# Types of data & levels of measurement ## Types of data

There are four types of data: nominal, ordinal, interval and ratio. Nominal and ordinal scales categorise qualitative (categorical) data and interval and ratio scales categorise quantitative (numerical) data.

It’s important to understand the difference between them because the type of data determines which statistical methods or tests we can use. Nominal and ordinal data cannot be used in calculations, whereas interval and ratio data can. We often try to use scales with the highest data level possible, because we can do more powerful statistical analyses. ### What we'll cover

In this article we will consider each of these data types and provide examples to illustrate them. We’ll also talk a little about the kinds of data analysis we can do with each type.

Qualitative data:

• Nominal level measurement
• Ordinal level measurement

Quantitative data:

• Interval level measurement
• Ratio level measurement

Before we start, let’s first very quickly note the difference between qualitative and quantitative data.

### Qualitative and quantitative data

Quantitative (categorical) data: numbers that represent counts or measurements.

Qualitative (numerical) data: data that has no numeric value but can be categorized.

## Qualitative data

### Nominal level measurement

Nominal measurement scales do not have any numerical value. Data consists of names, labels or categories. The data cannot be ordered (such as high to low). The scales must be mutually exclusive (there can be no overlap between them).

These are examples of nominal level scales:

• Gender: Male/Female
• Country of birth: Canada, Mexico, Brazil
• Educational institution: school, college, university
• Subject: Mathematics, Spanish, History

There is no numerical difference between the items in these scales. You cannot quantify the difference between Canada and Mexico. They are names of countries (or labels).

### Analyzing nominal data

Because there is no quantitative difference between them, we cannot perform any mathematical operations on the data. What we can do is basic counts – frequencies (the number of responses for each category) and percentages.

For example, 20 students in the History class were born in Canada (80%); 1 was born in Mexico (4%); 4 were born in Brazil (16%).

Because the values have no numerical value or order, we cannot calculate the average (mean) of nominal data. We measure the central tendency of nominal data with the mode (the category that occurs most frequently). In this example, the mode is Canada. We can also test the association between two categorical variables.

### Ordinal level measurement

With ordinal measurement scales (as the name implies!), data can be arranged in order. But we can’t say how big the difference between each value is. They can be ranked from highest to lowest, but the differences between them can’t be quantified, are inconsistent, or are meaningless. Ordinal scales are common in opinion or attitude surveys, like Likert-type scales.

Let’s say we are carrying out a survey to find out teachers’ satisfaction with their job. We ask teachers to rate their degree of agreement with a number of statements. We use a five point scale from strongly agree to strongly disagree. We know that strongly agree is better than agree, and that agree is better than disagree. There is an order, but how do we know if the difference between strongly agree and agree is the same as the difference between agree and disagree? We cannot know because we cannot quantify the difference. As with this example, ordinal scales typically measure non-numeric concepts like satisfaction, happiness, etc.

### Analysing data from ordinal measurement scales

As with nominal data, we do counts (frequencies) with ordinal data. We can also use the mode as a measure of central tendency, but because there is an order we can also calculate the median (the value lying at the midpoint in a distribution of values). Because data is qualitative (non-numeric) we don’t calculate the mean. As with nominal data, we can use bar and pie charts to visualize ordinal data. We can analyze ordinal data with a number of (non parametric) statistical tests.

## Quantitative data

### Interval level measurement

The interval level of measurement is similar to ordinal. Values can be ordered, but with interval data the difference between any two values (the interval) is meaningful and equal. We know the exact differences between the values.

In social or psychological research, examples of interval scales are standardized tests of achievement (e.g. SAT) and most IQ tests, as well as other psychology tests. In IQ scores, 100 represents the average IQ of a population. If a student receives an IQ score of 90 and another has a score of 110, each has a score 10 points from the mean. The units in the scale have the same meaning.

### Analysing data from interval scales

With interval scales, central tendency can be measured using the mode, median or the statistical mean. We can also calculate standard deviation. We can also apply lots of statistical tests to interval data.

With interval measurement, zero is an arbitrary point on a scale. A score of zero does not indicate the absence of something. This means it isn’t possible to calculate ratios. So, we can add or subtract but we cannot multiply or divide. We can say that a person has 70 IQ points higher than another person, but we cannot say that someone with an IQ of 140 is twice as intelligent as a person with an IQ of 70.

### Ratio level measurement

Let’s now talk about the highest level of measurement: ratio.

The difference between interval and ratio scales is quite subtle. Simply put, a ratio level measurement scale is an interval scale that has a true zero point. With a ratio scale, a zero indicates that none of the thing is present, whereas if there is a zero value on an interval scale, it is just another number on the scale. To tell the difference between them, ask whether a score of zero means a complete absence of the thing being measured. If it does, it’s a ratio scale; if not, it’s an interval scale.

Examples of ratio scales in social sciences research are individual scores such as “number of correct answers” or “number of mistakes made”.

Let’s say we are comparing three groups of students’ performance on a quiz. We can make statements such as Group B made twice as many errors as Group A. It’s also possible to say Group C got no answers correct. A zero score means a complete absence of correct answers.

### Analyzing data from ratio scales

With this level of data measurement, we can (as the name suggests!) calculate ratios. Because of the true zero, ratio values can be multiplied and divided. We can calculate the mean, standard deviation, and perform all sorts of descriptive and inferential statistics.

In social and survey research, we don’t need to worry too much about the distinction between interval and ratio scales, because we can use the same statistical tests for either. It is important, though, to understand the difference between these two scales and ordinal data. because we shouldn’t use the same (parametric) statistical tests with ordinal data.

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