## Ratio data

**A variable that is measured at a ratio scale has many values and has an absolute zero.**

A ratio variable has values that start with zero and can go sky high, up to infinity. Decimals are allowed too. It is okay to make any kind of calculations with it. An object that is measured in centimetres (or inches) will become twice as big when the length doubles (or the depth or the height, but not all at the same time).

A ratio variable is pretty much the same as an interval variable, and it is often disputable if a variable should be seen as an interval or an ratio variable. To cut short the discussion, it doesn’t really matter, because in statistics both types of variables are treated in the same way. The advantage of ratio variables is that they are easier to make calculations with and most of the time they are somewhat easier to interpret.

**Which types of analysis can be adjusted on ratio data?**

Variables measured at an interval and ratio level are both continuous and are treated the same. So what you read below is also applicable on interval 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. Most frequently used test 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 collect the data at interval or ratio level instead of at 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?

0 up to 20

0 21 to 30

0 31 to 40

0 41 to 50

0 51 or elder

Choose 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. Secondly, it is easier 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.

**Related topics to Ratio data**

**Variable****Nominal level****Ordinal level****Interval level****Ratio data**

**Mean****Median****Standard deviation****Skewness****Kurtosis**

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