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

### Interval Scale

The third scale of measurement is the *interval* scale.

Interval scale

**Definition**

The categories of an **interval** scale can be ordered like ordinal categories, but the *distance* between each category or value is known and equal.

An additional characteristic of an interval scale is that the *zero point* of the scale is arbitrary, meaning that a score of zero does not actually indicate a complete absence of the variable being measured.

**Examples:**

- Temperature measured in #^\circ{}#C
- Temperature measured in #^\circ{}#F
- Golf scores
- Gregorian calendar

Because the distances between the values of an interval 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 an interval scale. However, due to the lack of an absolute zero point, the ratio between two interval categories is misleading and should not be calculated.

\[\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}}\\

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

Temperature as an interval scale measurement

An example of an interval scale measurement would be to use a thermometer to measure the outside temperature in #^\circ#C. The numerical nature of the Celcius scale makes it easy to *detect differences *between two temperatures as well as determine the *direction *of such a difference. For example, a temperature of #20^\circ#C is *different *from and *larger *than a temperature of #10^\circ#C.

Additionally, because the distances between the values of the Celcius scale are fixed, it is possible to measure and compare the *size *of the difference between two temperatures. For instance, the difference between #24^\circ#C and #25^\circ#C is #1^\circ#C and this difference is equal to the difference between #25^\circ#C and #26^\circ#C.

As an interval scale, the Celsius scale does not have an *absolute zero* point and a temperature of #0^\circ#C does not mean there is no temperature. Instead, the zero point of the Celcius scale was chosen because it is the temperature at which water freezes. This lack of an absolute zero point prevents the ratio of two temperatures from being meaningful and it would be incorrect to state that a temperature of #20^\circ#C is twice as high as a temperature of #10^\circ#C.

**Pass Your Math**independent of your university. See pricing and more.

Or visit omptest.org if jou are taking an OMPT exam.