# 95% confidence intervals and the null hypothesis

I have performed an unpaired t-test comparing the means of two groups. My hypothesis was that the stroke group mean would be significantly higher than the control group mean. However, the t-test revealed no significant difference. Here are the results:

control mean   stroke mean   p value    95% confidence interval
0.0864        0.0927       0.76         -0.0388 to 0.0263


I understand that the range of the CI is high, suggesting that the study was underpowered. However, do the CI infer anything else about the possible true effect? So, the CI is located more within the negative zone than the positive zone. Does this mean that it is more likely that the control mean could be higher than the stroke mean?

• Maybe I am misunderstanding something, but is not the stroke mean 0.0063 higher (0.0927 - 0.0864)? – Mankka Apr 22 '15 at 22:13

• @svannoy The test statistic for a two-sample t-test is simply $\bar{x}_1 - \bar{x}_2$. (The different varieties of the test are to do with how to calculate the std error.) So the confidence interval will usually be offset from 0. – Hong Ooi Apr 22 '15 at 18:37