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Suppose you publish a campaign with 50% of your users in the Test campaign group (those who will see the Evergage message(s) and the other 50% as the Control (who will not see anything). After two weeks of running it, let's say you get the following conversion rates per day:
As you can see, the conversion rates vary by day; this happens with real data since the conversion rate isn't going to be constant for every day. Some days it will be higher, and other days it will be lower, as seen in the above example.
The Test group (the group that saw the message) clearly has a higher conversion rate than the control group; the average for test is much higher than the average for the control. But also notice this: the control group oscillates between a minimum of 0 and a maximum of 0.5. In contrast, the test group has a minimum of 0.6 - it never falls into the control group's range. Because of this we are extremely confident that the test group had a higher conversion rate than the control group.
Now suppose you run a completely different campaign and get the following results:
Here the Test group still has a higher average than the control, so we would still think the test group has a higher conversion rate than the control. However notice two things as compared to the last graph.
1. The distances between the averages are is much less. The two averages are closer together.
2. This time, the test group does fall within the range of the control group. On even days, the control group actually does better than the test group.
These two points don't change the fact that the test group has a higher average than the control group. However, these should make us less confident in our result. In this second scenario, we are less sure that the test group really was better than the control.
This is the intuition the confidence is trying to capture. However, the confidence which is reported is not based on guess work or our arbitrary judgements; they are based on your data and sound math and statistics.
Even though this example illustrated a case where the test was better than control, you can still measure confidence for the opposite result. For example, in a campaign where control has a negative impact on conversion rate, we can be more or less confident depending on the underlying data.