- A scale on which information is displayed in categories without any specific order.

Usage Notes:

- Typical scales include:
- Blue, Green, Yellow
- Fruits, Vegetables
- Cars, Trucks

Only the most simple operations, such as equivalence and set membership, are possible with nominal scale data.

]]>- Is an impact often expressed using an ordinal scale or nominal scale.

- A measurable value that an entity strives to achieve.

Usage Notes

- Targets are used to guide activity.
- A target is a single value.
- A range of acceptable values is expressed using a target and tolerance.

- The acceptable level of departure from a target.

Usage Notes

- Tolerance is usually expressed using the same unit of measure as the target– or some percentage of the target.
- As a range, tolerance will have one or both:
- Upper Limit specifies the top limit above the target.
- Lower Limit specifies the bottom limit below the target.
- Sometimes, there may only be a single limit. For example, and holding all other things equal, most organizations would not want to put an upper limit on revenue. Most people would not want to put an upper limit on health. And so on.

- A metric that can be used to judge underlying activity.

Usage Notes

- There are three types of indicators: leading indicator, lagging indicator and coincident indicator
- Indicators are metrics that can be used to judge the “goodness” or “badness” of underlying activity.
- Some examples:
- Performance Indicator provides information about whether or not performance targets have been/will be met.
- Risk Indicator provides information about whether or not risk appetite, risk tolerance or risk capacity have been/will be exceeded.
- Conformance Indicator provides information about whether or not conformance targets have been/will be met.
- Quality Indicator provides information about whether or not quality targets have been/will be met.

- A single value obtained by direct measurement, or calculated using several other constituent values.

Usage Notes

- “Total Sales” is a metric that directly measures the quantity of sales in a given period.
- “Sales per employee” is a calculated metric that divides “Total Sales” by “Total Number of Employees”.
- A metric that provides information about whether something is “good” or “bad” is called an indicator.

- An indicator that accurately represents current activity.

Usage Notes

- Coincident indicators are often called real-time indicators.

- An indicator that records past activity.

- An indicator that predicts future activity.

Usage Notes

- Leading indicators are difficult to design and, typically, require historical information to validate.

- To reduce the uncertainty of a value using a standardized unit of measure.

noun

- A value or a metric.

Usage Notes

- Measurement is not perfect. There will always be some sort of error in a measurement.
- Types of error include: Type A Error, Type B Error.
- Measurement and evaluation are related concepts. Measurement is, generally, free from judgement. Evaluation, on the other hand, uses one or more measures to judge the value of something against criteria.

Other Forms of the Word

- Measurement (noun). The reduction of uncertainty of a value.
- Measurably, Measurable (adj). Capable of measurement.

Usage Notes

- Quantitatively, velocity is expressed using a unit of time (days, hours, minutes, seconds or some sub-second measure).
- Qualitatively, velocity is expressed using an ordinal scale such as fast, medium, slow.

- The hypothetical probability that an event that has already occurred would yield a specific outcome.

Usage Notes

- Unlike probability, mathematical likelihood is used to evaluate past events.

Historical Notes

Formerly, likelihood was a synonym for probability, as it still is in everyday English. In his paper “On the Mathematical Foundations of Theoretical Statistics” (*Phil. Trans. Royal Soc.* Ser. A. **222**, (1922), p. 326). Fisher made clear for the first time the distinction between the mathematical properties of “likelihoods” and “probabilities”:

The solution of the problems of calculating from a sample the parameters of the hypothetical population, which we have put forward in the method of maximum likelihood, consists, then, simply of choosing such values of these parameters as have the maximum likelihood. Formally, therefore, it resembles the calculation of the mode of an inverse frequency distribution. This resemblance is quite superficial: if the scale of measurement of the hypothetical quantity be altered, the mode must change its position, and can be brought to have any value, by an appropriate change of scale; but the optimum, as the position of maximum likelihood may be called, is entirely unchanged by any such transformation. Likelihood also differs from probability in that it is not a differential element, and is incapable of being integrated: it is assigned to a particular point of the range of variation, not to a particular element of it.

Likelihood was first used in a Bayesian context by Harold Jeffreys in his “Probability and Scientific Method,” *Proceedings of the Royal Society* A, **146**, (1934) p. 10. Jeffreys wrote “the theorem of Inverse Probability” in the form

Posterior Probability Prior Probability × Likelihood

]]>- A measure of the chance that an event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty).

Usage Notes:

- Sometimes, probability is expressed as a percentage between 0 and 100%.
- Quantitatively, probability is typically expressed as:
- Mathematical Probability proportion of favourable outcomes to the total number of possibilities if these are indifferent
- Empirical Probability or the proportion observed in a sample
- Relative Frequency or the limit of this as the sample size tends to infinity
- Subjective Probability or by more subjective criteria

- A scale on which information is displayed in order of magnitude because there is no standard of measurement of differences.

Usage Notes:

- Typical scales include:
- High, Medium, Low
- Hot, Medium, Cold
- Tall, Medium, Short

Be careful using mathematical operations on ordinal scales since they only encode order. Formula such as “High x Low” does not necessarily produce any mathematically useful result.

When using an ordinal scale, the central tendency of a group of items can be described by using the group’s mode (or most common item) or its median (the middle-ranked item), but the mean (or average) cannot be defined.

- Something that an entity intends to attain or accomplish.

Usage Notes

- To be measurable, objectives must be mapped to indicators, targets and tolerances.

Synonyms

- Purpose
- Goal

- A measure of how an entity or its objectives are affected.

Usage Notes

- Quantitatively, impact is often expressed as:
- positive/negative affect on financial assets
- positive/negative affect on other tangible assets (facilities, equipment)
- positive/negative affect on other intangible assets (reputation, information, knowledge, skills)
- positive/negative affect on business continuity
- positive/negative affect on health & safety
- Qualitatively, impact is is often expressed using an ordinal scale.

Be careful when using ordinal scales to express impact. If you use an ordinal scale, math will be useless because “High x Low” does not yield a comparative result.

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