Assignment III for Biostats Course VHM 801 at AVC - Fall semester 2019

The assignment is worth 10% of the final course mark. Please be aware that by handing in the home assignment you implicitly acknowledge to have read and accepted the instructions for home assignments as described on the VHM 801 homepage.

The assignment is a continuation of the first home assignment on growth of Atlantic salmon in a field vaccine trial. You may want to revisit the first home assignment as a preparation for this assignment, and you will use the previously described and supplied dataset. For your work here, you should generally take into consideration all the information about the dataset obtained in the first home assignment (e.g., as described in the corresponding solution posted on the VHM 801 homepage).

A full mark requires satisfactory answers to the four questions below. Note that all statistical assumptions need to be stated and justified. It is perfectly valid (and also recommended) to use statistical software for the analyses, but all procedures should be described/specified in such detail that it is clear what has been done without looking at software outputs. (Hint: Methods can be specified without including the formulae, by giving their unequivocal names and explaining any inherent settings used.)

1. Our focus for the assignment will be on the weight gains from vaccination to transfer. Give a statistical model for these weight gains that does not differentiate between the characteristics contained in the additional variables recorded; that is, a model for the weight gain in the absence of any additional information about the fish. Estimate the mean weight gain, with a corresponding 95% confidence interval. Discuss any concerns you might have with the validity of the confidence interval, explore at least one way to demonstrate the impact of such concern(s) on your result, and draw conclusions. If you don't have any concerns with the validity of the confidence interval, explain carefully why there might be no concerns. (Note: You are not expected to get into considerations about the utility of an overall mean weight gain, when the data offer ways of splitting into sub-populations.)

2. Carry out a statistical analysis to compare the weight gains for the different sex groups (females, non-precocious males, precocious males). It is suggested to compare the non-precocious and precocious males first, and then based on the results from this analysis decide on how to best continue with the comparison(s) with females. Your comparisons should involve estimates and confidence intervals to quantify differences, as well as statistical tests to assess their statistical strength. As in the first question, address any concerns about the validity of the results, and include also here exploration of the impact of any such concerns. (Note: If your analysis involves several comparisons, you may restrict your discussion of concerns to one of these.)

3. The main objectives of the study were related to the vaccines. Even though the study was randomized, there may have been ways in which the distribution of sexes could become dissimilar between vaccines, thereby offering a potential to affect the results in undesired ways. Without necessarily going into details about how such dissimilarities might have occurred, carry out a statistical analysis to explore whether the sex distributions, as recorded in the data, appeared to be similar across the vaccine groups. Make sure to formulate and justify a statistical model as the basis of your analysis and inference, and to draw conclusions about the question of interest.

4. Carry out a statistical analysis to quantify any differences in the weight gains between vaccine groups. Your analysis should include estimates and confidence intervals for the mean weight for each vaccine group, possibly displayed graphically. For further comparisons, you may -- as there are six vaccines -- either use statistical methods to compare multiple samples (covered in Session 10 of VHM 801) or compare selected pairs of vaccines. A brief discussion of the validity of the results should be included here as well, but include extra analytical steps only if they add to what you already did in previous questions.