# Working With Denominators: Getting mathematical, without getting too mathematical

*The following pertains to the use of proportions for e-mail marketing strategies. How does changing the denominator in calculations change the analysis?*

The following table shows product categories for a small website, and the total amount of purchases for ten states. What we are concerned about is choosing the best states to market posters to.

The table below (**table 1**) shows the proportions of purchases made over ALL states. That is, every percentage in this table is calculated by (# of purchases) / (Total # of ALL purchases). In other words, if we grabbed a random purchase out of ALL total purchases, then there is a 3.89% chance that the purchase grabbed was a CD bought by someone in New York. The sum of all values in this table equals 100%. Using this table, we can see that the top 2 states to market posters to are FL, and CO.

The next table (**table 2**) shows the proportions of purchases made within EACH state. That is, every percentage in this table is calculated by (# of purchases) / (Total # of purchases within each state). In other words, if we grabbed a random purchase made from the state GA, then there is a 49% chance that the purchase grabbed was for a TV. The sum of values in each column equals 100%. Using this table we can see that the top 2 states to market posters to are AL, and IL.

**What’s the difference?**

The difference between the two tables is that **table 1** takes large amounts of purchases into account, while **table 2** takes purchase choices into account. Both tables can yield beneficial results. By using only **table 1**, we would be including states with the largest amounts of poster purchases. By using only **table 2**, we would be including states which favor posters over other categories.

In this case, I would market posters to all four of the states. This way we have included our largest markets, and included states which favor posters more than any other sales category. The best markets will have high proportions in both tables. That is, they have large amounts of purchases and show significant leaning toward one sales category.

Knowing and utilizing the differences between the two tables can be very helpful in choosing top markets.

Andrew

## 1 comment + Add a comment

Greg SobiechJune 20, 2012 at 4:58 pm

Nice post Andrew! Keep it up!