I'm trying to evaluate the impact of an intervention in the most statistically accurate way possible but I'm having a hard time figuring out a way measure incremental growth along with statistical validation (for e.g., MAPE for forecasting). The problem with this data is that there is no historical data to forecast or run a causalImpact on. This is because the product marketing intervention and product launch happens simultaneously, leaving no room for a non-intervention period.
Here is the sample data which contains daily time series sales of 4 Cars. One is a test car which has been exposed to a marketing intervention. The other 3 are control cars which are similar to the test in terms of the category of the product, price and launch season of product. The scale for these control cars will be different due to factors such as brand size. Additionally, among the 3 control cars, Control car #2 has its launch in the same quarter but different year(2016) when compared to the test product(2017).
To measure incremental growth, this is what I've done so far ( Tab 'Normalization and Scaling' of the data attached) :
- (Min-Max)Normalized all the control cars sales to a range 0 to 1.
- Take the average of the 3 normalized control cars
- Scale the averaged Normalizations to the ranges of the test group to seem like a similarly scaled baseline.
- The difference between the Test car and the scaled data points should give me the daily incremental.
However, the massive problem with this method is that there is no way to measure accuracy to this method. Clearly, this is a flawed method. Is there an alternative method? How do I make this more statistically sound and logical?