Let us say I have the following pair wise test data:
batch 1 2 3 4 5 6 7 8 10
non-control 18 16 15 19 36 24 25 30 31
control 20 23 25 19 28 24 26 21 22
Each data point is measurement of some attribute X in some units
The control part of the pair share some underlying similarity to the non-control pair
The non-control part of the pair share some underlying similarity to the control pair except that is has received an exposure to say a chemical C.
Now how would I prove (or disprove) if there is strong evidence (or the lack of it) that the exposure the chemical C results in greatly increased measurements of attribute X?
How would I construct a confidence interval of the difference between the values of the con-control and control (say 90%) for the difference between attribute X between the control and non-control versions of the measurements.
This is more to further my understanding but basically I want to apply two tests:
- Sign Test
- Wilcoxon Signed Rank Test
Thanks.
Best Answer
This "R" code produces accurate results ONLY if your test is RANDOMIZED
As can be seen below:
According to the null hypothesis, the difference population mean equals zero, the reference distribution against which the observed "pairedDifferenceMean" = 0.6666667 may be viewed as a scaled t distribution with eight degrees of freedom centered at zero with a scale factor "pairedStandardError" of 2.285218. The value of "tSubZero", below, associated with the null hypothesisis: