What is Ordinal Data?
Ordinal data have at least three categories that have a natural rank order. The categories are ranked, but the differences between ranks may not be equal. These data indicate the order of values but not the degree of difference between them. For example, first, second, and third places in a race are ordinal data. You can clearly understand the order of finishes. However, the time difference between first and second place might not be the same as between second and third place.
Ordinal data are prevalent in social science and survey research. These variables are relatively convenient for respondents to choose even when the underlying variable is complex, allowing you to compare the participants. For example, subject-area expertise can be tricky to measure using a continuous scale. However, ordinal data can make this evaluation much easier by using Beginner, Intermediate, and Expert ranking choices in a survey.
Likert scale items in a survey are ordinal data. These items typically have 5 or 7 possible responses.
While this data type is expedient, it has downsides that limit the valid summary values and analyses you can use. More on this later!
Ordinal Data Examples
The key concept behind ordinal data is that it ranks observations. However, these ranks don’t indicate the relative degree of difference between two observations. For instance, you know that a high-income person earns more than a middle-income individual, but you don’t know how much more they make. Keep that in mind as you consider the following examples.
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Comparisons to Other Types of Variables
Ordinal data share properties with both nominal and continuous variables yet are distinct from either.
Nominal vs Ordinal Data
However, you can rank ordinal data, which is impossible with nominal data.
For example, college major is nominal data; you can’t rank those categories using that variable alone. They’re simply names of distinct groups, such as statistics, political science, and psychology.
Conversely, ordinal data form groups that you can inherently rank. For example, the relative size of college majors at an institution can be small, medium, or large.
Related post: Discrete vs Continuous Variables
Continuous vs Ordinal
Ordinal and continuous data (both interval and ratio scale) can rank observations on a scale. In other words, you can record that one observation has more of a characteristic than another observation. However, as discussed earlier, ordinal data can’t describe the degree of difference between values, while a continuous variable can.
For example, the size of a college major at an institution can be small, medium, or large. If one major is large and another medium, you see that the former is larger than the latter. However, you don’t know the degree of difference.
Conversely, if you measure size using a continuous variable such as the number of students or budget, you can determine the degree of difference between two observations.
In some cases, you can choose to measure a variable either as continuous or ordinal data. Whenever practical, choose the continuous form because it retains more information and gives you more options during the analysis.
Amongst the various measurement scales, ordinal data fall between the nominal and interval scales. For more information, read Nominal, Ordinal, Interval, and Ratio Scales.
Ordinal Data Limitations
The inability to know the precise differences between observations limits the mathematical functions and summary statistics you can calculate for ordinal data.
While analysts often record values for these variables using numbers, such as 1-5 for a Likert scale of agreement, that doesn’t indicate all numeric calculations are valid.
You cannot meaningfully add and subtract values. For example, if you take ordinal data values of 1 and 2, you can’t trust that summing them to 3 is a valid result. Why?
When adding 1 and 2 to get 3, you’re assuming the difference between 1 and 2 equals the difference between 2 and 3 because they’re both one unit apart. However, that is not a safe assumption with this data type.
Because addition isn’t valid, you can’t subtract because it’s the inverse function. Also, calculating the mean is invalid because it involves addition and division (also invalid). Division is valid only for continuous variables using a ratio scale.
Analyzing Ordinal Data
So, what can you do with these variables? Which summary statistics are valid? And what kind of analyses can you perform?
Bar graphs are great for displaying discrete variables. Consequently, they’re an excellent choice for visually understanding ordinal data.
The bar chart below displays a Likert scale item for service ratings from Very Poor to Very Good.
It’s easy to see that most patrons rated the service as Good.
Measures of central tendency and variability are two standard summary statistics to report with your results. However, the mean and standard deviation are questionable for ordinal data. Consequently, consider using the following alternatives:
- Mode and Median for the central tendency.
- Range, interquartile range, and interval for two percentiles for variability.
Click the links to learn more about these concepts and statistics.
Similarly, the standard hypothesis tests for the mean (e.g., t-tests and ANOVA) are questionable for this type of variable. Means tests are parametric hypothesis tests.
Instead, consider using nonparametric hypothesis tests as an alternative. They assess medians and ranks, making them perfect for ordinal data. These tests include Mood’s Median, Mann-Whitney, Wilcoxon, Friedman’s Test, and Spearman’s rho.
Finally, statisticians have some disputes over using hypothesis tests for the mean with Likert scale items. I discussed the critical reason in this post—the mean is not valid. However, some make the case that for specific Likert scales the differences between values are equal by design. If that is true, then the mean might be valid.
However, for parametric hypothesis testing, there are additional concerns for ordinal data. Specifically, these variables are less likely to satisfy the analysis’ assumptions. To learn more about this issue, including some answers about what to do, read my post about Analyzing Likert Scale Data.