Measures are quantitative quantities that can be subjected to mathematical operations like summing, averaging and counting. They are a key input to calculations and can provide insights into relationships, efficiencies and performance.
They are also essential in establishing benchmarks and measuring progress against a target. Typically, measures are dependent on dimensions to add context and meaning to the data.
Definition
Measures are symbols that are used to classify observations. They have the basic property of being mutually exclusive and exhaustive; they must include all the possible observations, and no observation can belong to more than one category. Measures must also have rules for assigning labels to properties of variables, and they must be based on a consistent system of comparison frameworks.
The concept of measure is central to the fields of geometry, analysis and probability. It is also fundamental to the theory of the symplectic manifold and the field of quantum mechanics, where it is often referred to as the Liouville or Gibbs measure. The mathematical foundations of measure theory were laid by Emile Borel, Henri Lebesgue and others.
The most common measure is the number, a value that can be assigned to a variable in a set. Examples of measures are price and revenue, although some have no numerical value, such as date or time.
Purpose
Measures are used to perform calculations and conduct data analysis. They are calculated values that can be subjected to aggregations like sum, average and minimum, maximum or count and may be derived from a data field or from a more advanced calculation using Data Analysis Expressions (DAX).
As an important distinction from dimensions, the value of a measure always changes in response to your selections on rows, columns and filters, enabling dynamic ad hoc data exploration. In addition, measures display a different icon in the fields pane to help you identify them from other data.
While both dimensions and measures are valuable for gaining insights into your data, it is important to consider the specific goal of a project when choosing the type of measurement you will use. This will ensure that you are capturing all relevant data to deliver a successful result. You may also want to consider balancing measures, as they can be an important counterbalance to process-based metrics.
Techniques
When it comes to measurement, there are different tools for measuring different things. For instance, a simple ruler might not be enough to accurately measure the aerodynamics of a high-speed train. Instead, advanced measurement techniques like 3D scanning are required.
The simplest technique involves direct measurement of the property, for example, by comparing it with an exact quantity of the same type (eg weight on scales, length on a tape measure). This produces quantitative data that can be compared, analysed and reported.
Other methods include part-to-whole comparisons (eg ratio variables), frequency distributions and correlations. The information provided by these can help to identify trends and patterns. Usually, measures are plotted alongside dimensions to add context and enable deeper analysis. For example, sales data might be grouped by product and location to reveal insights such as best-selling locations and average daily sale for each product. This is known as ordinal measurement. It results in a ranking of values and is not always proportional.
Limitations
When taking measurements, there are always limitations that can lead to differences between the measured values and the real ones. These differences are called ‘errors’. Errors can be either systematic or random. Systematic errors have their origin in the instruments used, while random errors are the result of pure chance.
There are different kinds of measurement accuracy: absolute, relative and statistical. When describing the accuracy of a measure, it is important to distinguish these three types.
An absolute error limit indicates the maximum permissible deviation from the real value of the measured value, and is often indicated by a decimal point or a percent. A relative error limit is more useful because it varies according to the magnitude of the measured value. This is especially important when evaluating chemical analyses or electrical measuring devices. It is also helpful when comparing results from studies that use different methods.