How do I calculate uplift in a marketing campaign?

Question

I have a campaign that had two interventions A and B that were run in 3 markets each. I, also, had a control in 15 markets where no interventions were run.

For the markets where intervention A was run we had 5 units sold in the time period before intervention and 5 units during intervention.

For the markets where intervention B was run we had 10 units sold in the time period before intervention and 15 units during intervention.

Now, the control markets had 100 units prior to intervention and 200 during.

So...

            Prior         During
Control      100            200
Group A        5              5
Group B       10             15

The marked increase in the Control was due to seasonality.

Now, I want to calculate uplift (or downlift with this example data) by saying Group A should have expected to have 10 unit sales during intervention thus

 (5-10)/5  = -1

While Group B has an uplift of

(15-20)/10 = -0.5 

One of my colleagues wants to divide by the control values to account for the seasonality while I think we should subtract by the expected unit sales to account for the seasonality.

Sorry, I cannot give more details.

Answer 1

Usually uplift is a dimensionless entity (expressed in percentages) which implies a percentage observed change in reaction after an application of a treatment, adjusted to external factors (seasonality, etc)

In this case, the impact of factors external to the intervention is a 2x increase in sales.

Hence the uplift of group A = Observed change - change due to external factors uplift (A) = 5/5 - 200/100 = 100% - 200% = -100%, which could mean either of a) The impact of the treatment is negative b) The Control selection is not representative as some of the factors (such as critical mass of your product sales) are not applicably similar to the test

Answer 2

Depends on your definition of uplift, I guess. In my book, uplift would be the difference between the actual and the anticipated, related to the anticipated. Assuming seasonality equally effects all markets (by multiplying by 2), the anticipated value of group A is 10, so lift is (5-10)/10=-0.5 (or -50%). For group B, (15-20)/20=-0.25 (or -25%). Again, be sure to know your definitions (I find that they differ widely among companies even in the same sector). Also, I used a simplified seasonality "model" - if you have more data points, you may come up with something better than just "multiply by 2".