RE #1, that statement is correct but the corresponding picture implies assessing significance via overlap of the separate confidence intervals. However, separate 95% CIs may overlap and the test for the mean difference may be significant at alpha = .05. (See Cuming, "Inference by Eye: reading the overlap of independent confidence intervals," Statistics in Medicine, 2009, 28:205-220).
On Jan 14 the Suffolk University published a poll putting Brown ahead of Coakley by 4.4 points in the Mass Special Senate election. Quoting a margin of error = 4.38% (n=500); the press kept saying "too close to call." But a simple calculation shows that Brown had a 82% of winning assuming the poll is accurate apart from sampling error. How is that "too close to call." I guess they think when the MOE and the difference are about the same, the poll gives little information on who will win.
RE #1, that statement is correct but the corresponding picture implies assessing significance via overlap of the separate confidence intervals. However, separate 95% CIs may overlap and the test for the mean difference may be significant at alpha = .05. (See Cuming, "Inference by Eye: reading the overlap of independent confidence intervals," Statistics in Medicine, 2009, 28:205-220).
On Jan 14 the Suffolk University published a poll putting Brown ahead of Coakley by 4.4 points in the Mass Special Senate election. Quoting a margin of error = 4.38% (n=500); the press kept saying "too close to call." But a simple calculation shows that Brown had a 82% of winning assuming the poll is accurate apart from sampling error. How is that "too close to call." I guess they think when the MOE and the difference are about the same, the poll gives little information on who will win.