Welch Two Sample t-test

data:  sample1 and sample2
t = 2.658, df = 95.421, p-value = 0.009217
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 0.01615943 0.11150922
sample estimates:
mean of x mean of y
0.5585566 0.4947222

I have this result for a T test using t.test() function in R - please correct me if I am wrong - I understand that the test shows significant difference in population for sample1 and sample2 at 95% confidence level. I also understand that the point estimate for the difference in the means of sample1 and sample2 is the t-value = 2.658

What I don't understand is the confidence interval:

Does it say that the difference in means of sample1 and sample2 at 95% confidence level should be between 0.016 and 0.111 if they come from the same population?

Or does it say that the range estimate can be 0.016 to 0.111 units more than the point estimate at 95% confidence level.

It doesn't make sense to me.

  • $\begingroup$ Perhaps this Q&A will help stats.stackexchange.com/questions/178166/… $\endgroup$ – mdewey Dec 27 '16 at 15:35
  • $\begingroup$ Mean difference and t-value are different things. The mean difference is not 2.658, but rather (.5585566 - .4847222). That 95%CI is then the CI for your mean difference. $\endgroup$ – Penguin_Knight Dec 27 '16 at 16:16
  • $\begingroup$ @Penguin_Knight, What is t-value telling me then? $\endgroup$ – Minu Dec 27 '16 at 16:21
  • $\begingroup$ That is a long story... Basically it is a probability distribution that consists of many sample mean differences based on your sample size. It is centered at 0. You can see this as an all-encompassing results if the null hypothesis (two means are equal) is true. Now if your sample t-value is far enough, we can have reasonable doubt that perhaps the means are indeed different. And that threshold is set at 2.5% at each end, corresponding to the p-value threshold (5% chance). It turned out, for most t-distributions, the threshold is about 2 and -2. $\endgroup$ – Penguin_Knight Dec 27 '16 at 16:26
  • $\begingroup$ @Penguin_Knight, Thanks. What is the point estimate of the difference in means of samples 1 and 2? How is t-value different from this estimate? Is t-value just the difference in means of the two samples in standard error units? $\endgroup$ – Minu Dec 27 '16 at 16:52

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