Mann Whitney or Wilcoxin test?

#1
Lets say I have two brands of a machine which do the same thing. I have a sample of participants who have each used the two machines, one after the other. I now want to find out if there is a difference between the machines in three of the measurements they have produced. I've firstly determined that the measurements produced are not normally distributed, so need to use non-parametric tests.

I originally thought a mann whitney test, but would I only use that if it was two different groups of people using each machine rather than the same group using them both? Would a wilcoxin test be appropriate?

Also, either of these tests will tell me the difference overall. How do I also determine the difference between the measurements from each individual person?

Thank you
 

Karabiner

TS Contributor
#2
A t-test or analysis of variance never needs normally distributed variables.
In an independent samples t-test, the variables in each group separately
#should be normally distributed (in the populstion from which they were
sampled). In a dependent samples t-test, the differences should be normally
distributed in the population. Both tests are robust, though, against non-normality,
if sample size is large enough (often n > 30 is considered sufficient). I do not
know whether you need a t-test, oneway ANOVA or repeated-measures ANOVA.
A test for repeated/dependent measuresments would be needed if the machines
measured exactely the same objects.

With kind regards

Karabiner