Measurement Scales: Provide One Example Of Each ✓ Solved

Measurement Scales: Provide one example (your own) of each

Provide one example (your own) of each measurement scale and provide an example (your own) of how a variable might be measured by different scales. Explain which of these you found most challenging to identify and why.

Paper For Above Instructions

Introduction

Measurement scales are foundational to quantitative research because they determine how variables are defined, summarized, and analyzed (Stevens, 1946; Trochim, 2006). The four classic scales—nominal, ordinal, interval, and ratio—each impose different mathematical properties and therefore different analytical options (Creswell, 2014; Gravetter & Wallnau, 2014). Below I provide one original example for each scale and then illustrate how a single variable can be measured across multiple scales. I conclude by identifying the scale distinction I found most challenging and why.

Nominal Scale: Example and Commentary

Example: Favorite fruit category. Respondents select one option from {Apple, Banana, Orange, Other}. The categories are mutually exclusive and have no inherent order. The nominal scale supports counts and mode calculations but not arithmetic operations or meaningful medians (Stevens, 1946; Salkind, 2013).

Ordinal Scale: Example and Commentary

Example: Hotel service ranking. Guests rate service as {Poor, Fair, Good, Excellent}. The order reflects relative positions, but intervals between ranks are not guaranteed equal. Ordinal data allow median and rank-based statistics (e.g., Mann–Whitney) but do not justify means under strict interpretation (Gravetter & Wallnau, 2014; Field, 2013).

Interval Scale: Example and Commentary

Example: Temperature measured in Celsius. Differences between values are meaningful and equidistant, but there is no true zero that indicates absence of temperature in the Celsius scale. Interval measures permit addition and subtraction and support parametric tests when assumptions are met (Stevens, 1946; Creswell, 2014).

Ratio Scale: Example and Commentary

Example: Number of hours studied per week. This scale has equal intervals and an absolute zero (zero hours studied means none), allowing meaningful ratios (e.g., 8 hours is twice 4 hours). Ratio data support the full range of arithmetic and statistical procedures (DeVellis, 2016; Gravetter & Wallnau, 2014).

One Variable Measured on Multiple Scales: Customer Satisfaction

Variable: Customer satisfaction with an online purchase. This same underlying construct can be measured at different scales depending on the instrument and purpose:

• Nominal: Binary classification—Satisfied vs. Not satisfied. Useful for simple segmentation or when only presence/absence matters (Trochim, 2006).
• Ordinal: Five-point Likert: {Very dissatisfied, Dissatisfied, Neutral, Satisfied, Very satisfied}. This gives rank information and is widely used in surveys (Norman, 2010).
• Interval: If a validated psychometric instrument produces scores standardized with equal intervals (e.g., transformed Likert battery treated as interval), researchers may analyze mean differences across groups (Salkind, 2013; Field, 2013).
• Ratio: If satisfaction is operationalized as number of repeat purchases or net promoter counts (e.g., number of times a customer returned items), the measure becomes count-based with absolute zero, enabling ratio-level interpretation (DeVellis, 2016).

Each operationalization answers different research questions and constrains the statistical approaches available (Creswell, 2014).

Why Some Distinctions Are Challenging

The most challenging distinction for me is differentiating interval from ratio scales in practice. Conceptually the difference is simple—presence or absence of a true zero—but many social-science measures blur this line. For example, temperature in Celsius is interval versus Kelvin as ratio, but researchers rarely use Kelvin for social phenomena. More commonly, Likert-type composite scores are treated as interval by convention and for convenience, though strict measurement theory would classify them as ordinal unless validated for interval properties (Norman, 2010; Salkind, 2013).

Additionally, modern psychometric methods (e.g., item response theory, Rasch modeling) can transform ordinal responses into measures with interval-like properties, making scale classification contingent on statistics and validation processes rather than on the raw items alone (DeVellis, 2016). This methodological nuance—when ordinal items can produce interval-scale scores—complicates the researcher’s decision about which statistical tests are appropriate and what inferences are defensible (Field, 2013; Trochim, 2006).

Implications for Research Design and Analysis

The scale chosen affects data collection and analysis. Nominal data limit analyses to frequencies and chi-square tests, ordinal data lend themselves to medians and nonparametric tests, interval data enable parametric procedures when assumptions hold, and ratio data allow the most extensive set of analyses including means, standard deviations, and multiplicative comparisons (Gravetter & Wallnau, 2014; Creswell, 2014). Misclassifying scales risks applying inappropriate analysis techniques or misinterpreting results (APA, 2019).

Conclusion

Nominal, ordinal, interval, and ratio scales each have distinct properties and uses. Providing clear operational definitions for each variable in a study is essential for valid analysis. In practice the interval-versus-ratio distinction and the treatment of Likert-type composites are the most challenging issues because modern measurement methods and practical conventions sometimes blur theoretical boundaries. Careful instrument validation and transparent reporting help ensure that scale decisions are defensible and that analyses align with measurement properties (Creswell, 2014; DeVellis, 2016).

References

• American Psychological Association. (2019). Publication manual of the American Psychological Association (7th ed.). Washington, DC: APA.
• Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). Thousand Oaks, CA: Sage.
• DeVellis, R. F. (2016). Scale development: Theory and applications (4th ed.). Thousand Oaks, CA: Sage.
• Field, A. (2013). Discovering statistics using IBM SPSS statistics (4th ed.). London: Sage.
• Gravetter, F. J., & Wallnau, L. B. (2014). Essentials of statistics for the behavioral sciences (8th ed.). Belmont, CA: Wadsworth.
• Malec, T., & Newman, M. (2013). Research methods: Building a knowledge base. San Diego, CA: Bridgepoint Education, Inc.
• Norman, G. (2010). Likert scales, levels of measurement and the “laws” of statistics. Advances in Health Sciences Education, 15(5), 625–632. https://doi.org/10.1007/s10459-010-9222-y
• Salkind, N. J. (2013). Statistics for people who (think they) hate statistics (5th ed.). Thousand Oaks, CA: Sage.
• Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103(2684), 677–680.
• Trochim, W. M. K. (2006). Research methods knowledge base. Cincinnati, OH: Atomic Dog Publishing. (Online edition)