Hi — interesting topic! I dont understand how you have reached the conclusion that there is no relationship!? The relationship may just not be obvious by eye. You have simply proven that your assumption that you will have a nice neat graph with a bump at “X o’clock” is wrong. There could still be strong engagement time patterns hidden in this very complex data. NYT have a very good post on modelling the effect of publishing on Twitter and its effect using stat models. This would be a good starting point for methodology.