Intro to Marketing Research: Measurement and Scaling - Levels of Measurement, Nominal Ordinal Interval Ratio Operations Permitted for Each Level

What It Is

Levels of Measurement refer to the way data is categorized and analyzed in research. There are four primary levels: Nominal, Ordinal, Interval, and Ratio. Each level has specific operations permitted, such as data analysis and statistical tests. A canonical example of this concept is the Likert scale, a widely used survey instrument that measures attitudes and opinions on a scale from 1 to 5. This matters for marketing decision-making because understanding the level of measurement is crucial for selecting the right statistical analysis and interpreting results accurately.

Key Terms & Concepts

• Nominal Level: A level of measurement where data is categorized without any inherent order or ranking. Examples include gender, nationality, or brand name.
  • Example: A survey asking respondents to choose their favorite coffee brand (e.g., Starbucks, Dunkin', or Folgers).
  • Key researcher: Charles Spearman, who introduced the concept of levels of measurement.
• Ordinal Level: A level of measurement where data is categorized with a natural order or ranking, but the intervals between categories are not equal. Examples include satisfaction ratings (e.g., very dissatisfied, dissatisfied, neutral, satisfied, very satisfied) or education level (e.g., high school, college, graduate degree).
  • Example: A customer satisfaction survey with a rating scale from 1 to 5.
  • Key researcher: Stanley Smith Stevens, who developed the levels of measurement framework.
• Interval Level: A level of measurement where data is categorized with a natural order or ranking, and the intervals between categories are equal. Examples include temperature (e.g., 20°C, 25°C, 30°C) or IQ scores.
  • Example: A survey asking respondents to rate their perceived quality of life on a scale from 1 to 10.
  • Key formula: The formula for calculating the standard deviation (?) is-= ?[(?(xi - ?)²) / (n - 1)], where xi is each data point,-is the mean, and n is the sample size.
• Ratio Level: A level of measurement where data is categorized with a natural order or ranking, and the intervals between categories are equal, with a true zero point. Examples include weight (e.g., 50 kg, 60 kg, 70 kg) or height (e.g., 160 cm, 170 cm, 180 cm).
  • Example: A survey asking respondents to report their household income in dollars.
  • Key researcher: Charles Spearman, who introduced the concept of levels of measurement.
• Data Analysis Operations: Different levels of measurement permit different data analysis operations, such as:
  • Nominal Level: Chi-square tests, contingency tables.
  • Ordinal Level: Non-parametric tests (e.g., Mann-Whitney U test), ordinal regression.
  • Interval Level: Parametric tests (e.g., t-test, ANOVA), linear regression.
  • Ratio Level: All data analysis operations permitted for interval level, plus ratio-specific operations (e.g., calculating means, medians).
• Level of Measurement and Statistical Tests: The level of measurement determines the type of statistical test that can be used. For example, a t-test requires interval or ratio level data, while a chi-square test requires nominal or ordinal level data.
• Data Transformation: Data can be transformed from one level of measurement to another, but this may affect the results and interpretation of the analysis.
• Measurement Scales: Measurement scales are used to categorize data, such as Likert scales, rating scales, or categorical variables.
• Data Quality: The level of measurement affects data quality, with ratio level data generally considered more reliable than nominal or ordinal level data.
• Sampling Method: The level of measurement affects the sampling method, with ratio level data often requiring more complex sampling designs.

Common Misunderstandings

• Misunderstanding: Nominal level data can be analyzed using parametric tests.
• Correction: Nominal level data can only be analyzed using non-parametric tests, such as chi-square tests or contingency tables.
• Misunderstanding: Interval level data can be analyzed using non-parametric tests.
• Correction: Interval level data can be analyzed using parametric tests, such as t-tests or ANOVA.
• Misunderstanding: Ratio level data can be analyzed using only ratio-specific operations.
• Correction: Ratio level data can be analyzed using all data analysis operations permitted for interval level, plus ratio-specific operations.

Quick Application / Identification

Scenario: A marketing researcher wants to analyze customer satisfaction ratings on a scale from 1 to 5. What level of measurement is this data?

Answer: Ordinal level. Explanation: The data is categorized with a natural order or ranking, but the intervals between categories are not equal.

Scenario: A survey asks respondents to report their household income in dollars. What level of measurement is this data?

Answer: Ratio level. Explanation: The data is categorized with a natural order or ranking, and the intervals between categories are equal, with a true zero point.

Scenario: A marketing manager wants to analyze the relationship between customer satisfaction and purchase intention using a Likert scale. What level of measurement is this data?

Answer: Ordinal level. Explanation: The data is categorized with a natural order or ranking, but the intervals between categories are not equal.

Last-Minute Revision

• Nominal level data can only be analyzed using non-parametric tests.
• Interval level data can be analyzed using parametric tests, such as t-tests or ANOVA.
• Ratio level data can be analyzed using all data analysis operations permitted for interval level, plus ratio-specific operations.
• The level of measurement determines the type of statistical test that can be used.
• Data transformation can affect the results and interpretation of the analysis.
• Measurement scales are used to categorize data.
• Data quality is affected by the level of measurement.
• Sampling method is affected by the level of measurement.
• Ratio level data has a true zero point.
• Interval level data does not have a true zero point.
• Nominal level data does not have a natural order or ranking.
• Ordinal level data has a natural order or ranking, but the intervals between categories are not equal.
• The Likert scale is an example of an ordinal level measurement scale.
• The t-test requires interval or ratio level data.
• The chi-square test requires nominal or ordinal level data.
• Data analysis operations permitted for each level of measurement:
  • Nominal level: Chi-square tests, contingency tables.
  • Ordinal level: Non-parametric tests (e.g., Mann-Whitney U test), ordinal regression.
  • Interval level: Parametric tests (e.g., t-test, ANOVA), linear regression.
  • Ratio level: All data analysis operations permitted for interval level, plus ratio-specific operations.