Question

You would like to know whether there is a difference between the rate of cooling of freshly killed corpses versus those that were reheated (to determine if you could fool a coroner about time of death). You tested several rats for their cooling constant, both when the rat was freshly killed and after the same rat was reheated. Assuming the distribution ofn differences is normal, is there any difference in the cooling constants between freshly killed and reheated rats?

Test the same hypothesis, but this time assume that the differences are not distributed normally.

Without data, what formula would you use to set up a way to answer this question?

Answer 1

We can use non-parametric test when the distribution of the population is not known

The non- parametric test used in this case will be sign test for two samples which is equivalent of paired t-test to test the difference between two population means.

H₀- The median of population of difference zero.

H₁- The median of the population difference is not equal to zero.

For each pair of observation record the difference between the observation.Record positive sign if the difference is positive and negative sign if difference is negative.

Discard the observation if the difference is zero and reduce the sample size.

If H₀ is true there will be equal number of positive and negative sings. We will reject H₀ is there is sufficiently small number of positive or negative sign,

K⁺- Number of positive signs , K^- - Number of negative signs

K = minimum(K⁺,K^-)

We reject H₀ if K<= C where K follows binomial distribution with parameters (n, 1/2)

P[K<=C/H₀] = alpha/2 where alpha is the level of significance.