Basic stats question that's been bothering me. Let's say I've put out a survey question with two possible answers, and have gotten back responses that have overlapping confidence intervals (at 95%).
This means I can't yet say one answer is statistically more likely than the other.
But how do these results differ from something like this:
In this example, there's far less overlap between the two confidence intervals. Is there some mathematical way that represents a higher likelihood of a significant result, or is this wishful thinking?