Nonadditive Facts in Software

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Nonadditive Facts
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Although a fact table stores facts at a specific level of detail, the facts themselves can be expressed at various levels of summarization. This principle enables facts to be combined with various dimensions to answer an array of business questions. The sample query shown in Figure 1-6, for example, took order_dollars, which was stored by day, product, customer, and salesperson, and aggregated it to the product level. The ability to summarize individual facts by adding them together is referred to as additivity. Figure 3-3 depicts four facts: quantity_ordered, order_dollars, cost_dollars, and margin_dollars. Each of these facts is fully additive; they may be summed up across any and all of the dimensions in the schema, producing a meaningful result. Unfortunately, not every measurement exhibits additivity. Many key business metrics are expressed as rates or percentages. This type of measurement is never additive. For example, Table 3-2 shows the margin rate on each of the orders for Gel Pen Red on January 1.
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Day 1/1/2009 1/1/2009 1/1/2009 1/1/2009 1/1/2009 1/1/2009 1/1/2009 1/1/2009 1/1/2009
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Table 3-2
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Salesperson Jones Jones Baldwin Baldwin Baldwin Sebenik Sebenik Sebenik Sgamma
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Product Gel Pen Red Gel Pen Red Gel Pen Red Gel Pen Red Gel Pen Red Gel Pen Red Gel Pen Red Gel Pen Red Gel Pen Red
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Customer Balter Inc. Raytech Venerable Holdings eMart LLC Shatter & Lose Comstock Realty RizSpace StarComp Implosion Town Sum:
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Margin Rate 3.02% 3.02% 3.02% 3.02% 3.02% 3.02% 3.02% 3.02% 3.02% 27.18%
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Margin Rates Cannot Be Added Together
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The margin rate is the percentage of the sale that represents profit, and it is closely monitored by management. In this table, each individual transaction has a margin rate of 3.02 percent. It is not possible to summarize the margin rate for these transactions by adding them together. This would produce a margin rate of over 27 percent, which is clearly incorrect. Luckily, there is a solution. Ratios can be broken down into underlying components that are additive. In this case, the margin rate is the ratio of the margin dollars to order dollars. These components are fully additive. They can be stored in a fact table and safely aggregated to any level of detail within a query or report. An example report is shown in Figure 3-4. The nonadditive fact margin_rate is not stored in the fact table; it is computed as the ratio of the sums of margin dollars and order dollars. This computation may be done in a query or by additional processing logic in the reporting tool. Care must be taken with subtotals and grand totals in the report; the margin rate in these rows must be computed as the ratio of the subtotals for margin dollars and order dollars. While nonadditive facts are not stored in fact tables, it is important not to lose track of them. For many processes, ratios are critical measurements without which a solution would leave much to be desired. Nonadditive facts should be documented as part of the schema design, as described in 18, How to Design and Document a Dimensional Model.
Margin Report Date: January 1, 2009 Product: Gel Pen Red Salesperson Jones Customer Balter Inc. Raytech Subtotal : Baldwin Venerable Holdings eMart LLC Shatter & Lose Subtotal : Sebenik Comstock Realty RizSpace Starcomp Subtotal : Sgamma Implosion Town DemiSpace Subtotal : Grand Total: Margin Dollars 192.74 39.05 231.79 121.50 253.44 8.74 383.68 12.06 58.10 90.36 160.52 213.88 113.92 327.80 1,103.80 Order Dollars 6,382.21 1,293.11 7,675.32 4,023.22 8,392.00 289.54 12,704.76 399.29 1,923.93 2,992.11 5,315,33 7,082.22 3,772.11 10,854.33 36,549.74 Margin Rate 3.02% 3.02% 3.02% 3.02% 3.02% 3.02% 3.02% 3.02% 3.02% 3.02% 3.02% 3.02% 3.02% 3.02% 3.02%
Margin Rate is a nonadditive fact.
Summary row is computed as a ratio of the subtotals, not by summing margin rates for the salesperson.
Figure 3-4
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