Statistical Business Analysis
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Case Against Indices:


Here is a typical table of shipment or volume results over 3 years that are typically analyzed to assess business performance. The Index Versus Year Ago (IYA) begins Jul 01 and is the result of dividing 3,693 of Jul-01 by 3,335 of Jul-00. The IYA becomes the basis of most analytical approaches, with arbitrary values, say less than .96 and larger than 1.04 triggering addition analysis, questions and problem solving. There is a better way!

The average IYA for the above data is 1.00, which would suggest that volume is “flat”. The highest index is a 1.25, with the lowest being 0.88. You can be sure that any monthly index higher or lower than our arbitrary 1.04 and 0.96, generated many inquiries and actions. Actually, 78% of the indices exceed these subjective values.

Using our objective analysis (Control Charts) on this very same volume data, you can see that all 36 months are within the control limits. There have NOT been any statistically relevant changes in performance over these 3 years. All the business actions taken during this time only SUSTAINED the results. Any organization that used indices to “analyze” these results would have celebrated the positive growth indices greater than 104 and problem solved the “downturns” of indices less than 96.

If the first and last data points were used to estimate the actual compound growth rate (taking the cube root of the overall index), you would find an erroneous Compound Annual Growth Rate (CAGR) of 9.5%! However, the statistically valid growth of only 0.3% is determined from the best fit compound growth line which properly accounts for the monthly variation.




PLAY THE INDEX GAME.
There are 4 preprogrammed Scenarios in the Index Game: Alternating higher, then lower years; Alternating lower, then higher years; 3 higher, then 3 lower years; 3 lower, then 3 higher years. Notice that the average index in each scenario initially is 1.00. However, the last result is always LOWER than the base. This is always true when averaging indices to 1.00. Play the game by changing the red Hi and Lo Index in the two boxes at the top of the table. The higher the spread of the Hi and Lo Index, the lower the final value will be. You may try to select 2 indices that make Year 6 equal to the base year of 267 which will make an average index greater than 1.00.

The Index Game
 

Hi Index

Lo Index

 

   
Base Year 1 Year 2 Year 3 Year 4 Year 5 Year 6
Scenario 1, Alt Hi/Lo 267
IYA  
Avg IYA            
Scenario 2, Alt Hi/Lo 267
IYA  
Avg IYA            
Scenario 3, Alt Hi/Lo 267
IYA  
Avg IYA            
Scenario 4, Alt Hi/Lo 267
IYA  
Avg IYA            
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