In an era of “reproducibility” and “theory” crises, measurement literacy helps to make scientific discourse meaningful. Measures and metrics provide the raw data; they also contextualize that data to give us insight into what we should change or do differently.
A measure is a countably additive set function on a measurable space with values in the non-negative reals and/or infinity. Positive measures and signed measures are generalizations of this concept.
Definition
In the context of business metrics, measures refer to individual numerical values that can be summed and averaged. These numbers can be anything from sales and leads to distances, temperatures and durations. They are the quantitative side of a measurement, in contrast to dimensions which are categorical buckets like regions and product types.
Euclid, in Book V of his Elements, gives 18 definitions of measure, which mainly relate to ratios. Modern axiomatic theories of measurement use ideas from this work, but do not depend on any specific physical object as a standard.
A measure is a countably additive set function on a space (or a symplectic manifold). It has the property that every negligible set is measurable and that its Lebesgue measure is finite. This property is called the s-finiteness of the measure. A generalization of s-finiteness is called semifiniteness and yields localizable measures, used in Hamiltonian and classical statistical mechanics. Another generalization is Gibbs measure, which is a natural volume form on a symplectic manifold.
Purpose
The primary purpose of a measure is to quantify a characteristic. This can be done either by direct observation or through indirect observations using a measurement instrument. The measurement results can then be compared to a standard, and the resulting information can be used to improve a process.
For example, a process measure might focus on the steps in a medical procedure. An outcome measure might evaluate how well a procedure performs, such as the likelihood that patients will receive the proper treatment. A balancing measure might identify the potential for systemic inequities and ensure that improvement efforts aim to close those gaps.
A mathematical concept, a measure is a countably additive set function with values in the (signed) real numbers or, more generally, the reals and infinity. Its properties are studied in the field of measure theory. In music, measures are a way to organize musical ideas and give songs clear structure. They are also the building blocks for reading and writing music in musical notation software.
Types
The different types of measures allow for differing levels of data analysis. Generally, they are categorized into four scales of measurement: nominal, ordinal, interval and ratio. Each one of these has properties that determine how a variable should be analysed. For example, nominal data has an identity property but can’t be ranked, contains intervals and cannot be divided or added together. Gender is a good example of nominal data.
Diagnostic measurement moves beyond descriptive and allows you to identify trends over time and attribute them to specific actions. It is useful for monitoring a system and identifying potential problems.
Unfortunately, many systems have trouble with diagnosing issues. For instance, prominent scientific metrics such as H-indices and journal impact factors collaberate important multifaceted features into simplistic ones that may not accurately reflect the underlying issues. This can lead to an over-reliance on a single metric for hiring, tenure and promotion which may also create incentives for cheating.
Examples
Using metrics to measure performance provides context and helps you see trends over time. It can also help you identify specific areas for improvement. However, there are some pitfalls to be aware of. Some common mistakes include confusing correlation with causation and misaligning metrics with goals.
A set of measures
A metric can be useful for monitoring and motivating participants, but it is important to make sure that the metrics are aligned with your business goals and that they are not being used to game the system or give false incentives. In many cases, this requires thoughtful design and planning. It may also be necessary to use qualitative feedback and supervision instead of relying on quantitative rewards. These systems may be more difficult to implement but are often more effective at eliminating perverse incentives.