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intervention effect clearly varies according to the number of products' is appealing... However, since the estimated effects are statistically insignificant can/ should one interpret these '0's?
I would completely ignore statistical significance here. By the way, see https://www.nature.com/articles/d41586-019-00857-9 for a more general commentary about statistical significance (this is just out today!) The confidence intervals, particularly in the post = 1 condition are wide. This suggests that the data are some combination of noisy and scanty there. But some of the estimated effects are quite large and I think would be considered important. So the fact that they are not statistically significant is, I think, of no importance here. Also, in the post = 1 group, the predicted rate is 3 times as high at products = 10 as it as when products = 0. Moreover, if you really insist on taking statistical significance seriously, don't forget that the interaction term in the regression output was highly statistically significant--so the difference between the patterns seen in post = 1 and post = 0 conditions is not something you would choose to ignore.
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