Thursday, September 30, 2010

Alternative ways of using index calculations

After years of using indices to identify differences in comparable variables it occurred to me that not all indices are created equal. I’m going to use a generic example of hypothetical grocery stores and market (Capital City DMA) to demonstrate some of these different methods.

Here is a basic report you may be able to retrieve from any given research resource (Exhibit A):





For novices or those unfamiliar with reports like this, here is how the percentages read in Exhibit A:

Note: Proj (or projections) equal the number of households that fit that given criteria


80% of Capital City households have an income less than $99,999
20% of Capital City households have an income more than $100,000

50% of Capital City households shopped ABC in the past 7 days
50% of Capital City households shopped XYZ in the past 7 days

75% of ABC shoppers have an income less than $99,999
25% of ABC shoppers have an income more than $100,000
85% of XYZ shoppers have an income less than $99,999
15% of XYZ shoppers have an income more than $100,000

46.88% of Capital City households with an income less than $99,999 shopped ABC in the past 7 days
53.13% of Capital City households with an income less than $99,999 shopped XYZ in the past 7 days
62.50% of Capital City households with an income more than $100,000 shopped ABC in the past 7 days
37.50% of Capital City households with an income less than $100,000 shopped ABC in the past 7 days


What is an index?
According to Merriam-Webster’s dictionary,

Index: a number (as a ratio) derived from a series of observations and used as an indicator or measure; specifically: index number
Index number: a number used to indicate change in magnitude (as of cost or price) as compared with the magnitude at some specified time usually taken as 100

The “traditional” calculation of an index
A) Using Vertical Percentages: [(% of Target A) / (% of Base)] x 100
Example: [(75%) / (80%)] x 100 = 94
How to read: Compared to the average Capital City household, ABC shoppers are 6% less likely to have an income of $99,999 or less.

B) Using Horizontal Percentages: [(% of Demo A) / (Market %)] x 100
Example: [(46.88%) / (50.00%)] x 100 = 94
How to read: Compared to the average Capital City household, those with an income less than $99,999 are 6% less likely to shop ABC.

Reading Indices Summary
An index of 100 means the target looks like the comparison variable.
An index less than 100 means the target is X% less likely to look like the comparison variable.
An index more than 100 means the target is X% more likely to look like the comparison variable. Translation, 100 minus the index number = % more or less likely.

Not a lot of people know there is actually two different ways to calculate a traditional index. Most people gravitate toward using the vertical calculation as seen in “traditional” calculation A.

True comparisons and alternative methods

I wanted to demonstrate a better alternative in calculating indices. In some instances, the traditional calculation may be the best option, but if indices are for comparative use, why are we comparing one set to another that includes the original set (see Exhibit B for visual example)?



As the original variable (A) gets larger the more like the comparative set (B) its starts to look which pushes indices closer to 100.

I’ve started gravitating toward an index I’m calling a True Comparison Index. See Exhibit C for visual difference to Exhibit B.



Some may have already figured this, but let’s see what happens when we compare our set to the remaining set (excluding the original set) using a True Comparative Index. See Exhibit D for new calculations that compare store to store and income level to income level instead of to the market as a whole.



Notice how the indices have greater variance than the ones calculated in Exhibit A. This has greater relevance as far as I’m concerned. Now the original variable set has no weight on the comparative set. When we use this method the two different ways to calculate the same index no longer applies. Notice that there are now multiple ways to communicate an index (Vertical and Horizontal or by store and by demography in this example).

I've found this method of calculating indices to be extremely valuable in finding differences and making comparisons. Again, feel free to use or dismiss this method at your own discretion.

The next post should include some of my latest book reviews.