# Section 3.3: Scales of Measurement

Variables can also be described in terms of how much information they contain.  There are four scales of measurement that do this.  The levels of measurement are important in social research because they have an impact on the types of statistics we can use to simplify and describe our data.  As a rule, always use the most informative level of measurement possible.

## Nominal Scale

The nominal scale, at its core, is a measurement scale that consists solely of categories. These categories are distinguishable from one another through names or labels, and the scale does not provide any quantitative distinction between them. Essentially, it is a system of labeling wherein the named categories do not have any inherent order or ranking. For instance, consider the variable of “favorite color.” Colors such as blue, red, or yellow are categorized and labeled, but there is no numerical or quantitative value assigned to these categories that indicates any kind of hierarchy or preference. One cannot assert that blue holds a greater or lesser value than red in the context of favorite color; they merely represent different choices.

In the realm of criminal justice, the nominal scale might be used to categorize types of crimes: theft, assault, or fraud, for example. Each of these categories has a distinct label, yet they do not inherently indicate the severity or frequency of the crime. Similarly, in political science, political parties or affiliations can be categorized nominally. Democrats, Republicans, Liberals, and Conservatives are named entities that do not provide quantitative information about the size, power, or popularity of each group.

Psychology, another essential social science discipline, utilizes the nominal scale in various research settings. Consider the categorization of different therapeutic methods: cognitive-behavioral therapy, psychoanalysis, and group therapy. While these categories might indicate a particular approach to treatment, they don’t inherently signify which method is superior or more effective than another. Social work, meanwhile, may use nominal scales to classify types of interventions, such as counseling, community engagement, or crisis intervention. Each category identifies a unique approach, without suggesting a hierarchy or ranking of effectiveness.

However, a potential source of confusion arises when numbers are employed as labels in a nominal scale. For instance, the numbers printed on athletic jerseys serve to identify different players. If the number “10” is given to a player, it does not quantitatively imply that the player is in any way superior or inferior to a player with the number “7.” It is crucial to understand that in such contexts, numbers merely serve as convenient labels, retaining the essence of a nominal scale. The mere presence of numbers should not mislead one into thinking there is an inherent order or value associated with them in this context.

## Ordinal Scale

The ordinal scale is a step beyond the nominal scale in terms of data classification. While the nominal scale involves mere categorization of data without any particular order, the ordinal scale introduces the element of rank or hierarchy. Measurements or data points within an ordinal scale are not only categorized but also organized based on magnitude or importance. A classic example is when someone states, “I graduated third in my class.” This information reveals the rank of the student, indicating that they performed better than the fourth but not as well as the second-ranking student. However, the ordinal scale does not offer clarity about the exact differences between these rankings – we know the order, but we don’t understand the magnitude of difference between, say, the second and third ranks.

In the field of criminal justice, the ordinal scale can be used to classify the severity of crimes or the risk level of prisoners. For instance, offenses can be classified as low, medium, or high severity. While we can deduce that a high-severity crime is more serious than a medium-severity one, we do not have exact metrics to quantify the difference in severity between the two. Similarly, in assessing the risk of prisoners, designations like ‘minimum security’ and ‘maximum security’ can be viewed in an ordinal context.

Political science offers another setting where the ordinal scale might be pertinent. Consider a scenario where nations are ranked based on their commitment to democratic values: “low”, “medium”, or “high”. While this system tells us about the relative commitment of one country to another, it doesn’t specify by what margin one country is more democratic than the next.

In the realm of psychology, therapists might use an ordinal scale to gauge the severity of a patient’s symptoms, classifying them as mild, moderate, or severe. The ranking provides a hierarchical perspective on the patient’s condition, yet it doesn’t convey the exact difference in intensity between ‘mild’ and ‘moderate’. In social work, an ordinal scale can be used to assess the urgency of cases, ranking them as low, medium, or high priority. While this system can guide social workers in allocating resources, it does not detail the specific disparities between each urgency level.

In essence, the ordinal scale offers a valuable perspective in various disciplines by introducing the concept of hierarchy. Yet, its limitation lies in its inability to specify the quantitative difference between each ranking, making it essential to understand the context in which it’s used to interpret data correctly.

## Interval Scale

The interval scale represents a more nuanced level of measurement than the ordinal scale. While the ordinal scale introduces the concept of rank or hierarchy, the interval scale maintains this ordered categorization but adds a consistent, equal difference between data points or intervals. This consistent interval ensures a standardized measure, making comparisons and computations more straightforward and accurate. A quintessential example of this scale is the measurement of distance in inches. Regardless of where you look on a ruler, the distance between the 2-inch and the 3-inch mark is identical to the space between the 35-inch and the 36-inch mark. The implication is clear: an inch remains consistent, irrespective of its position on the scale.

In the realm of criminal justice, the interval scale can be applied in standardized tests that evaluate the psychological profiles of inmates. Here, the difference in score points might represent consistent differences in psychological attributes or tendencies, ensuring that a two-point difference at the lower end of the scale is equivalent to a two-point difference at the higher end.

Political science offers fertile ground for the application of interval scales, especially in survey research. Imagine a questionnaire measuring political ideologies on a scale from 1 to 10, where a score of 1 denotes extreme conservatism and 10 indicates extreme liberalism. The consistent interval ensures that the ideological difference between scores 2 and 3 is the same as that between scores 8 and 9.

Within psychology, interval scales are widely utilized, especially in standardized testing scenarios. Consider IQ tests: a person with a score of 110 has an intellectual capability consistently higher than someone scoring 100, similar to how someone with a score of 130 has a consistently higher capability than someone scoring 120. This uniformity in intervals makes the data more actionable and interpretable.

In social work, interval scales might be used in assessments to measure the well-being or satisfaction levels of individuals. A scale from 1 to 10 might be employed to measure the satisfaction of residents in a care home, with the understanding that the difference in well-being between scores 4 and 5 is identical to that between scores 7 and 8.

In summary, the interval scale provides a powerful tool for various disciplines, offering both a sense of order and a standardized, consistent difference between measurements. This dual advantage ensures that data is both hierarchically meaningful and quantitatively comparable across the spectrum of the scale.

## Ratio Scale

The ratio scale is the pinnacle of measurement scales, encompassing all the features of the interval scale while also introducing a distinct concept: the absolute zero point. This zero isn’t just a mere placeholder or reference point; it represents the complete absence of the variable being measured. In essence, the ratio scale offers both a consistent interval between measurements and a genuine starting point that implies the non-existence or nullity of a particular attribute.

Consider the example of annual household income. When it’s said that a household’s income is zero dollars for a given year, it’s indicative of the fact that no money was earned. This zero isn’t arbitrary; it signifies a lack of income entirely. In the realm of economics or social studies, such absolute zero points can be crucial in analyses, allowing for a comprehensive understanding of disparities, growth trajectories, or the efficacy of financial interventions.

However, it’s essential to distinguish between variables that seem to have a zero but don’t truly represent the absence of a variable and those that do. For instance, temperature measured in Fahrenheit can reach zero, but this does not indicate the absence of heat. It’s merely a point on the scale, with temperatures plunging below it. In contrast, the Kelvin scale in physics is anchored at an absolute zero, representing the absence of any thermal motion. Nothing can be colder than zero Kelvin, making it a true ratio scale.

Despite its distinctive feature, the differences between ratio and interval scales are subtle, especially in practical applications. Both scales provide an ordered set of categories with consistent intervals. In many statistical analyses or methodologies, the techniques that apply to interval scales often hold for ratio scales, explaining why they are frequently referenced interchangeably in academic and research literature.

The ratio scale serves as a robust tool for various academic disciplines, allowing for precise, meaningful measurements rooted in an absolute zero. This grounding in reality—where zero represents a true absence—offers nuanced insights, especially in comparative and longitudinal studies. Whether it’s assessing economic growth, tracking scientific phenomena, or analyzing sociological trends, the ratio scale stands out as a definitive, holistic metric system.

## Choosing the Appropriate Level of Measurement

Choosing the right level of measurement is pivotal for researchers. The level of measurement not only influences the type of statistical analyses that can be performed but also the quality and depth of insights that can be derived from the data. Given the hierarchy of measurement levels – nominal, ordinal, interval, and ratio – it’s generally advised to aim for the highest level that is feasible and appropriate for the research scenario. This is because higher levels of measurement inherently contain more information, making them more versatile and information-rich.

1. Understand the Nature of Your Variable: Before settling on a level of measurement, understand the inherent nature of the variable you’re dealing with. Some variables might not fit neatly into higher levels of measurement. For instance, while ‘gender’ is best suited as a nominal variable, ‘annual income’ can be scaled at the ratio level.
2. Aim for Depth and Precision: Higher levels of measurement offer more granularity. For example, while an ordinal scale might tell you that one student performed better than another, an interval or ratio scale could tell you how much better they performed. The added precision can be invaluable, especially when making comparisons or looking for nuanced patterns.
3. Consider the Research Question: Tailor your measurement level to your research question. If your study seeks to understand the order of preference, an ordinal scale might suffice. But if you need to understand precise differences or relationships, aim for interval or ratio scales.
4. Weigh Practicality: While it’s beneficial to aim for higher levels of measurement, it’s also essential to consider the practicality and the cost. Collecting data at the ratio level might require more sophisticated instruments or methodologies, which could be resource-intensive.
5. Statistical Analysis Considerations: Higher levels of measurement often allow for a broader range of statistical analyses. For instance, while nominal data might be limited to frequency distributions or chi-square tests, interval and ratio data can be subjected to t-tests, ANOVA, regression analyses, and more. Therefore, consider your planned analyses when deciding on the measurement level.
6. Flexibility for Future Research: Opting for a higher level of measurement can also provide more flexibility for future research. Data collected at the ratio or interval level can always be simplified to fit nominal or ordinal scales if needed, but the reverse isn’t true.

In conclusion, while it’s tempting to always aim for the highest level of measurement, it’s crucial to strike a balance between the research objectives, the inherent nature of the data, and practical considerations. By doing so, researchers can ensure that their findings are both robust and meaningful, maximizing the impact and validity of their work.

## Summary

In research, the richness of data is often determined by the scale of measurement used. The four primary scales – nominal, ordinal, interval, and ratio – offer different levels of information. The nominal scale categorizes data without any inherent order, such as categorizing types of crimes or political affiliations. Ordinal scales, a step above, introduce rank and hierarchy, exemplified by class rankings. The interval scale, more intricate, not only categorizes and ranks data but ensures consistent intervals between points, much like measuring distance in inches. The most comprehensive, the ratio scale, embodies the features of the interval scale and boasts an absolute zero point, representing complete absence of the variable.

When conducting research, it’s pivotal to choose the most informative scale feasible. The chosen scale impacts the depth of insights and the statistical methods applicable. While nominal and ordinal scales offer categorization and ranking respectively, interval and ratio scales give added granularity, precision, and consistency. However, practicality and research objectives should guide the selection. Conclusively, using the highest appropriate level of measurement harnesses the full potential of the data, ensuring robust and nuanced findings.

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File Created:  07/25/2018