# Quantitative Scales of Measurement

# Quantitative Scales of Measurement

This module discusses the basics of measurement and scales of measurement commonly used in quantitative research.

**Learning Objectives:**

- List and describe the four types of scales of measurement used in quantitative research.
- Provide examples of uses of the four scales of measurement.
- Determine the appropriate measurement scale for a research problem.

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Quantitative research requires that measurements be both accurate and reliable. Researchers commonly assign numbers or values to the attributes of people, objects, events, perceptions, or concepts. This process is referred to as measurement. The variables that are measured are commonly classified as being measured on a nominal, ordinal, interval or ratio scale. The following discussion defines and provides examples of each of the four levels of measurement.

**Nominal Scale:** The nominal scales is essentially a type of coding that simply puts people, events, perceptions, objects or attributes into categories based on a common trait or characteristic. The coding can be accomplished by using numbers, letters, colors, labels or any symbol that can distinguish between the groups. The nominal scale is the lowest form of a measurement because it is used simply to categorize and not to capture additional information. Other features of a nominal scale are that each participant or object measured is placed exclusively into one category and there is no relative ordering of the categories. Some examples include distinguishing between smokers and nonsmokers, males and females, types of religious affiliations, blondes vs. brunettes and so on. In a study related to smoking, smokers may be assigned a value of 1 and nonsmokers may be assigned a value of 2. The assignment of the number is purely arbitrary and at the researcher’s discretion.

**Ordinal Scale:** The ordinal scale differs from the nominal scale in that it ranks the data from lowest to highest and provides information regarding where the data points lie in relation to one another. An ordinal scale typically uses non-numerical categories such as low, medium and high to demonstrate the relationships between the data points. The disadvantage of the ordinal scale is that it does not provide information regarding the magnitude of the difference between the data points or rankings. An example of the use of an ordinal scale would be a study that examines the smoking rates of teenagers. The data collected may indicate that the teenage smokers in the study smoked anywhere from 15 to 40 cigarettes per day. The data could be arranged in order and examined in terms of the number of smokers at each level.

**Interval Scale:** An interval scale is one in which the actual distances, or intervals between the categories or points on the scale can be compared. The distance between the numbers or units on the scale are equal across the scale. An example would be a temperature scale, such as the Farenheit scale. The distance between 20 degrees and 40 degrees is the same as between 60 degrees and 80 degrees. A distinguishing feature of interval scales is that there is no absolute zero point because the key is simply the consistent distance or interval between categories or data points.

**Ratio Scale:** The ratio scale contains the most information about the values in a study. It contains all of the information of the other three categories because it categorizes the data, places the data along a continuum so that researchers can examine categories or data points in relation to each other, and the data points or categories are equal distances or intervals apart. However, the difference is the ratio scale also contains a non-arbitrary absolute zero point. The lowest data point collected serves as a meaningful absolute zero point which allows for interpretation of ratio comparisons. Time is one example of the use of a ration measurement scale in a study because it is divided into equal intervals and a ratio comparison can be made. For example, 20 minutes is twice as long as 10 minutes.

The following Slideshare presentation, *Measurement and Scales,* provides an excellent overview of measurement terminology, the four scales of measurements, a concept map of when to use each type of scale, specific examples and information concerning the development of a scale.

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**Suggested Readings:**

- Abramson, J. H., & Abramson, Z. H. (2008). Scales of Measurement.
*Research Methods in Community Medicine: Surveys, Epidemiological Research, Programme Evaluation, Clinical Trials, Sixth Edition*, 125-132. - Berka, K. (1983). Scales of measurement. In
*Language, Logic and Method*(pp. 1-73). Springer Netherlands - Creswell, J. W. (2002).
*Educational research: Planning, conducting, and evaluating quantitative*. Prentice Hall. - Creswell, J. W. (2013).
*Research design: Qualitative, quantitative, and mixed methods approaches*. Sage Publications, Incorporated. - Gaito, J. (1980). Measurement scales and statistics: Resurgence of an old misconception.
- Neuman, W. L., & Robson, K. (2004).
*Basics of social research*. Pearson. - Neuman, W. L., & Neuman, W. L. (2006). Social research methods: Qualitative and quantitative approaches.
- Malterud, K. (2001). Qualitative research: standards, challenges, and guidelines.
*The lancet*,*358*(9280), 483-488. - Robson, C. (2002).
*Real world research*(Vol. 2). Oxford: Blackwell publishers. - Stevens, S. S. (1946). On the theory of scales of measurement.

## Research Ready: Quantitative Research

- Overview of Quantitative Methods
- When to Use Quantitative Methods
- Writing Research Questions and Hypotheses
- Variables and Operational Definitions
- Key Issues in Quantitative Research
- Quantitative Approaches
- Quantitative Scales of Measurement
- Quantitative Data
- Sampling Methods for Quantitative Research
- Analyzing Quantitative Data
- Ethical Considerations
- Introduction to Quantitative Software

## Resource Links:

**Scales of Measurement –** This link provides a simple definition for each of the four types of scales of measurement.

**Measurement Scales in Social Science Research** – The following provides basic information regarding primary scales of measurement.

**Measurement Scales –** The following resource is a brief and concise description of measurement scales and the corresponding statistics.

**4 Levels of Measurement in Social Science Research –** This link discusses scales of measurements and provides examples of each.

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