## Interval data

**A variable is said to be measured at an interval scale when there are a lot of values. The values might go down to minus infinity or up to plus infinity. An absolute zero is not necessary.**

It is not so easy to define a variable with data at interval level. The best way to describe it – in my opinion – is that there are a lot of values with a minimum of minus infinity and a maximum of plus infinity. An interval variable can contain decimals. A good example is bank account. A bank account can be very low (then you have debts) or very high (then you have credits). In theory – and it has to be stressed, only in theory – a bank account can go down to minus infinity (but I think they will declare you bankrupt before that time) or up to plus infinity (owners of a bank never tell you to stop putting more money on your bank account).

In textbooks it is often said that a variable that is measured at the interval level has no absolute zero. Therefore it is not allowed to make computations with interval variables. A common example is temperature, because 24 degrees Celsius (75.2 degrees Fahrenheit) is not twice as hot as 12 degrees Celsius (53.6 degrees Fahrenheit). I think this is disputable on at least two aspects. First of all, hot is a qualification at an ordinal level, so you mix up two levels of measurement. In the second place, if the temperature is measured in degrees of Kelvin, it has an absolute point of zero, though the scale dimension remains divided the same way as degrees of Celsius. Now a change from 12 degrees Celsius (= 285,15 degrees Kelvin) to 24 degrees Celsius (= 297,15 degrees Kelvin) is a change of 12 for both scales. So some calculations are allowed, but be careful with giving it a qualitative interpretation on any value of variables measured on an interval level.

Measurements at interval levels often occur in research in which Likert scales are used and the answers to the questions are summed. For instance with seven items on a five point Likert scale, the minimum is 7 and the maximum is 35. With twelve items the minimum score is 12 and the maximum score is 60. Working this way, it takes more time to interpret a score like 30. With 7 items this score is high, but with 12 items this score is below the mean. Best of all, don’t summarize the numbers, but compute the means. Now a score like 3.75 can be interpreted the same way in both scales.

In both examples of the Likert scale there is no zero. And it is not necessary to have a zero in an interval variable. Even well known tests don’t always include a zero in their scale. Scales like intelligence, introversion – extraversion, school performance and so on really have no zero in their scale scores.

**What types of analysis can be performed with interval data?**

Variables measured at the interval and ratio level are both continuous and are treated the same way. So what you read below is also applicable to ratio variables. As a matter of fact, it is the same text.

To describe continuous variables always the mean, the median, the standard deviation can be computed, the minimum and maximum values can be registered so the range can be computed, and also the skewness and kurtosis can be computed. We described these characteristics for centrality and dispersion elsewhere, so we will not repeat it here.

Interval and ratio variables are used in a lot of tests. The most frequently used tests are ANOVA, t-test (which is actually a special case of ANOVA), MANOVA, ANCOVA, correlation and (univariate and multiple) regression.

Tip: if you have to decide whether you want to measure the data at interval or ratio level instead of ordinal or nominal level, then always choose for the interval/ratio level. For instance the age of a respondent can be questioned like:

**What is your age? ……… years**

or

**What is your age category?**

0 21 to 30

0 31 to 40

0 41 to 50

0 51 or elder

Choose for the first one, because this will be a variable at interval/ratio level. Now there are several advantages compared with nominal and ordinal data. First, more kinds of analysis are allowed, especially when three or more variables should be used. In the second place, it is more easy to find significant differences. Thirdly, less respondents are needed to get a satisfying insight in the research object. And finally, it is always possible to transform a continuous variable to ordinal or nominal while the opposite is not possible.