# t-test CI

## T-test and Confidence Interval (CI)

The t-test is used to find out if two data sets are significantly different from each other. The t-test can be used to compare samples before and after a treatment or to compare two different ways of treatments in order to understand if a specific treatment can lead to significantly improvements.

The confidence interval describes the range that may contain the true difference between means of the two groups. It's usally given for a 95% specific reliability level. The confidence interval can be considered as an margin of error around the most likely value. In the same way as the p-value, a confidence interval can be used to show statistical significance (null hypothesis value included or not), but in addition it shows also the range of the tested difference value.

Example of t-test comparing two groups x and y

x = c(6.6,5.3,2.2,2.3,7.1,1.6,6.1,2.0,2.5,3.7)

y = c(6.3,14.7,10.3,7.8,3.7,5.8,4.5,7.8,11.1,10.8)

t.test(x,y)

Welch Two Sample t-test

data: x and y

t = -3.4068, df = 15.045, p-value = 0.003889

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-7.054604 -1.625396

sample estimates:

mean of x mean of y

3.94 8.28

The p-value < 0.05 shows a strong evidence for a difference between data set x and y.

Instead of using the p-value, we can make the same conclusions using the confidence interval:

As the confidence interval of the true difference does not include 0, there is strong evidence that the means of x and y are different.

(95% CI and 0.05 p-value referring to the same significance level)

Welch's t-test: adjustment for differences in variance of the two groups. It corrects the number of degree of freedom (df).

https://en.wikipedia.org/wiki/Confidence_interval