### Chapter 1. Descriptive Statistics: Types of Data and Measurements

### Ratio Scale

The fourth and strongest scale of measurement is the *ratio *scale.

Ratio scale

**Definition**

Similar to the interval scale, the categories of a **ratio **scale can be ordered and the distance between each category or value is known and equal.

The difference between an interval and a ratio scale is that a ratio scale does have an *absolute zero* point, meaning that a score of zero is indicative of a complete absence of the variable being measured.

**Examples:**

- Height measured in cm
- Weight measured in kg
- Time measured in seconds
- Temperature measured in Kelvin

Because the distances between the values of a ratio scale are known and equal, it is not only possible to *detect differences* between individuals, but it is also possible to determine the *direction *and the *size *of the difference. These fixed distances allow for the addition and subtraction of data measured on a ratio scale. Additionally, the inclusion of an absolute zero point unlocks the mathematical operations of multiplication and division. This, in turn, makes it meaningful to calculate the ratio between two values.

\[\begin{array}{r|cccc}\begin{array}{r|cccc}

&\text{Detect differences}?&\text{Direction of the difference?}&\text{Size of the difference?}&\text{Calculate ratios?}\\

&(=, \neq)&(>,<)&(+,-)&(\times , \div)\\

\hline

\text{Nominal}&\green{\text{Yes}}&\red{\text{No}}&\red{\text{No}}&\red{\text{No}}\\

\text{Ordinal}&\green{\text{Yes}}&\green{\text{Yes}}&\red{\text{No}}&\red{\text{No}}\\

\text{Interval}&\green{\text{Yes}}&\green{\text{Yes}}&\green{\text{Yes}}&\red{\text{No}}\\

\text{Ratio}&\green{\text{Yes}}&\green{\text{Yes}}&\green{\text{Yes}}&\green{\text{Yes}}\\

\end{array}\\ \phantom{x}\end{array}\]

Height as a ratio scale measurement

An example of a ratio scale measurement would be to use a tape measure to determine a object's height. In this case, height is a numerical scale which makes it easy to *detect differences *between two heights as well as determine the *direction *of such a difference. For example, an object that is 180cm tall is *different *from and *larger* than a object that is 150cm tall.

Additionally, because the distances between the values of a ratio scale are fixed, it is possible to measure and compare the *size *of the difference between two heights. For instance, the difference between 20cm and 30cm is 10 cm and this difference is equal to the difference between 30cm and 40cm.

As a ratio scale, height does have an *absolute zero* point and a height of 0cm means that the object being measured is completely flat. The existence of an absolute zero points makes the calculation of ratios meaningful and it would be correct to state that an object of 100cm is twice as tall as an object of 50cm.

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