Data Classification and Levels of Measurement in Statistics

Section 1.2: Data Classification

Introduction

Data classification is a foundational concept in statistics, enabling researchers to organize, analyze, and interpret data effectively. This section covers the distinction between qualitative and quantitative data and explains the four levels of measurement: nominal, ordinal, interval, and ratio.

Types of Data

• Qualitative Data: Consists of attributes, labels, or non-numerical entries. Examples include major, place of birth, and eye color.

• Quantitative Data: Consists of numerical measurements or counts. Examples include age, weight of a letter, and temperature.

Example: Classifying Data by Type

The following table shows sports-related head injuries treated in U.S. emergency rooms. The type of sport is qualitative data, while the number of head injuries treated is quantitative data.

Sport	Head injuries treated
Basketball	131,930
Baseball	83,532
Football	220,258
Gymnastics	33,265
Hockey	41,450
Soccer	98,710
Softball	41,216
Swimming	44,815
Volleyball	13,848

Levels of Measurement

Data can be classified into four levels of measurement, each with increasing mathematical meaning and application.

Nominal Level

• Qualitative data only

• Data categorized using names, labels, or qualities

• No mathematical computations can be made

Ordinal Level

• Qualitative or quantitative data

• Data can be arranged in order or ranked

• Differences between data entries are not meaningful

Interval Level

• Quantitative data

• Data can be ordered

• Differences between data entries are meaningful

• Zero represents a position on a scale (not an inherent zero; zero does not imply "none")

Ratio Level

• Quantitative data

• Similar to interval level

• Zero entry is an inherent zero (implies "none")

• A ratio of two data values can be formed

• One data value can be expressed as a multiple of another

Examples: Classifying Data by Level

• Ordinal Level: Ranking the top five U.S. occupations with the most job growth (e.g., 1. Home health and personal care aides, 2. Fast food and counter workers, etc.). The order is meaningful, but the difference between ranks is not.

• Nominal Level: Listing movie genres (e.g., Action, Adventure, Comedy, Drama, Horror). No mathematical computations can be made, and the data cannot be ranked.

• Interval Level: Years of New York Yankees' World Series victories (e.g., 1923, 1927, 1928, etc.). Differences between years are meaningful, but ratios are not.

• Ratio Level: Number of wins by American League baseball teams. Both differences and ratios are meaningful.

Summary Table: Four Levels of Measurement

Level of Measurement	Put data in categories	Arrange data in order	Subtract data values	Determine if one data value is a multiple of another
Nominal	Yes	No	No	No
Ordinal	Yes	Yes	No	No
Interval	Yes	Yes	Yes	No
Ratio	Yes	Yes	Yes	Yes

Summary Table: Examples and Calculations for Each Level

Level	Example of a data set	Meaningful calculations
Nominal (Qualitative data)	Types of Shows Televised by a Network (Comedy, Drama, Reality Shows, Sports, Documentaries, Cooking, Soap Operas, Talk Shows)	Put in a category. For instance, a show televised by the network could be put into any one of the eight categories shown.
Ordinal (Qualitative or quantitative data)	Motion Picture Association of America Ratings (G, PG, PG-13, R, NC-17)	Put in a category and put in order. For instance, a PG rating has a stronger restriction than a G rating.
Interval (Quantitative data)	Average Monthly Temperatures (in degrees Fahrenheit) for Denver, CO: Jan 30.7, Feb 34.7, Mar 41.0, Apr 47.4, May 57.4, Jun 67.4, Jul 74.2, Aug 72.4, Sep 64.4, Oct 52.6, Nov 39.7, Dec 30.6	Put in a category, put in order, and find differences between data entries. For instance, $72.5 - 63.4 = 9.1^{\circ}F$. So, August is $9.1^{\circ}F$ warmer than September.
Ratio (Quantitative data)	Average Monthly Precipitation (in inches) for Orlando, FL: Jan 2.35, Feb 2.77, Mar 3.77, Apr 2.77, May 3.77, Jun 7.58, Jul 7.27, Aug 7.07, Sep 6.02, Oct 3.31, Nov 2.36, Dec 2.58	Put in a category, put in order, find differences between data entries, and find ratios of data entries. For instance, $7.58 / 3.77 = 2.01$. So, there is about twice as much precipitation in June as in March.

Key Takeaways

• Understanding the type and level of data is essential for selecting appropriate statistical methods.

• Qualitative data describes attributes, while quantitative data measures quantities.

• The four levels of measurement (nominal, ordinal, interval, ratio) determine the permissible mathematical operations and analyses.