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Non-Additivity is that, when you cannot use a sum operator to generate the needed aggregation. Here are non-additive measures:
Ratios and Percentages:
Some examples of the ratios and %ages is the Profit-margin, revenue to asset ratio, default rate etc. If you add the profit-margin % of all the products for a retail company, you may get a figure of much more than 100%. Therefore you need to first take the sum of the numerator (profits) and denominator (revenue) for all the products and then calculate the ratio. When you are applying aggregation on a ratio, one need to take the 'ratio of the sums', instead of 'sum of the ratios'. Similarly for %ages, the same rule will apply.
The same constraint will also apply on averaging. Just like sum, even the average operator will fail here.
Solution: Store the numerator and denominator in separate fields and the ratio OR % age in a separate field as derived measure-Fact.
Measures of Intensity
These are more of clinical and scientific measurements. For example, blood pressure, temperature, gauge pressure, wind speed etc. The handling of these kind measures can be simple average (like average blood pressure of the sample of patients with same medical history and between ages of 40 and 50 comes out to 140/110..). However, the designers could apply very specific rules to calculate the summations (like placing weights to different instances). This is primarily due to the scientific nature.
Solution: Use alternate aggregation functions like averages, minimum and maximum. Track the constraints in the meta-data.
Grades and scales
This is same as measures of intensity, but more of business domain. Some examples are risk grade of customer, level of risk scale associated with a loan.
Solution: Use alternate aggregation functions like averages, minimum and maximum. Track the constraints in the meta-data.
Averages/Maximum/Minimum and similar measures
You may have derived measures in current data OR historical snap-shots. If you have averages OR max-min figures, these will not be additive. In other words, the attributes which do not contain the 'activity', but the 'characterization' measure, do not follow the additive path. 'Characterization' measure is a kind of measure, which characterizes the activity. For example, while the 'turn-around time' is an activity measure, but average TAT, maximum TAT, minimum TAT for a period (say), characterize the TAT activity.
Solution: Use alternate aggregation functions like minimum (minimum of minimums) and maximum (maximum of maximums). Track the constraints in the meta-data. However, the solution does not apply on averages.
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