Introductory Concepts:Quantitative vs Qualitative Variables, Discrete vs Continuous Variables, Levels of Measurement, Samples and Populations

Quantitative vs Qualitative Variables: Definition, Guide, and Examples

Quantitative variables are variables that can be measured and expressed in numbers. They can be further classified into two types: discrete and continuous. Discrete variables can only take on a finite number of values, such as the number of students in a class or the number of cars in a parking lot. Continuous variables can take on an infinite number of values, such as the weight of a person or the temperature of a room.

Qualitative variables are variables that cannot be measured or expressed in numbers. They are typically described in words or categories. For example, a person's eye color or a car's make and model are qualitative variables.

Here are some examples of quantitative and qualitative variables:

• Quantitative variables:

  • Number of students in a class

  • Weight of a person

  • Temperature of a room

  • Distance between two cities

  • Speed of a car

• Qualitative variables:

  • Eye color

  • Make and model of a car

  • Gender

  • Political affiliation

  • Favorite food

In general, quantitative variables are used to answer questions about how much or how many, while qualitative variables are used to answer questions about what kind or which.

Exceptions to the general rule: Quantitative variables are number (numerical) variables. Qualitative variables are not number (non-numerical) variables, EXCEPT in the following cases:

• A number is used an  identifier. For example: a student number, a part number, or any ID number

• Numbers are used to represent categories.  For example:  if a question states: 1 = Yes , 0 = No ;  or a problem states:  1 = Electric , 2 = Hybrid etc

Discrete vs Continuous Variables: Identification Guide, and Examples

How to distinguish between discrete and continuous variables:

• Discrete variables can only take on a finite number of values, such as the number of students in a class or the number of cars in a parking lot.

• Continuous variables can take on an infinite number of values, such as the weight of a person or the temperature of a room.

Here are some examples of discrete and continuous variables:

• Discrete variables:

  • Number of students in a class

  • Number of cars in a parking lot

  • Number of fingers on a hand

  • Number of days in a week

• Continuous variables:

  • Weight of a person

  • Temperature of a room

  • Distance between two cities

  • Speed of a car

In general, discrete variables are used to answer questions about how many, while continuous variables are used to answer questions about how much.

Samples and Populations: Definitions, Identification Guide and Examples

1. Definitions:

   - Population: A population refers to the entire group of individuals, objects, or events that we want to study and draw conclusions about. It includes all possible elements of interest in a particular context. However, it is often large and difficult to observe or analyze in its entirety.

   - Sample: A sample is a subset or smaller representative group selected from the population. It is chosen to study and make inferences about the larger population. The sample should ideally be representative of the population to ensure accurate conclusions.

2. Characteristics:

   - Population: The population consists of all the individuals or items that possess the characteristics of interest. It represents the complete set that you want to generalize your findings to.

   - Sample: The sample is a smaller group selected from the population. It is chosen in a way that it represents the characteristics and diversity of the population. The goal is to make inferences about the population based on the analysis of the sample.

3. Examples:

   - Example 1: Suppose you want to determine the average age of all students in a university. The population in this case would be all the students enrolled in that university. If you randomly select 100 students from that population and calculate their average age, this group of 100 students would be considered a sample.

   - Example 2: Imagine you are conducting a survey to understand the preferences of smartphone users in a country. The population would be all smartphone users in that country. If you survey a randomly selected group of 500 smartphone users, this group of 500 individuals would be your sample.

   - Example 3: Let's say you are studying the effects of a new medication on a specific medical condition. The population would be all individuals diagnosed with that medical condition. If you recruit 200 individuals diagnosed with the condition for your study, these 200 individuals would be your sample.

In these examples, the population represents the entire group of interest (all students, all smartphone users, all individuals with the medical condition), while the sample is a smaller subset selected from that population (100 students, 500 smartphone users, 200 individuals).

Remember, the sample is used to make inferences about the population, and it should be representative of the population to ensure the validity of the conclusions drawn.

Levels of Measurement Identification Guide and Examples:

1. Nominal Level: The nominal level of measurement involves categorizing data into distinct groups or categories. In this level, data are assigned labels or names that are used to differentiate between categories. Nominal data do not have any inherent order or numerical significance. Examples include gender (male/female), marital status (single/married/divorced), or types of cars (sedan/SUV/hatchback).

2. Ordinal Level: The ordinal level of measurement involves arranging data into ordered categories or ranks. The key characteristic here is that the categories have a relative order or ranking, but the differences between the ranks may not be equal or measurable. Examples include rating scales (e.g., Likert scale) where respondents rank their satisfaction levels as "very satisfied," "satisfied," "neutral," "dissatisfied," or "very dissatisfied."

3. Interval Level: The interval level of measurement involves data where the differences between values are meaningful and can be measured on a consistent scale. However, the interval level does not have a true zero point. In this level, you can perform addition and subtraction operations but not multiplication or division. Examples include temperature measured in Celsius or Fahrenheit, where the difference between 10 and 20 degrees is the same as the difference between 20 and 30 degrees.

4. Ratio Level: The ratio level of measurement is similar to the interval level but includes a true zero point. Data at the ratio level have meaningful and equal intervals, and you can perform all arithmetic operations, including multiplication and division. Examples include height, weight, time, and counts. For instance, if someone's weight is twice as much as another person, it means the weight is actually twice as heavy.

Here are some additional things to keep in mind when identifying the level of measurement:

• The level of measurement is determined by the nature of the data, not by the way it is presented. For example, the variable "grade point average" could be presented as a number, but it is still measured at the ordinal level because the intervals between the groups are not equal.

• The level of measurement determines the type of statistical analysis that can be performed on the data. For example, only variables that are measured at the interval or ratio level can be used to calculate means and standard deviations.

• When identifying the level of measurement, consider the characteristics and properties of the data and the operations that can be performed on them. Keep in mind that some data can be interpreted at multiple levels depending on the context and how they are used.

Tips for Quizzes and Assignments 

Interval and Ratio levels are always associated with numerical variables (numbers). Nominal and Ordinal levels are usually associated with non-numerical variables, but there are certain exceptions: When a number is used as an identifier, for example: a student number, a part number, or any ID number, these numbers are examples of nominal levels of measurement. When numbers are used to identify categories for example: 0 = not satisfied , 1 = satisfied , 2 =very satisfied , this is an example of an ordinal scale of measurement. Lastly, when trying to distinguish between interval and ratio levels, ask yourself: does zero have a meaning. For example if your income is $0, it means you do not earn any money, income measured in $  is an example of a ratio level of measurement. As opposed to a  0-sized dress, this indicates that the dress is very small, not that the dress has no size, this is an example of an interval level of measurement.