Example: Online Courses Taught

A survey designed for online instructors asks, "How many online courses have you taught?" Three options are given: "none," "some," or "many." While there is a meaningful order of magnitudes, there are not equal intervals. This is a categorical variable.

If the survey had asked, "How many online courses have you taught? Enter a number." this would be a quantitative variable. Here, participants are answering with the number of online courses they have taught. This is a numerical value with a meaningful order of magnitudes and equal intervals.

# 1.1.2 - Explanatory & Response Variables

1.1.2 - Explanatory & Response Variables

In some research studies one variable is used to predict or explain differences in another variable. In those cases, the explanatory variable is used to predict or explain differences in the response variable. In an experimental study, the explanatory variable is the variable that is manipulated by the researcher.

Explanatory Variable

Also known as the independent or predictor variable, it explains variations in the response variable; in an experimental study, it is manipulated by the researcher

Response Variable

Also known as the dependent or outcome variable, its value is predicted or its variation is explained by the explanatory variable; in an experimental study, this is the outcome that is measured following manipulation of the explanatory variable

## Example: Panda Fertility Treatments

A team of veterinarians wants to compare the effectiveness of two fertility treatments for pandas in captivity. The two treatments are in-vitro fertilization and male fertility medications. This experiment has one explanatory variable: type of fertility treatment. The response variable is a measure of fertility rate.

## Example: Public Speaking Approaches

A public speaking teacher has developed a new lesson that she believes decreases student anxiety in public speaking situations more than the old lesson. She designs an experiment to test if her new lesson works better than the old lesson. Public speaking students are randomly assigned to receive either the new or old lesson; their anxiety levels during a variety of public speaking experiences are measured.  This experiment has one explanatory variable: the lesson received. The response variable is anxiety level.

## Example: Coffee Bean Origin

A researcher believes that the origin of the beans used to make a cup of coffee affects hyperactivity. He wants to compare coffee from three different regions: Africa, South America, and Mexico. The explanatory variable is the origin of coffee bean; this has three levels: Africa, South America, and Mexico. The response variable is hyperactivity level.

## Example: Height & Age

A group of middle school students wants to know if they can use height to predict age. They take a random sample of 50 people at their school, both students and teachers, and record each individual's height and age. This is an observational study. The students want to use height to predict age so the explanatory variable is height and the response variable is age.