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Levels of Measurement
The four levels of measurement: Nominal, Ordinal, Interval, and Ratio, and their implications for data visualization.

Data exists in various forms, and this image outlines the four key measurement scales: Nominal, Ordinal, Interval, and Ratio. Differentiating these scales is crucial as their unique properties dictate appropriate visualization techniques.

Levels of Measurement

Nominal Scale

The nominal scale is the most basic level of measurement, where data is categorized without any order or ranking. Examples include:

  • Gender (male, female, other)
  • Eye color (blue, green, brown)
  • Marital status (single, married, divorced)
  • Car brands (Toyota, Ford, BMW)
  • Political affiliation (Democrat, Republican, Independent)
  • Seasons (spring, summer, fall, winter)
  • Types of cuisine (Italian, Chinese, Mexican)
  • Types of pets (dog, cat, bird)
  • Types of music genres (rock, pop, jazz)
  • Types of sports (football, basketball, soccer)
  • Types of fruits (apple, banana, orange)

Data in the nominal scale is not ordered, green is not greater than blue. And the data has no equal intervals, the difference between a dog and a cat is not quantifiable. Data in the nominal scale can also not be added or multiplied, you cannot say that an apple is twice as good as a banana.

When creating a chart with nominal data, use chart types that display categories without implying any order:

Recommended charts:

  • Bar charts or column charts (aka vertical bar charts)
  • Waffle charts
  • Treemaps (for hierarchical nominal data)
  • Bubble charts (when showing quantities)

Charts to avoid:

  • Line charts
  • Area charts
  • Scatter plots
  • Any chart type that implies ordering or ranking between categories

The order of categories in these charts should be chosen based on other factors like alphabetical order or frequency, not any inherent ordering of the categories themselves.

Ordinal Scale

The ordinal scale is a level of measurement where data can be ordered or ranked, but the intervals between the ranks are not necessarily equal. Examples include:

  • Customer satisfaction ratings (satisfied, neutral, dissatisfied)
  • Movie ratings (1 star, 2 stars, 3 stars)
  • Food ratings (disgusting, unappetizing, acceptable, tasty, delicious)
  • Education levels (high school, bachelor's, master's, doctorate)
  • Socioeconomic status (low, middle, high)
  • Surveys (strongly agree, agree, neutral, disagree, strongly disagree)
  • Pain levels (no pain, mild pain, moderate pain, severe pain)

For example, the difference in satisfaction between "satisfied" and "neutral" may not be the same as between "neutral" and "dissatisfied." It is also not possible to say that a "2-star" movie is twice as good as a "1-star" movie, as this is more a matter of opinion than a measurable fact.

Recommended charts:

  • Bar charts or column charts (aka vertical bar charts)
  • Dot plots
  • Lollipop charts
  • Heat maps (when showing intensity)

Charts to avoid:

  • Line charts (implies continuous data between points)
  • Area charts
  • Scatter plots

Interval Scale

The interval scale is a level of measurement where data can be ordered, and the intervals between the ranks are equal, but there is no true zero point. Examples include:

  • Temperature in Celsius or Fahrenheit
  • IQ scores (0 does not mean no intelligence)
  • pH levels (0 does not mean no acidity)
  • Credit scores (0 does not mean no creditworthiness)
  • Stock market indices (0 does not mean no market)

In the interval scale, the difference between two values is meaningful, but the ratio is not. For example, 20 degrees Celsius is not twice as hot as 10 degrees Celsius, even though the difference between them is 10 degrees. And 0 degrees Celsius does not mean there is no temperature, it is just a point on the scale. The same is true for the Fahrenheit scale.

Recommended charts:

  • Line charts
  • Area charts
  • Bar charts
  • Box plots
  • Scatter plots
  • Heat maps
  • Histograms

Charts to avoid:

  • Treemaps

Ratio Scale

The ratio scale is the highest level of measurement, where data can be ordered, the intervals between the ranks are equal, and there is a true zero point. Examples include:

  • Height (0 cm means no height)
  • Weight (0 kg means no weight)
  • Age (0 years means no age)
  • Income (0 dollars means no income)
  • Distance (0 meters means no distance)
  • Speed (0 km/h means no speed)
  • Temperature in Kelvin (0 K means no temperature)

In the ratio scale, all mathematical operations are possible. For example, you can say that a person who is 180 cm tall is twice as tall as a person who is 90 cm tall, and that a person who weighs 80 kg is twice as heavy as a person who weighs 40 kg. The ratio scale is the most informative level of measurement, as it provides the most information about the data.

Recommended charts:

  • All charts suitable for interval data
  • Pie charts (when showing proportions)
  • Stacked bar charts (for part-to-whole)
  • Treemaps (for hierarchical data)
  • Bubble charts (using size to represent values)
  • Scatter plots with size encoding

Charts to avoid:

  • Any chart that doesn't maintain proportional relationships

Understanding Temporal Data

While temporal data (dates and times) is often treated as a distinct type, it actually fits within the standard measurement scales in different ways:

Temporal Data as Interval Scale

Calendar dates and clock times typically function as interval data:

  • Differences between dates are meaningful
  • No true zero point exists (year 0 is arbitrary)
  • Example: The distance between 2023 and 2024 is the same as between 1023 and 1024
  • But: Year 2024 is not "twice as much" as year 1012

Temporal Data as Ratio Scale

Durations and time differences function as ratio data:

  • Has a meaningful zero point (0 seconds = no time)
  • Ratios are meaningful (2 hours is twice as long as 1 hour)
  • Example: A 30-minute task takes twice as long as a 15-minute task

Special Properties of Temporal Data

Temporal data often has unique characteristics:

  • Cyclical nature (hours in a day, months in a year)
  • Natural ordering (past to future)
  • Multiple granularities (years, months, days, hours)
  • Cultural variations (calendar systems, time zones)

Visualization Considerations

When visualizing temporal data, consider:

  • Maintaining chronological order
  • Handling different time scales
  • Dealing with gaps in time
  • Showing periodic patterns
  • Emphasizing temporal context

These special properties make temporal data unique, even though it fits within the standard measurement scales.

Sample Dataset for Practice

If you want to try DataPicta with all possible measurement scales in one dataset, you can play with this employee records dataset:

id,hire_date,department,gender,education_level,satisfaction_rating,temperature_celsius,age,salary,performance_score
1,2020-03-15,Marketing,Female,Bachelor,High,23.5,34,58000,87
2,2018-06-22,Engineering,Male,Master,Medium,22.8,41,92000,92
3,2022-01-10,Sales,Female,High School,Low,24.1,26,45000,73
4,2019-11-05,HR,Non-binary,PhD,Very High,21.9,38,72000,95
5,2021-08-30,Engineering,Male,Bachelor,Medium,23.7,29,65000,82
6,2017-04-18,Marketing,Female,Master,High,22.5,45,88000,90
7,2022-05-03,Sales,Male,Associate,Very Low,25.2,24,41000,65
8,2020-10-12,IT,Female,Bachelor,Medium,23.1,32,69000,85
9,2018-02-28,Finance,Male,PhD,Low,22.3,49,105000,88
10,2021-12-01,Customer Service,Female,High School,High,24.5,27,43000,78

This dataset contains all five types of data discussed in this document:

Nominal Data

  • department: Marketing, Engineering, Sales, etc.
  • gender: Female, Male, Non-binary

Ordinal Data

  • education_level: High School, Associate, Bachelor, Master, PhD
  • satisfaction_rating: Very Low, Low, Medium, High, Very High

Interval Data

  • temperature_celsius: Office temperature
  • performance_score: Rating on a 0-100 scale

Ratio Data

  • age: Employee age in years
  • salary: Annual compensation

Temporal Data

  • hire_date: When the employee was hired

Visualization Ideas

  • Try a bar chart showing average salary by department (ratio by nominal)
  • Create a scatter plot of age vs. performance score (ratio by interval)
  • Build a line chart showing hiring patterns over time (temporal)
  • Make a heat map of satisfaction rating by education level (ordinal by ordinal)

This dataset allows you to practice appropriate visualization techniques for each measurement scale and explore relationships between different types