Understand the difference between ordinal, interval, and ratio variables. Learn why data types matter for choosing the correct statistical test and how to analyze each one correctly.
Why Data Type Matters in Statistics
Before you analyze any data, you need to know what kind of data you have. Using the wrong statistical method for your data type is like using a screwdriver to hammer a nail—it might not work and could damage your results. Knowing if your data is ordinal, interval, or ratio helps you pick the right tools for accurate and meaningful analysis.
The Four Types of Data
Data can be classified into four main types, each with its own rules about what you can and cannot do with it mathematically. These types were introduced by psychologist Stanley Smith Stevens and are still essential today.
1. Nominal Data
What it is: Data that fits into named categories with no inherent order or ranking. The numbers you might assign are just labels; they don’t mean anything mathematically.
- Examples:
- Gender (Male, Female, Other)
- Blood Type (A, B, AB, O)
- Zip Code
- Favorite Color (Red, Blue, Green)
- What you can calculate: You can count how many are in each category (frequency). You cannot calculate a mean or average zip code—it would be meaningless.
2. Ordinal Data
What it is: Data where the order matters, but the precise difference between values is not known or consistent. You know that one is more than another, but not by exactly how much.
- Examples:
- Satisfaction Survey (Very Unsatisfied, Unsatisfied, Neutral, Satisfied, Very Satisfied)
- Education Level (High School, Bachelor’s, Master’s, PhD)
- Income Bracket (“Less than 50K”, “50K-100K”, “Over 100K”)
- Finishing Place in a Race (1st, 2nd, 3rd)
- What you can calculate: You can calculate the median (the middle value) and percentiles. You generally should not calculate a mean for ordinal data because the gaps between levels are not equal.
3. Interval Data
What it is: Data where the order matters AND the difference between two values is meaningful and consistent. However, there is no true “zero” starting point.
- Examples:
- Temperature in Celsius or Fahrenheit (20°C is 5° hotter than 15°C, but 0°C does not mean “no temperature”).
- pH Score
- Standardized Test Scores (like SAT from 200-800)
- What you can calculate: You can safely add, subtract, and calculate the mean and standard deviation. You cannot calculate meaningful ratios. For example, 40°C is not “twice as hot” as 20°C.
4. Ratio Data
What it is: The most flexible type of data. It has all the properties of interval data, but with a true zero point. This means you can calculate ratios meaningfully.
- Examples:
- Weight (0 kg means no weight)
- Height (0 cm means no height)
- Age (0 years means newborn)
- Reaction Time
- Number of Children in a Family (0 means no children)
- What you can calculate: You can do all mathematical operations: addition, subtraction, multiplication, and division. You can say that 100 kg is twice as heavy as 50 kg.
Quick Reference Table: What Can You Calculate?
| Data Type | Key Feature | Example | Can you calculate a Mean? | Can you calculate a Ratio? |
|---|---|---|---|---|
| Nominal | Categories | Blood Type | ❌ No | ❌ No |
| Ordinal | Order matters | Satisfaction Rating | ⚠️ Usually Not | ❌ No |
| Interval | Consistent differences | Temperature (°C) | ✅ Yes | ❌ No |
| Ratio | True zero point | Weight (kg) | ✅ Yes | ✅ Yes |
Why You Should Care About Data Types
Choosing the wrong statistical test because you misunderstood your data type can lead to incorrect conclusions. Here’s why it matters:
- Picking the Right Graph: You wouldn’t use a pie chart for height data (ratio) or a scatter plot for blood types (nominal). Each data type has visualizations that work best.
- Selecting the Correct Statistical Test:
- To compare the means of two groups, you use a t-test. This only works for interval or ratio data.
- To compare the ranks of two groups (like survey responses), you use a Mann-Whitney test. This is for ordinal data.
- To see if two categories are related (like gender and blood type), you use a Chi-square test. This is for nominal data.
- Avoiding Meaningless Calculations: Calculating the average zip code or saying a pH of 4 is “twice as acidic” as a pH of 2 are common mistakes that happen when data types are ignored.
How to Apply This Knowledge
When you start analyzing your data, always ask yourself: “What type of data is this?”
- Does it fit into categories? → It’s probably Nominal.
- Can I order it, but not measure the exact difference? → It’s probably Ordinal.
- Can I measure the difference, but there’s no true zero? → It’s probably Interval.
- Does it have a true zero and can I say “twice as much”? → It’s Ratio.
Using software like Biostat Prime can help guide this process. Its structured analysis workflow ensures you define your variables correctly from the start, preventing fundamental errors and leading you to the most appropriate statistical tests and graphs for your specific data types.
Is age a ratio or interval variable?
Age is a classic example of a ratio variable. A value of zero means birth, and it is meaningful to say that a 40-year-old is twice as old as a 20-year-old.
Is Likert scale data (e.g., 1-5 ratings) ordinal or interval?
This is a common debate. Technically, the difference between “Agree” (4) and “Neutral” (3) may not be the same as between “Neutral” (3) and “Disagree” (2), so it is ordinal. However, many researchers treat it as interval to calculate means and use more powerful parametric tests, but this requires caution and an understanding of the assumptions.
What is the difference between discrete and continuous data?
This is another way to classify data, often within the ratio and interval types.
- Discrete data can be counted and has clear spaces between values (e.g., Number of patients, Number of cars).
- Continuous data can be measured and can take on any value within a range (e.g., Height, Weight, Temperature).
Why can’t I calculate the mean for ordinal data?
You can calculate a number, but it may not be meaningful. For example, if you code “PhD=4, Master’s=3, Bachelor’s=2, High School=1,” a mean of 2.5 doesn’t mean someone has a “Bachelor’s and a half” degree. The median (the middle value) is often a better measure for ordinal data.
How can I change my data to a better type?
Often, you can collect data in a more precise form. Instead of collecting income in brackets (ordinal), try to collect the exact amount (ratio). Instead of a rank order (ordinal), try to get a precise score (interval/ratio). Moving from nominal or ordinal to interval or ratio data gives you more powerful analytical options.