Statistical Tests with Data Having Measurement Errors

For example, can the results of the t test on y1 and y2 be interpreted in the usual way (i.e., like the results of the t test on x1 and x2)? If not, how should I go about testing whether or not y1 and y2 are drawn from the same population?

#Error-free measurements follow a N(10,1)
#I don't know these values
x1 <- rnorm(100,10,1)
x2 <- rnorm(100,10,1)

#Do a t test on the values I don't have
t.test(x1,x2)


• If you have a model $y = \mu + \xi +\eta$ where $\xi$ is a zero-mean error term representing underlying variation about the population mean and $\eta$ is a zero-mean error term representing measurement error, what's the difference from a model where $y = \mu + \epsilon$ where $\epsilon$ is the variation in the observations around the population mean? (i.e. where $\epsilon = \xi +\eta$) – Glen_b Mar 6 '13 at 21:45