Suppose I am given two groups of mass measurements (in mg), which are referred to as y1 and y2. I want to do a test to determine if the two samples are drawn from populations with different means. Something like this for example (in R):
y1 <- c(10.5,2.9,2.0,4.4,2.8,5.9,4.2,2.7,4.7,6.6) y2 <- c(3.8,4.3,2.8,5.0,9.3,6.0,7.6,3.8,6.8,7.9) t.test(y1,y2)
I get a p-value of 0.3234, and at a significance level of 0.05 don't reject the null hypothesis that the two groups are drawn from populations with the same mean. Now I am given uncertainties for each measurement:
u1 <- c(2.3,1.7,1.7,1.7,2.0,2.2,2.1,1.7,2.3,2.2) u2 <- c(2.4,1.8,1.6,2.3,2.5,1.8,1.9,1.5,2.3,2.3)
where u1 is the combined standard uncertainty in measurement y1 (and so on). How do I incorporate these uncertainties into the statistical test?