Interpreting the confidence interval from CausalImpact
I am not sure how to interpret the confidence interval obtained when using the CausalImpact function in the CausalImpact R package.
I am confused because I think there is a contradiction - the model is returning a very low p-value (0.009) which indicates that there is a casual effect, and yet the "actual" line (the solid line) appears to be well within the 95% confidence band of the counterfactual. If there was a causal impact, wouldn't you expect the line to be outside the blue band?
These are my results:
and here are the model summary results (my apologies for the large text)
What's happening here?
The two results answer different questions.
The plot shows daily effects. The fact that the CIs contain zero means that the effect wasn't significant on any day by itself.
The table shows overall effects. Unlike the plot, the table pools information over time, which increases statistical power. The fact that effects were consistently negative throughout the post-period provides evidence that, overall, there probably was a negative effect. It's just too subtle to show up on any day by itself.
A side note: There seems to be a strong dip in the gap between pre- and post-period. You may want to be extra careful here and think about whether the effect in the post-period could have been caused by whatever happened in the gap rather than by the treatment.
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