Escalas de medición en estadística

Main ideas and lessons

• Measurement (in statistics) is defined as:
  • Observing a phenomenon or property, and
  • Assigning a number or category to represent it.

• “Observe” is treated as a synonym of “measure” in this context.

• A measurement scale is described as:

  • The set of possible values that a given measurement can take.

• The type of statistical procedure depends on the level (scale) of measurement:

  • Calculations are not automatically appropriate; you must avoid applying statistical operations that do not match the data’s scale.
  • Example: computing an average of social security numbers is meaningless because they are just identifiers, not measured quantities.

• The video reviews Stevens’ four measurement scales (1946):

  1. Nominal
  2. Ordinal
  3. Interval
  4. Ratio

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The four measurement scales (outlined)

1) Nominal scale

• What it is: Data are names/labels/categories with no order.
• Key property: No meaningful ordering and no meaningful arithmetic.
• Examples mentioned:
  • People’s favorite colors
  • Favorite food
  • Favorite sport
  • Car brand they would like to drive
  • Jersey numbers on soccer players (treated as identification labels like “player number 10”)

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2) Ordinal scale

• What it is: Data can be ranked in order, but differences between values are not meaningful.
• Key property: Order exists, but you can’t say how much one category differs from another in a quantitative way.
• Examples mentioned:
  • Headache intensity: “hurts a lot” → “hurts a little” → etc.
  • Educational level: Primary → Secondary → High School → University (ordered, but distances aren’t quantified)
  • Movie-watching frequency: “always,” “never,” “sometimes,” “almost always,” etc.
  • Socioeconomic level: high / medium / low (or variations)

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3) Interval scale

• What it is: Data are ordered and the difference between values is meaningful, but there is no true zero origin.
• Key property: You can meaningfully compute differences, but ratios don’t make sense the same way because zero is not “absence.”
• Examples mentioned:
  • Temperature in °C:
    • “42°C is twice as much as 40°C” (as stated in the video) and you can measure differences
    • Zero does not mean absence of temperature; values can be below zero
  • Time measured in years:
    • No inherent true starting point (year zero isn’t “absence of time”)
  • Location along a road relative to a point (no meaningful true zero)
  • Survey response example: age grouped into intervals (e.g., 15–25, 26–50)

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4) Ratio scale

• What it is: Like interval, but with a true inherent zero meaning absence of the measured quantity.
• Key property:
  • Differences are meaningful
  • Ratios are meaningful
  • Zero indicates nothing of the variable
• Examples mentioned:
  • Number of children:
    • Answers can be 0 or more, where 0 means no children
  • Number of goals scored:
    • Starts at 0; 0 means no goals
  • Speedometer reading:
    • Zero means no speed (or absence of motion/displacement/acceleration as described)

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Survey/interview question classification (instruction-like list)

The video instructs viewers to:

• Take a survey/interview question
• Look at its answer options
• Classify the variable on one of the four measurement scales (nominal, ordinal, interval, ratio)

Example classifications provided

• Nominal

  • “How did you find out about our website?”
    • Answers: television, newspaper, social networks, search engine, friend recommendation, other
  • Reason: categories/labels with no order

• Ordinal

  • “How satisfied are you with the company?” / “How satisfied are you with the company in general?”
    • Answers: very satisfied → satisfied → somewhat satisfied → not satisfied at all
  • “How likely are you to recommend our products or services?”
    • Answers: very likely → somewhat unlikely → not likely
  • Reason: responses can be ranked, but distances between categories aren’t quantified

• Interval

  • “Which of the following categories corresponds to your age?”
    • Answers: numbers grouped into interval categories
  • Reason: ordered categories representing interval-like grouping with meaningful differences (as presented)

• Ratio

  • “How many children do you have?”
    • Answers: 0 or higher, where 0 means absence of the variable
  • “Approximately how much money do you give each year to registered charities?”
    • Answers: 0 or higher, where 0 means no giving

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Concluding takeaway

• When using statistics in real problems, it is crucial to identify the measurement scale of each question/variable and then:
  • Use appropriate procedures, and
  • Avoid calculations/methods that don’t make sense for the data type.

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Speakers / sources featured

• No specific speaker name is provided in the subtitles.
• Source referenced: S. S. Stevens (measurement scales presented in 1946).
• Institutions referenced (as examples of survey organizations): INEGI, CONAPO.