Nominal, Ordinal, Interval, and Ratio are defined as the **four fundamental levels of measurement scales** that are used to represent data from quantitative and qualitative studies. Each scale is an incremental level of measurement, meaning, each scale fulfills the function of the previous scale.

Categorical: Nominal or ordinal (Non-Metric)

Nominal scales

Ordinal scales

Metric Scales

Interval scales

Ratio scales

### Nominal

A nominal scale describes a variable with categories that do not have a natural order or ranking. You can code nominal variables with numbers if you want, but the order is arbitrary and any calculations, such as **conducting a mean, median, or standard deviation, would be inappropriate**. Even more, Median or Mean are not appropriate measures of central tendency. Mode is the appropriate measures of central tendency.

Examples of nominal variables include:

Genotype, blood type, zip code, gender, race, eye color, political party

Things they can do

Useful for identification and classification

• Things they can not do

• Relative position can not be indicated

• Magnitude of differences can not be compared

• Ratios of scale values can not be compared. No

fixed zero point- Zero point is arbitrary

• Use different numbers (e.g. 1, 2 and 3)

• Categories should be mutually exclusive and

collective exhaustive (e.g. Gender: male 2; female 1)

### Ordinal

An ordinal scale is one where the order matters but not the difference between values.

Examples of ordinal variables include:

Socio-economic status (“low income”,”middle income”,”high income”), education level (“high school”,”BS”,”MS”,”PhD”), income level (“less than 50K”, “50K-100K”, “over 100K”), satisfaction rating (“extremely dislike”, “dislike”, “neutral”, “like”, “extremely like”).

Note the differences between adjacent categories do not necessarily have the same meaning. For example, the difference between the two income levels “less than 50K” and “50K-100K” does not have the same meaning as the difference between the two income levels “50K-100K” and “over 100K”.

Median and Mode both are appropriate measures of central tendency.

They can do all the things nominal scales can do

Useful for identification and classification

• And more

Numbers indicate relative positions

Things they can not do

• Magnitude of differences can not be compared

• Ratios of scale values can not be compared.

• No fixed zero point – Zero is arbitrary

• Use different numbers

• Numbers used should be in an order

### Interval

An interval scale is one where there is order and the difference between two values is meaningful.

Examples of interval variables include:

temperature (Farenheit), temperature (Celcius), pH, SAT score (200-800), credit score (300-850).

Mean, Median and Mode are all appropriate measures of central tendency.

### Ratio

A ratio variable, has all the properties of an interval variable, and also has a clear definition of 0.0. When the variable equals 0.0, there is none of that variable. Ratio data have all properties of measurement of the previous mentioned variables.

Examples of ratio variables include:

- Enzyme activity,
- Reaction rate,
- Flow rate,
- Weight,
- Length,
- Temperature in Kelvin (0.0 Kelvin really does mean “no heat”),

When working with ratio variables, but not interval variables, the ratio of two measurements has a meaningful interpretation. For example, because weight is a ratio variable, a weight of 4 grams is twice as heavy as a weight of 2 grams. However, a temperature of 10 degrees C should not be considered twice as hot as 5 degrees C. If it were, a conflict would be created because 10 degrees C is 50 degrees F and 5 degrees C is 41 degrees F. Clearly, 50 degrees is not twice 41 degrees. Another example, a pH of 3 is not twice as acidic as a pH of 6, because pH is not a ratio variable.

Mean, Median and Mode are all appropriate measures of central tendency.

### When to identify in quantitative or qualitative data?

The Type of Statistical Analysis You can Use Depends on the Scale of Measurement