Question

Let's say you measure the rate of CO2 production during respi- ration in a sample of ten Drosophila flies with a mutation in the Dg gene and ten wildtype Drosophila flies and want to test if the mutation has an effect on respiration. (a) What test would you perform? (b) What is the value of the parameter that determines the shape of the sampling distribution for the test? (c) Let's say your samples appear strongly right-skewed. What assumption for the test does this violate? (d) What might happen if you don't meet the assumptions of the test? (e) What can you do to your data to attempt to meet the assump- tion of the test? Be specific. (f) If you are unable to meet the assumption, what is an alterna tive test you could perform?

Answer 1

a) We can perform an unpaired t-test for sample means. For this, we calculate the T-statistic and compare this to the critical t-score. The null hypothesis is rejected if the T-statistic is greater than the critical t-score.

b) The degrees of freedom determine the shape of the sampling distribution for the test.

c) Right skewness would violate the normality/symmetricity assumption of the data.

d) If we don't meet the assumptions of the test, the test results might not be robust, something which the unpaired t-test is primarily used for.

e) We can trim the outliers to meet the assumptions, or use medians instead of mean for the test

f) If unable to meet the assumptions, we can use a modified t test like the trimmed means t-test or Yuen-Welch's test