The talk represents part of the material from the speaker's joint work with Sara Algeri (U.Minnesota). The talk could have been called ``Statistical analysis of large number of infrequent events", or ``On theory of Poisson regression", or ``When Pearson's chi^2 is not a goodness of fit test". Whatever it is called, it is clear we will start with well trodden topic of statistics - and if we think, as the speaker did, that we have enough knowledge about the phenomena there, or enough intuition about the subject, we may be not entirely correct.

The talk is our attempt to say something useful for everyday statistical work. The key words are:

divisible statistics, fine partitioning, large number of groups (or urns, boxes, pixels, etc.), contiguous alternatives, useless parts of useful tests, real astronomical data, testing uniformity, spectral statistics, statistics of empty boxes.

Sara Algeri, Estate V. Khmaladze (2026), On the statistical analysis of grouped data: when Pearson chi^2 and other divisible statistics are not goodness-of-fit, JRSS B, September 26, online - 23 June 2026.