In a mobile app that I am creating the user can tap and view content in detail by tapping on headlines. I want to keep track of how "important" the user considers the content detail to be by monitoring the time they spend on it. To that end I do the following
- Keep track of the number of views in different content categories (N)
- Keep track of the mean viewing time in each category (MUn)
- Keep track of the current standard deviation (SIGn)
I then use these quantitites internally to report back a measure of "view importance". The standard deviation is used to filter out outliers - the user accidentally viewing content and quickly dismissing it or the viewer called away whilst viewing content and then appearing to be excessively interested in it.
The number of views in each category may grow quite rapidly so I do not have the luxury of keeping track of the view time popluation itself.
When a new view occurs in a given category I update N and MuN - easy. I also update SIGn for which I follow the method described in this thread. That thread uses the sample standard deviation. I am using the population standard deviation.
As the number of views in a category grows I doubt that the choice of standard deviation (sample vs popluation) will make much of a difference.
However, each category will start off with 0 views and grow from there. Am I introducing a systematic bias of some description in the "view importance" estimates I am making? Should I, for instance, switch the SD I am updating at some point once a pre-defined population size threshold is crossed.
