VARIABLES- QUALITATIVE AND QUANTITATIVE

A variable is any measured characteristic or attribute that differs for different subjects. For example, if the length of 30 desks were measured, then length would be a variable.

Key Learning Skills – 
•  Understand the difference between a qualitative (categorical) variable and a quantitative variable. 
•  Understand the types of qualitative (categorical) variables: Nominal, Ordinal, and Binary.
•  Understand the difference between a discrete and a continuous quantitative variable. 

Terms and Definitions:

Qualitative Data (Categorical Variables or Attributes) 

Qualitative data involves assigning non-numerical items into groups or categories. Qualitative data also are referred to as categorical data. The
qualitative characteristic or classification group of an item is an attribute.

Some examples of qualitative data are:
•  The pizza was delivered on time. 
•  Categorical Variable: Delivery Result
•  Attribute: On Time, Not On Time
•  The survey responses include disagree, neutral, or agree. 
•  Categorical Variable: Survey Response
•  Attribute: Disagree, Neutral, Agree
•  This car comes in black, white, red, blue, or yellow. 
•  Categorical Variable: Color 
•  Attribute: Black, White, Red, Blue, or Yellow.

Categorical variables are typically assigned attributes using a nominal, ordinal, or binary scale.  
•  Nominal variables are categorical variables that have three or more possible levels with no natural ordering. Car color would be considered a nominal variable. Again, in a nominal scale, no quantitative information is conveyed and no ordering of the items is implied. Other examples of nominal scales include religious preference, production facility, and organizational function.
•  Ordinal variables are categorical variables that have three or more possible levels with a natural ordering, such as strongly disagree, disagree, neutral, agree, and strongly agree. With ordinal data, quality analysts often convert it to a quantitative scale. For example, a survey may assign a scale from 1-5 to cover the range from strongly disagree, to neutral, to strongly agree. When converting an ordinal categorical variable to a quantitative scale, a quality analyst must exercise caution in the interpretation of the difference between values. For instance, the difference between the responses strongly disagree (1) and disagree (2) may not equal the difference between disagree (2) and neutral (3).
•  Binary variables are categorical variables that have two possible levels (e.g., yes/no). Binary variables are the most common type of categorical variables because they are the easiest to convert to a quantitative scale. Binary variables typically are assigned a 0 (e.g., defective) or 1 (e.g., not defective). This use of the 0 / 1 designation allows experimenters to use proportions or counts for data analysis. As a general rule, the desired outcome is assigned the 1. 

Quantitative Data 

Quantitative Data result from measurement or numerical estimation. These measurements yield discrete or continuous variables. Discrete variables vary only by whole numbers such as the number of students in a class (variable: class size). Continuous variables vary to any degree, limited only by the precision of the measurement system. Some examples include the width of a desk, the time to complete a task, or the height of students (variables: length, time, and height).  In the case of measuring the width of a desk, the measurement could read 1.54 m, or 1.541 m, or 1.5409, or 1.54087, ... Here, the observed measurement is limited only by the precision of the measurement instrument.

Some additional examples of continuous quantitative measurements are:
•  The time to deliver the pizza was 26.7 minutes.
•  The diameter of the cylinder was 83.1 mm.

In converting a categorical variable to a quantitative scale, the variable is typically treated as a discrete variable. For example, a rating scale from 1 to 5 or a binary scale of 0 or 1 would be analyzed as a discrete variable. In computing a statistic for a discrete variable such as the average survey response, the statistic (e.g., the average) is considered continuous. So, the average for a 5-points scale might be 3.72 even though this particular value is not possible to obtain.

For analysis purposes, discrete variables often are approximated using continuous distributions. For instance, suppose student test scores are discrete ranging from 0 to 100 points. Here, we might assume the distribution of test scores follows a normal distribution (continuous) in order to estimate the likelihood of a student scoring greater than a 70.   

In general, analysts try to convert all data to an approximately continuous, numerical scale for making inferences or conclusions.