# Determine statistically whether new product cannibalise old product by using data

Assume that $$A$$ is a cab company which offers online cab booking through their standard account.

Recently, the company launched a pre-paid premium account with features such as discounted rides,special offers, guaranteed pick up and low waiting time.

A survey is conducted to public and it shows that the response to the new premium account is encouraging.

Question: Does the encouraging response stem from new customers or existing customers?

We are given a data consisting of time (booking is placed), pick-up and drop-off location, journey fees, ride type (premium or standard), customer demographic and pricing information.

I am totally lost here. What can we do to answer the question above? Any hint is appreciated.

If I were asked to determine whether customers have any fixed budget to transport, how can I solve it using data above?

My plan is to split the spending into monthly sales, then calculate their means. Let's say we have $$12$$ sample means and sample variances. Since the sample variances might not be equal, I employ Welch ANOVA test. Is this sufficient?

You do not have the data to directly answer the question if a ride for a given service is new customer or old customer. You need to have a customer id to properly attribute if there is new growth or just service switching.

Any statistics you run will, at best, show a correlation between new service and increased revenue. There can be no causation attributed. For example, the changes could be due to seasonal differences or other factors unrelated to the new service.

• I see. If customer's IDs are given in customer demographic, would this help in answering the questions? Mar 17, 2020 at 13:02
• And you have all transaction records for every customer. Mar 17, 2020 at 13:12
• Suppose that we have customer's ID and all transaction records, what statistical tests should we use to answer the questions? Or the questions can be answered using other tools? Mar 17, 2020 at 13:13

You could try carrying out some form of hypothesis testing.

• Null Hypothesis: Mean sales of the standard product in a day $$= \mu$$.
• Alternate Hypothesis: Mean sales of the standard product in a day $$\neq \mu$$

You could then extract the rows where ride type is standard and split it into 2 time periods - before and after the premium services were introduced. You could then aggregate your sales by days or weeks (your choice on the time frame) and then carry out a Z/T-test using the above hypothesis with a chosen significance level.

• I also thought of using hypothesis testing but do no know what test statistic to calculate. In this case, what metrics should we used? Mar 14, 2020 at 14:23
• That depends on the data that you have. If you are certain that the data before premium services were introduced is representative of ALL rides before premium services, you could use the Z-test which assumes that you know the population parameters such as the population standard deviation. Otherwise, you could use T-test which assumes that you are unsure of the population parameters and allows you to use the sample (data collected) parameters. More info can be found here: towardsdatascience.com/… Mar 14, 2020 at 14:33
• When carrying out the test, I think we need some assumptions such as rides follow a uniform distribution in a day? Because weekdays might have more rides than weekends. Mar 14, 2020 at 14:38
• Yes you are right. You could also sum the sales over a time frame of one week to cancel out that effect. However, there are also other factors that you have to consider. For example, there might be a change in your company's pricing strategies over time and you might also have to take into account the inflation rate. Mar 14, 2020 at 15:16
• I see. By the way, do we need to assume anything on the data? Mar 14, 2020 at 15:32