Interpret your Compass chart, part 2: Correlation and cohorts

This article explains correlation and how it applies to your Compass chart, and how to create a cohort from its results. Refer to Interpret your Compass chart, part 1 for a breakdown of how to read and interpret a Compass chart.

Understanding correlation

Correlation measures how two statistical variables relate to each other. Possible values range from -1 to 1. A score of zero indicates no statistical relationship between the variables. A score of 1 indicates perfect positive correlation; a score of -1 indicates perfect negative correlation.

Amplitude categorizes correlation scores like this:

• Highly Predictive: |correlation| >= 0.4.
• Moderately Predictive: 0.3 <= |correlation| < 0.4.
• Slightly Predictive: 0.2 <= |correlation| < 0.3.
• Not Predictive: |correlation| < 0.2.

In a Compass chart, the two variables to correlate are:

• Whether the user triggered the event in question at least a certain number of times.
• Whether the user was retained in the target cohort.

You may have heard of different variations and definitions of correlation. Well-known examples include Matthews correlation, Pearson correlation, phi coefficient, and R-value. In this case, all these methods generate equivalent results, because Compass looks at pairs of binary random variables.

Correlation isn't causation, so test and verify any hypotheses you form from a Compass analysis.

Why correlation is a good metric to use here

When you're looking for the metric that captures your users' "a-ha" moment, you want one where most users above a certain threshold go on to be retained, and most users below the threshold aren't retained. Such a metric has a threshold with a good positive predictive value (PPV).

You also have to consider how easy it will be to move users across that threshold. If you find a threshold with a strong PPV and NPV but moving users across it proves difficult, that metric won't help much in growing your user base. A tell-tale sign is when few of your users have crossed the threshold or almost all of them have already crossed it. This isn't always the case, but in the absence of more specific information, it's generally a good assumption.

Compass uses correlation to locate these thresholds because correlation accounts for PPV, NPV, and the proportion above the threshold. If the PPV is higher, the NPV is higher, or the fraction of users above the threshold is closer to 50%, then the correlation is also higher. If the PPV is lower, the NPV is lower, or the fraction of users above the threshold is further from 50%, then the correlation is lower.

Create a cohort from your results

You can create a cohort from your results by clicking Create Cohort. Amplitude automatically compares the cohort's retention to new user retention.

This comparison is based on Any Active Event, not Any Event.

Clicking Show (next to Correlation Table) brings up a detailed contingency table that shows the count of users in your base cohort in each of four categories: true positives, false positives, false negatives, and true negatives.

You can also see detailed statistics on your cohort by clicking Show (next to Detailed Statistics).

Read more about these statistics in Find your company's inflection metrics with Compass.

Next, refer to the Help Center article on how to use Compass to identify the moments in the user journey that are critical to driving growth.