# User-Specific Activity Level Along Weeks

I am assigning Low | Medium | High activity levels to users once a week.

At the end of an entire period,a user has been assign n weekly activity levels among {Low, Medium, High}.

Let k be the total number of users, then the data table would look like this:

User   Week_1   Week_2   ...   Week_n
User_1 Low      Low      ...   High
User_2 Medium   Low      ...   Low
.      .        .        .     .
.      .        .        .     .
.      .        .        .     .
User_k High     Medium   ...   Medium


How would you formulate a metric within [0,1] that quantifies the "stickiness" of user, that is, the variability of it's activity label over the entire period.

With such a metric, a user which is assigned always the same activity level (let's say, n times "High"), would have a 100% metric.

• Does the order matter? That is, would a sequence of High-Low-High-Low be equal to 0.5? So the same as High-High-Low-Low? – user2974951 Feb 12 at 9:26
• In the second example there is only one transition to different level, whereas in the first one there are three transitions to different levels so I would expect the metric of the second one to be higher than the first one. – Ronicho Feb 12 at 15:36
• In that case you need a measure that takes into effect the sequence of events, variance will not do that. – user2974951 Feb 13 at 14:19