Understanding the Fundamental Data Types
To answer the question, we must first understand the fundamental differences between ordinal and interval data. These are two of the four primary levels of measurement, alongside nominal and ratio data, and they dictate what types of statistical analyses can be appropriately performed.
What is Ordinal Data?
Ordinal data is a categorical, statistical data type where variables exist in a ranked order or sequence. The numbers or labels on an ordinal scale tell you the relative position of items, but not the magnitude of the difference between them. For example, a quality-of-service survey using ratings like 'very poor,' 'poor,' 'average,' 'good,' and 'excellent' is a perfect example. We know 'excellent' is better than 'good,' but we can't quantify exactly how much better it is. The same principle applies to a 1-10 rating scale in a health context.
What is Interval Data?
Interval data is a numerical, statistical data type where the order of items and the exact differences between values are known. The key feature is that the intervals between points on the scale are equal and meaningful. However, interval data lacks a true zero point. A classic example is temperature measured in Celsius or Fahrenheit. The difference between 10°C and 20°C is the same as the difference between 30°C and 40°C. But 0°C doesn't mean a complete absence of temperature.
Why a 1-10 Scale is Typically Ordinal
When we ask a patient to rate their pain on a scale from 1 (mild) to 10 (worst imaginable), we are asking for a subjective ranking. Here's why this is considered an ordinal scale:
- Unequal Intervals: The difference in perceived pain between a '1' and a '2' is not necessarily the same as the difference between a '9' and a '10'. One patient's jump from a '4' to a '5' might represent a much larger increase in discomfort than another patient's jump from a '6' to a '7'. The scale ranks the order of pain intensity, but the psychological distance between the points is not constant.
- No True Zero: In this context, a rating of '0' might represent no pain, but it's not a true zero in the mathematical sense that we could say a '10' is ten times more painful than a '1'. The scale doesn't allow for meaningful multiplication or division.
- Subjectivity: The rating is entirely dependent on the individual's perception, making objective, equal intervals impossible to guarantee across a population.
The Grey Area: When a 1-10 Scale Might be Treated as Interval
Despite the fundamental ordinal nature, it is not uncommon for researchers, particularly in social and health sciences, to treat 1-10 scales as interval data. This is a common practice, but it's an assumption rather than a fact. Here are the circumstances under which this might occur:
- Parametric Statistical Tests: Many powerful statistical tests, like t-tests or ANOVA, assume that the data is interval or ratio. To use these tests, researchers might make the assumption that the intervals are close enough to equal for their purposes, especially with a sufficiently large sample size.
- Sufficiently Fine-Grained Scale: For scales with many points (e.g., 10 or more), the assumption of equal intervals becomes more plausible, though still not proven. A 10-point scale is more likely to be treated this way than a 3-point scale.
However, it's critical for researchers to acknowledge this assumption and justify it. Robust studies will often use non-parametric tests, which are more appropriate for ordinal data, or will perform a sensitivity analysis to see if the results change when treating the data differently.
A Comparison of Ordinal vs. Interval Data
| Feature | Ordinal Data | Interval Data |
|---|---|---|
| Ranking | Yes (ordered) | Yes (ordered) |
| Equal Intervals | No | Yes |
| True Zero | No | No |
| Example (Health) | Pain scale (1-10), Likert scales | Temperature (Celsius/Fahrenheit) |
| Permissible Operations | Frequency distribution, median, mode | Mean, standard deviation, addition/subtraction |
| Statistical Tests | Non-parametric (e.g., Mann-Whitney U) | Parametric (e.g., t-test, ANOVA) |
The Health Implications of Correct Classification
For health professionals and researchers, classifying the data correctly has significant implications. Misclassifying an ordinal scale as interval can lead to incorrect conclusions, particularly when comparing different groups or treatments. For instance:
- Comparing Averages: The mean (average) is a powerful statistic for interval data. However, for ordinal data, the median (the middle value) is a more appropriate measure of central tendency. Calculating the mean of a 1-10 pain scale and reporting that one group's average pain is '5.2' while another's is '5.8' might be misleading. The median could tell a different story, which is why understanding the data's underlying properties is so important.
- Patient-Reported Outcomes (PROs): Scales like the 1-10 pain scale are a common type of PRO. The way this data is analyzed directly impacts how we understand patient experience, treatment effectiveness, and quality of life. The choice of statistical methods must align with the nature of the data to ensure the findings are valid and reliable. For more information on health statistics, resources like the World Health Organization (WHO) are invaluable: https://www.who.int/data/data-collection-tools/standards/statistical-standards.
Conclusion
While a 1-10 scale is often used in a way that suggests equal intervals, its true nature, especially in subjective health assessments, is ordinal. The numbers represent a rank order, not a precise measurement with a constant unit of distance. Making the conscious choice to acknowledge this distinction and use appropriate statistical methods ensures the validity and integrity of health research. For most practical purposes, especially when dealing with patient experience, treating it as ordinal is the most statistically sound and defensible approach. Treating it as interval is a common shortcut, but one that must be done with caution and a clear understanding of its limitations.
