Variables and the Levels at Which They Are Measured, Explained

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Variables and the Levels at Which They Are Measured

Research Methods in Psychology · Chapter 9: Measurement, Reliability, and ValiditySection 9.3 · lesson 52 of 9411 min · free with a free account

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In this lesson

Measurement scales, and their implications for analysis and interpretation.

  • Distinguish the main types of research variable
  • Identify nominal, ordinal, interval and ratio levels
  • Explain the statistical implications of each level
  • Recognize the common errors of level mismatch

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Everything said in the video, section by section (1,478 words). Read along, or search it.

Measurement, Reliability, and Validity

Variables and the Levels at Which They Are Measured

Not all numbers in psychology mean the same thing. A four on a rating scale, a reaction time of four milliseconds, and participant number four. Three fours, carrying three completely different kinds of information. This section explains the difference, and why your statistics depend on it. You will distinguish the main types of variable in research. You will identify the four levels of measurement, and what each one permits. You will learn which statistics belong at which level. And you will recognize three errors that appear constantly in published work.

Not All Numbers Are Alike

Why the Level of Measurement Matters

Each of those three fours represents a different level of measurement. A different type of relationship between the number and the quantity it stands for. Use the wrong statistical procedure for a given level, and something odd happens. You get results that are technically impressive and completely meaningless. Consider a researcher who averages diagnostic group codes. One for depression, two for anxiety, three for post-traumatic stress disorder. The average of those codes is a number that cannot be true or false. The framework for avoiding this is nearly eighty years old. Stanley Stevens published his taxonomy of measurement scales in nineteen forty-six. Nominal, ordinal, interval, and ratio. It remains the most widely used framework for understanding psychological data.

Before the Levels

Five Types of Variable

Before the levels, distinguish five types of variable. A continuous variable can take any value within a range, including fractions. In principle its precision is limited only by the instrument. Reaction time is continuous, and so is a cortisol level. A discrete variable can take only specific, separate values. The number of errors on a task, or the number of children someone has. A dichotomous variable is a special case of the discrete, with only two possible values. Diagnosis present or absent. Task success, yes or no. A categorical variable takes values representing qualitatively distinct categories. Not quantities. Diagnostic category, country of origin, type of therapy received. And a latent variable is unobserved, inferred from observable indicators. General intelligence, depression severity, extraversion. Every construct is one of these.

Level One

Nominal: Numbers That Only Label

The first level is nominal, and it is the least informative. Here numbers or labels serve only to classify. They place observations into categories with no order and no quantitative relationship. The numbers are entirely arbitrary. You could use letters or names instead, and lose nothing at all. So addition, subtraction, and averaging are meaningless at this level. Nominal variables include gender identity and nationality. Also diagnostic categories, and attachment types like secure, anxious, avoidant, or disorganized. The appropriate statistics are frequencies, percentages, the mode, and the chi-square test. Somebody calculates a mean of the nominal codes. The average diagnostic group was one point seven. That is not a finding.

Level Two

Ordinal: Order Without Distance

The second level is ordinal, and it adds one thing. Order. Categories can now be meaningfully ranked. You know which is more and which is less. But the intervals between adjacent values are not necessarily equal. Ranking tells you about order. It does not tell you about the size of the differences. Class rank is ordinal. So are letter grades, and pain ratings of mild, moderate, and severe. So are individual rating-scale items, from strongly disagree to strongly agree. The appropriate statistics are the median and percentiles. Plus Spearman's rank correlation, the Mann-Whitney U test, and the Wilcoxon signed-rank test. The common error here is subtler than the nominal one. Researchers treat rating-scale items as interval data, and compute means, without justifying it. The gap between strongly disagree and disagree may not equal the gap between agree and strongly agree.

Level Three

Interval: Equal Distances, No True Zero

The third level is interval, and it adds equal spacing. The differences between adjacent values are now equal and meaningful. You can say not only that one score is higher, but by exactly how much. The distance between scores carries real information. What is still missing is a true zero point. A score of zero does not mean the complete absence of the attribute. An intelligence quotient of zero does not mean zero intelligence. Zero degrees Celsius does not mean no temperature. Most psychometric scales sit at this level. Mean, standard deviation, Pearson's correlation, t-tests, analysis of variance, regression. But one thing stays forbidden, and it is the common error at this level. Treating the data as if ratios were meaningful. Saying that an intelligence quotient of one hundred twenty is twice that of sixty is simply false.

Level Four

Ratio: A Zero That Means Nothing Is There

The fourth level is ratio, and it adds the missing zero. It has every property of interval measurement, plus a true zero point. That means a score of zero genuinely indicates the complete absence of the attribute. Reaction time is ratio-level. So is the number of errors. So are weight, height, cortisol concentration, and the frequency of a behavior. Zero errors really does mean no errors at all. Every parametric and non-parametric statistic is available here. Plus two that need the zero, the geometric mean and the coefficient of variation. Ratio statements finally become meaningful. A reaction time of eight hundred milliseconds is genuinely twice as long as four hundred. At this level, and only at this level, you are entitled to say twice.

Side by Side

What Each Level Adds

Line the four levels up on the four properties. All four levels classify. That is the minimum any measurement does. Ordinal, interval, and ratio also carry order. Interval and ratio also have equal intervals between values. And only ratio has a true zero. So read the table as a staircase rather than as four separate boxes. Each level keeps everything the previous one had, and adds exactly one property. That is why the sequence is fixed and cannot be rearranged. And it is why the statistics available to you expand as you move down. Diagnostic category, class rank, intelligence quotient, reaction time. One example from each rung, worth memorizing as anchors.

The Live Debate

The Controversy Over Rating Scales

Now the most debated question in psychological measurement. How should we treat data from Likert-type scales? An individual item, such as I feel anxious rated from one to five, is strictly ordinal. The intervals between its categories are not necessarily equal. Yet many researchers treat composite scales as approximately interval-level. A composite is the sum or the mean of several items together. The argument is that combining items produces a more continuous score. This practice is controversial, but widely accepted, when three conditions hold. The scale has a sufficient number of items, typically five or more. The distribution of composite scores is approximately normal. And the use of parametric statistics is justified by robust reliability evidence. Whatever you decide, be explicit that you decided it. And consider reporting non-parametric alternatives alongside, where appropriate.

Choosing the Test

Selecting Statistics by Level

Put the whole thing to work in choosing an analysis. For nominal data, use chi-square tests, frequencies, and the mode. Do not compute means. There is nothing there to average. For ordinal data, use the median and Spearman's rank correlation. Plus the Mann-Whitney U test and the Wilcoxon test. Use means only cautiously, and only for composite scales. For interval data, the full parametric set is appropriate. Mean, standard deviation, Pearson's correlation, t-tests, analysis of variance, and regression. For ratio data, everything appropriate for interval data applies. And you additionally get the geometric mean and the coefficient of variation. And when you genuinely are not sure which level you have, there is a good default. Report both parametric and non-parametric analyses, and note any discrepancies. If they agree, that is reassuring. If they disagree, that itself is worth telling the reader.

Three Errors

The Mistakes This Section Prevents

The first is averaging a label. Attachment styles coded one through four, then reported as an average of two point three. The codes carry no quantity, so the mean carries no meaning. The correct approach is frequencies and a chi-square test. The second is promoting an item. Treating a single rating-scale item as interval, and computing its mean, with no justification. The third is inventing a ratio. Reading an intelligence quotient of one hundred twenty as twice one of sixty. Without a true zero there is simply no ratio there to read. Notice why all three survive review so easily. Each produces a number that looks perfectly respectable on the page. Nothing in the software objects. The incoherence is in the meaning, not the arithmetic.

Carrying It Forward

The Level Decides the Analysis

Four definitions to carry forward. At the nominal level, numbers serve only to classify into unordered categories. At the ordinal level, categories can be ordered, but the intervals between them are unequal. At the interval level, the intervals are equal, but there is no true zero point. At the ratio level you get equal intervals and a true zero together. Which is what makes ratio comparisons meaningful. Compress the whole section into one line if you like. Nominal data classify. Ordinal data rank. Interval data measure differences with equal spacing. Ratio data add a true zero. Mismatching a statistical procedure to the measurement level is common, and consequential. Next, the major categories of test and assessment used in psychological research.

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FAQ

Questions students ask us

About Variables and the Levels at Which They Are Measured

What are the four levels of measurement?
The four levels of measurement are nominal, ordinal, interval, and ratio, from Stanley Stevens's 1946 taxonomy. Nominal data only classify, such as diagnostic category. Ordinal data add rank order, such as class rank. Interval data add equal spacing between values, such as IQ scores. Ratio data add a true zero, such as reaction time. Each level keeps the properties of the one before it and adds one more.
Which statistics can you use at each level of measurement?
Nominal data call for frequencies, percentages, the mode, and chi-square tests. Ordinal data call for the median, percentiles, Spearman's rank correlation, the Mann-Whitney U test, and the Wilcoxon signed-rank test. Interval data allow the mean, standard deviation, Pearson's correlation, t-tests, ANOVA, and regression. Ratio data allow all of these plus the geometric mean and the coefficient of variation. Averaging nominal codes, such as diagnostic group numbers, produces a meaningless number.
Are Likert scale data ordinal or interval?
A single Likert-type item is ordinal, because the gaps between response options such as disagree and strongly disagree are not necessarily equal. Many researchers treat a composite score, the sum or mean of several items, as approximately interval. That practice is debated but widely accepted when the scale has enough items, typically five or more, composite scores are roughly normal, and reliability evidence is strong. Reporting non-parametric results alongside is a sensible safeguard.
Why can't you say an IQ of 120 is twice an IQ of 60?
IQ is measured on an interval scale, which has equal spacing between values but no true zero, so ratio statements are meaningless. An IQ of zero does not mean zero intelligence, just as 0 degrees Celsius does not mean no temperature. Ratio statements are valid only on ratio scales such as reaction time, where 800 milliseconds really is twice as long as 400 milliseconds.

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