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Interval Data and How to Analyze It | Definitions & Examples

Published on August 28, 2020 by Pritha Bhandari. Revised on May 31, 2022.

Interval data is measured along a numerical scale that has equal distances between adjacent values. These distances are called "intervals."

There is no true zero on an interval scale, which is what distinguishes it from a ratio scale. On an interval scale, zero is an arbitrary point, not a complete absence of the variable.

Common examples of interval scales include standardized tests, such as the SAT, and psychological inventories.

Levels of measurement

Interval is one of four hierarchical levels of measurement. The levels of measurement indicate how precisely data is recorded. The higher the level, the more complex the measurement is.

While nominal and ordinal variables are categorical, interval and ratio variables are quantitative. Many more statistical tests can be performed on quantitative than categorical data.

Interval vs ratio scales

Interval and ratio scales both have equal intervals between values. However, only ratio scales have a true zero that represents a total absence of the variable.

Celsius and Fahrenheit are examples of interval scales. Each point on these scales differs from neighboring points by intervals of exactly one degree. The difference between 20 and 21 degrees is identical to the difference between 225 and 226 degrees.

However, these scales have arbitrary zero points – zero degrees isn't the lowest possible temperature.

Because there's no true zero, you can't multiply or divide scores on interval scales. 30°C is not twice as hot as 15°C. Similarly, -5°F is not half as cold as -10°F.

In contrast, the Kelvin temperature scale is a ratio scale. In the Kelvin scale, nothing can be colder than 0 K. Therefore, temperature ratios in Kelvin are meaningful: 20 K is twice as hot as 10 K.

Examples of interval data

Psychological concepts like intelligence are often quantified through operationalization in tests or inventories. These tests have equal intervals between scores, but they do not have true zeros because they cannot measure "zero intelligence" or "zero personality."

Type	Examples
Standardized tests	IQ SAT GRE GMAT
Psychological inventories	Beck's Depression Inventory Raven's Progressive Matrices Big Five personality trait tests

To identify whether a scale is interval or ordinal, consider whether it uses values with fixed measurement units, where the distances between any two points are of known size. For example:

• A pain rating scale from 0 (no pain) to 10 (worst possible pain) is interval.
• A pain rating scale that goes from no pain, mild pain, moderate pain, severe pain, to the worst pain possible is ordinal.

Treating your data as interval data allows for more powerful statistical tests to be performed.

Interval data analysis

To get an overview of your data, you can first gather the following descriptive statistics:

• the frequency distribution in numbers or percentages,
• the mode, median, or mean to find the central tendency,
• the range, standard deviation and variance to indicate the variability.

Interval data example

You collect the SAT scores of a group of 59 graduating students from City A. Test-takers can score anywhere between 400–1600 on the SAT.

Distribution

Tables and graphs can be used to organize your data and visualize its distribution.

To organize your data, enter it into a grouped frequency distribution table.

SAT score	Frequency
401 – 600	0
601 – 800	4
801 – 1000	15
1001 – 1200	19
1201 – 1400	16
1401 – 1600	5

To visualize your data, plot it on a frequency distribution polygon. Plot the groupings on the x-axis and the frequencies on the y-axis, and join the midpoint of each interval using lines.

Central tendency

From your graph, you can see that your data is fairly normally distributed. Since there is no skew, to find where most of your values lie, you can use all 3 common measures of central tendency: the mode, median and mean.

The mode is the most frequently repeating value in your data set. In this case, there is no mode because each value only appears once.

The median is the value exactly in the middle of your data set. To find the middle position, take the value at (n+1)/2 where n is the total number of values.

(n+1)/2 = (59+1)/2 = 30

The median is in the 30th position, which has a value of 1120.

The mean uses all values to give you a single number for the central tendency of your data. To find the mean, use the formula of ⅀x/n. Sum up all values (⅀x) and divide the sum by n.

⅀x = 65850
n = 59
⅀x/ n = 65850/59 = 1116.1

The mean is usually considered the best measure of central tendency when you have normally distributed quantitative data. That's because it uses every single value in your data set for the computation, unlike the mode or the median.

Variability

The range, standard deviation and variance describe how spread your data is. The range is the easiest to compute while the standard deviation and variance are more complicated, but also more informative.

To find the range, subtract the lowest from the highest value in your data set. Our maximum value is 1500, and our minimum is 620.

Range = 1500 – 620 = 880

The standard deviation (s) is the average amount of variability in your dataset. It tells you, on average, how far each score lies from the mean. Most computer programs will easily calculate the standard deviation for you. If you want to do it by hand, use these steps.

s = 210.42

The variance (s ² ) is the average squared deviation from the mean. A deviation from the mean is the difference between a value in your data set and the mean. To find the variance, square the standard deviation.

s ² = 44279.36

Statistical tests

Now that you have an overview of your data, you can select appropriate tests for making statistical inferences. With a normal distribution of interval data, both parametric and non-parametric tests are possible.

Parametric tests are more powerful than non-parametric tests and let you make stronger conclusions regarding your data. However, your data must meet several requirements for parametric tests to apply.

The following parametric tests are some of the most common ones applied to test hypotheses about interval data.

Aim	Samples or variables	Test	Example
Comparison of means	2 samples	T-test	What is the difference in the average SAT scores of students from 2 different high schools?
Comparison of means	3 or more samples	ANOVA	What is the difference in the average SAT scores of students from 3 test prep programs?
Correlation	2 variables	Pearson's r	How are SAT scores and GPAs related?
Regression	2 variables	Simple linear regression	What is the effect of parental income on SAT scores?

Frequently asked questions about interval data

What is the difference between interval and ratio data?

While interval and ratio data can both be categorized, ranked, and have equal spacing between adjacent values, only ratio scales have a true zero.

For example, temperature in Celsius or Fahrenheit is at an interval scale because zero is not the lowest possible temperature. In the Kelvin scale, a ratio scale, zero represents a total lack of thermal energy.

Are Likert scales ordinal or interval scales?

Individual Likert-type questions are generally considered ordinal data, because the items have clear rank order, but don't have an even distribution.

Overall Likert scale scores are sometimes treated as interval data. These scores are considered to have directionality and even spacing between them.

The type of data determines what statistical tests you should use to analyze your data.

Sources in this article

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Bhandari, P. (May 31, 2022). Interval Data and How to Analyze It | Definitions & Examples. Scribbr. Retrieved October 24, 2022, from https://www.scribbr.com/statistics/interval-data/

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