Measures are the observations collected by researchers and processed into the numbers that enable testing of pre-conceived hypotheses or derive new ones from exploratory analyses. This process may involve either designing a new measurement protocol or connecting existing validated scales to data.

In mathematics, a measure on a set has the properties of countable additivity and complete translation invariance. The Lebesgue measure is a special case of such a measure.

## Scales of Measurement

The level of measurement or scale of a variable is one of the most important aspects to consider when performing statistical analysis. It determines the appropriate statistical techniques to use for the analysis of the data.

Scales of measurement vary in complexity and characteristics, ranging from simple and categorical (nominal) to more complex and quantitative (ratio). Understanding the different levels of measurement and their properties helps researchers properly analyze the data they collect.

Nominal scales are the crudest level of measurement and involve using numbers to label or categorize observations. They lack magnitude and have no true zero point. For example, when a researcher asks respondents to rate their favorite music styles, the ratings may be recorded on a nominal scale with names such as pop, rock, hip-hop, etc. Each of these categories represents a unique class or category of music but does not indicate any difference in type or quality. The interval scale combines the properties of the nominal and ordinal scales by having both identity and order and also by providing interval values with a meaningful relationship between them. The Fahrenheit and Celsius temperature scales are examples of an interval scale.

## Ratio Scales

A ratio scale possesses all the characteristics of an interval scale, but also includes a true zero point. This makes it possible for data scientists to use a range of statistical techniques that cannot be applied to nominal, ordinal, or interval data. This includes descriptive and inferential statistics.

Ratio scales allow for a meaningful comparison between variables. This is because they have equal intervals and a real zero value. As such, they can be used to calculate meaningful multiplication and division. This is a crucial feature, which can be used in a number of ways, from calculating IQ scores to determining how much time a respondent spends playing video games. Moreover, they can be used to generate actionable feedback and conduct research. For example, respondents can be asked to rate their level of military experience on a ratio scale. They can then compare their results with other data points from the same survey. This will help to identify patterns and trends.

## Quantitative Scales

Whether your data comes from a scientific experiment, or from your daily experiences, there are four primary levels of measurement scale type: nominal, ordinal, interval and ratio. Each has specific characteristics that define the type of data you collect.

Nominal (also known as categorical) scales assign numbers to observations that act as labels. They have no underlying relationship and don’t allow for any form of arithmetic computation (+, -, x, etc.).

The ordinal scale indicates order and rank, such as gender or ethnicity. Interval scales have all of the properties of an ordinal scale but allow for the calculation of differences between values using a true zero point. For example, the Celsius and Fahrenheit temperature scales use an interval scale. Lastly, the ratio scale has properties of both interval and ordinal, as well as allowing for calculation of mean, median and mode. It’s a great choice for data that requires an exact measure. Data from a student’s GPA would fit this category.

## Qualitative Scales

Knowing the different types of data and scales of measurement can help you choose the right statistical tool for your survey. Nominal scales allow you to label observations as categories; ordinal scales define a sequence; interval scales measure the order of values and have a true zero point; and ratio scales combine characteristics of the previous two scales.

Nominal scales categorize observations into unique categories like male vs. female or a product’s features. This allows respondents to identify and evaluate the data.

Ordinal scales are similar to nominal in that they classify the data but also denote an order, for example male vs. female or educated vs. un-educated. Interval scales have properties of both the above, but they can also be used to rank data e.g. heaviest to lightest or ranks of players or students. The ratio scale combines the qualities of all these scales, except that it can be used to calculate central tendencies such as mean, median and mode.