I have a question about Simulation Process and Independent Vs Paired
Samples.
Given two related samples, in order to enhance the sensitivity of t-
test,
1 sample t-test should be applied to the two samples differences (null
hypothesis: the differences average is statistically zero), instead of
applying 2 sample t-test to both the samples separately (null
hypothesis:
both the samples come from the same population).
Simulations made to decide whether to modify or not a certain device,
yield paired (=related) samples (i.e.: before- and after-modification
measurements) spontaneously, however.
Sometimes it happens that the two samples differences result
significantly different from zero (i.e.: 1 sample t-test is
significant),
while both samples seem to come from the same population (i.e.: 2
sample
t-test is not significant).
In these cases, I do not want to modify the device under test because
I am
not able to reject the null hypothesis of the 2 sample t-test. The
"paired
t-test" (i.e.: 1 sample t-test applied to the two samples differences)
suggests to modifying the device under test, however.
What is the proper treatment of paired samples resulting spontaneously
from simulation?
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