Q:

ANOVA: Confidence Interval interpretation

I'm reading through an example of 1-way ANOVA:

In an experiment to determine the effect of nutrition on the attention spans of ele- mentary school students, a group of 15 students were randomly assigned to each of three meal plans: no breakfast, light breakfast, and full breakfast. Their attention spans (in minutes) were recorded during a morning reading period and are shown in Table 11.1:
  None  |  Light  |  Full
---------------------------
    8   |   14    |  10
    7   |   16    |  12
    9   |   12    |  16
   13   |   17    |  15
   10   |   11    |  12
T1 = 47 | T2 = 70 | T3 = 65

The question is:

The researcher in Example 11.4 believes that students who have no breakfast will have significantly shorter attention spans but that there may be no difference between those who eat a light or a full breakfast. Find a 95% confidence interval for the average at- tention span for students who eat no breakfast, as well as a 95% confidence interval for the difference in the average attention spans for light versus full breakfast eaters.

And the given solution is:

I totally understand the solution, but I don't understand how they came up with this conclusion (emphasis mine):

You can see that the second confidence interval does not indicate a difference in the average attention spans for students who ate light versus full breakfasts, as the researcher suspected. If the researcher, because of prior beliefs, wishes to test the other two possible pairs of means—none versus light breakfast, and none versus full breakfast—the methods given in Section 11.6 should be used for testing all three pairs.

I may be completely missing something simple, but I just don't understand how they came about the conclusion in bold. What property of the 1 ± 3.36 result suggests there's no difference in the average attention spans?

A:

A rule of thumb is that if the Confidence Interval (CI) does not include a 0, the difference between the two groups is statistically significant. In your example, the CI range is (-2.36 and 4.36) which does include a 0, therefore the two groups are not significantly different from one another. Or in other words, a difference in the average attention span does not exist.

