Assignment IV for Biostats Course VHM 801 at AVC - Fall semester 2003

The assignment is worth 15% of the final course mark.

The home assignment has two parts with several questions in each, all of which should be answered. The data for the home assignment are taken from the textbook (IPS; Introduction to the Practice of Statistics, 4th ed.) and can be found on the CD-ROM or at the IPS website.

Part 1.
Consider the Plants2 dataset in the IPS Appendix; these data originate from a laboratory (growth chamber or greenhouse) experiment where fresh and dry weights of plants were measured. The plants were of 4 different species and had been exposed to different watering conditions.

1. Describe the statistical design of the experiment.
2. Explain how randomization should be carried out in an experiment like this.
3. Use an ANOVA model and analysis to determine whether the fresh biomass weights differ between species and/or watering conditions.
4. Check the model assumptions carefully; pay particular attention to whether the variance seems constant across the data.
5. One approach to deal with violations of model assumptions is to transform the data. In practice, power and log-transformations often work well. Transform these data by the square-root and logarithm (natural or base 10), and repeat the ANOVA analysis. Do you see any improvements with regard to the model assumptions? Are the conclusions the same? Which analysis do you prefer? (you may try to find a better transformation if you like)
6. Continue the analysis beyond the ANOVA table to give estimates and confidence intervals for the different species and watering conditions, and to compare specific watering conditions and species. If you preferred the analysis of transformed data, don't forget to backtransform estimates and confidence intervals to the original scale.

Part 2.
Consider the Plants1 dataset in the IPS Appendix; these data originate from another, similar experiment in which the percent of the plants consisting of nitrogen was measured. The plants were of the same 4 different species and had been exposed to the same watering conditions.

1. Use an ANOVA model to determine whether the nitrogen percentages differ between species and/or watering conditions. Don't forget to check the model assumptions. Draw conclusions and give an informal assessment of any differences between specific species and/or watering conditions.
2. One approach to analyzing multifactorial data when the data show huge differences between the levels of one variable, is to do separate analyses for each of the levels of that variable. Carry out such an analysis for these data, and draw conclusions.
3. The description of the experiment does not give any detail about how it was practically organized. If the 9 plants from each species with the same watering condition were physically located next to each other and served by the same watering mechanism (e.g., a rose or a vessel), it might be more appropriate to consider them as one experimental unit instead of 9 separate units. In that case, the data analysis should be based on averages of the 9 plants per species and watering condition. Carry out such an analysis, and draw conclusions.