Please demonstrate, rather than claiming, that they did this.

Here is their criteria: motherjones.com

They specify lone shooter, then make exceptions for Columbine and Westside. They specify public shootings, but make exceptions for Crandon and Seattle. They then threw in a handful of spree killings. These are not consistent criteria. And again, the sample is drawn from news reports going back to the pre-internet era. Note when the intervals and variance are smallest — when Mother Jones started actively tracking these events rather than relying on archived media reports.

The ANOVA test does not address the big problem which is an incomplete and sparse sample, especially from the pre-internet years. And the ANOVA test is not appropriate for a sample that is not normally distributed, as this is not. It is highly skewed sample. In the time interval analysis, the average is 172 days. But the sample is heavily skewed by huge intervals in the 1980’s. The median of the data is 94. If you use the median as your guideline, their trend of 14 below average intervals becomes 11. If you restrict it to post-1999 data, when reporting criteria are more uniform (and they overlap the FBI active shooter data) the median becomes 62 and the supposed trend is very week. Furthermore, the time intervals suddenly changes if, say, they changes their criteria to requires 5 dead or 3 dead. Or if they missed a mass shooting from the 1980’s.