# Statistically significant difference

I am reading a medical paper, where it says:

There was a statistically significant improvement in dyspnea in the IPC group at 6 months, with a mean difference in VAS score between the IPC group and the talc group of −14.0 mm (95% CI, −25.2 to −2.8 mm; P = .01)

However, I thought that since -14 lies within the CI of -25.2 to -2.8 that this is NOT statistically significant.

Am I wrong?

• They are saying $0$ is not in the $[-25.2,-2.8]$ confidence interval. Commented Feb 17 at 12:06

The authors are telling you that the VAS score for IPC group is "significantly different" from the VAS score from the talc group. In other words, they are saying that the SIZE of the difference between these two scores is significantly greater than zero. Then they go further and estimate the actual size of that difference: -14. The also give you a 95% confidence interval around that difference: with "95% confidence" the difference could be as small as -2 or as large as -25 (thinking in absolute values here). But note that the confidence interval does not include 0 (which would mean no difference in scores between the two groups), which is just another way of showing that the difference between the scores is significantly different from zero, which is what the term "statistically significant" really means: it's a claim about the likelihood that a particular difference is different from zero.

Implicit in the comment is that the test is of a null hypothesis that the value is zero. It is possible to test other null hypotheses, but “is it zero or not” is a common question to have and common to test.

The point estimate (the $$-14$$) will almost always be within the confidence interval (I suppose a bootstrap confidence interval has some chance of excluding the point estimate, even if that chance is outrageously small), so that is a poor criterion of statistical significance.

You got that wrong, -14 is the "middle" (not necessarily) of the CI, the result would be suspect if the CI contained 0 in it, so for ex. a CI from -25 to +2.

User2974951's is correct and to the point.

For further readers that are still wondering where that 0 comes from and why it doesn't make sense to look at the '-14', which is a common mistake for novices, here is why:

• First of all, remember what is initially the goal and what is going on. In this example, they want to test if a certain difference (let's call it $$\Delta$$) is significantly different from 0 or not. (i.e.: $$H_0: \Delta = 0$$ & $$H_a: \Delta \neq 0$$).

• Next, remember how a confidence interval is constructed, i.e.: point estimate $$\pm$$ error margin, or in this case in terms of formula, one often uses: $$\Delta \pm CritVal \times se(\Delta)$$, where the critical value is for example 1.96 in the case of a normal approximation.

Now in this example: $$\Delta$$ = -14, meaning that to construct the confidence interval, you would substract some error margin/uncertainty from this -14 and add some. This will of course create an interval that includes -14 already since you added and substracted from -14 to make the interval in the first place! Therefore it does not make sense to check if -14 is in there to prove significance, since it will by construction of the interval automatically be in there. However, since you want to test if the difference $$\Delta$$ is different from 0, you rather check that 0 is in the interval or not. Similarly, if you want to check, if it is also significantly different from 10, you can set up an analogue hypothesis and check if 10 is in the interval or not.

• There's only one s in "subtracted". Commented Feb 17 at 0:48