Ttest and Confidence Interval (CI)
The ttest is used to find out if two data sets are significantly different from each other. The ttest 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 pvalue, 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 ttest 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 ttest data: x and y t = 3.4068, df = 15.045, pvalue = 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 pvalue < 0.05 shows a strong evidence for a difference between data set x and y.
Instead of using the pvalue, 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 pvalue referring to the same significance level)
Welch's ttest: adjustment for differences in variance of the two groups. It corrects the number of degree of freedom (df).
