I am interested in learning whether the two groups below are statistically significant:
ex0112 = (
BP Diet
1 8 FishOil
2 13 FishOil
3 10 FishOil
4 14 FishOil
5 2 FishOil
6 1 FishOil
7 0 FishOil
8 -6 RegularOil
9 1 RegularOil
10 1 RegularOil
11 2 RegularOil
12 -3 RegularOil
13 -4 RegularOil
14 3 RegularOil
I run the following t-test:
t.test(BP ~ Diet, data = ex0112, conf.level = 0.99)
The results are:
Welch Two Sample t-test
data: BP by Diet
t = 3.0109, df = 9.7071, p-value = 0.01352
alternative hypothesis: true difference in means between group FishOil and group RegularOil is not equal to 0
99 percent confidence interval:
-0.4610773 15.8896488
sample estimates:
mean in group FishOil mean in group RegularOil
6.8571429 -0.8571429
As you can see, the p-value for this test is
p-value = 0.014
which is significant at .05, but the confidence interval is
99 percent confidence interval:
-0.4610773 15.8896488
which includes zero, and hence makes the difference between the groups insignificant. How can this be explained?
Best Answer
You're calculating a $99\,\%$-confidence interval. If you decided on a significance level of $0.01$, you would not reject the null hypothesis based on the $p$-value, because it's larger than $0.01$. If you want to use a significance level of $0.05$, corresponding to a $95\,\%$-confidence interval, specify
conf.level = 0.95
:The $95\,\%$-confidence interval $(1.98; 13.45)$ does not include $0$, as expected.