Karl L. Wuensch wrote:
Yes, Paul, fair reading -- of course, in general, one should not ignore the lower end of the CI, but in this case, they don't much differ between examples.
Yes, as I assume was part of your intention in picking those particular examples.
In case A the CI suggests that we might have a large effect, but there is a hulluva-lotta error in the estimate (very wide CI). In case B the CI suggests that we can have great confidence in asserting that the effect is very small, in one direction or the other. This, of course, can be a very important conclusion, for example, for establishing the equivalence of two treatments. I we altered the p in case B to .049, the difference would be "significant" but, IMHO, we could still use the barely altered CI to assert equivalence.
So you might have for the sake of further comparison added another example in which there was a narrow confidence interval, but around a much larger difference (and of course there would be a much smaller p-value to go with it).
I see your point (I think). I'm getting pretty close to convinced enough to change how I teach this.
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