STAT 602 - Assignment #6 Repeated Measures & MANOVA
Include your JMP results for all problems.
Problem 1 – Rat Weight Gain (Study 1) – Ratweight.JMP
Twenty rats, 10 in each group, were randomly assigned to receive two different doses of a drug (0 = control and 1 = active dose) and their weight was measured weekly for six weeks. Use an appropriate repeated measures analysis to determine if there was a dose effect, a time effect, or a time*dose interaction effect. Summarize your findings. (10 pts.)
Problem 2 – Rat Weight Gain (Study 2)
16 rats were randomly assigned to receive one of three diets. Eight rats were assigned to diet 1, 4 rats were assigned to diet 2, and 4 rats were assigned to diet 3. Their weights were measured at day 1 of the experiment and every 7 days for 64 days total.
Using the file: Ratbody.JMP
a) Conduct an appropriate repeated measures analysis to determine if there is diet, time, and time*diet interaction effects. Summarize your findings. (6 pts.)
b) The diet effect is clearly significant but this clearly deceiving, why? (3 pts.)
Using the file: Ratbody Differenced.JMP
c) Conduct an appropriate repeated measures analysis to determine if there is diet, time, and time*diet interaction effects, but this time use the weight gains from day 1 as the repeated measures (d8-d1, d15-d1, etc…) Summarize your findings. (6 pts.)
d) Explain why your analysis in part (c) is more appropriate than the analysis in
part (a). (2 pts.)
Problem 3 – Plastic Film
The optimum conditions for extruding plastic film have been examined using a technique called Evolutionary Operation. In the course study that was done, three responses - Y1=tear resistance, Y2=gloss, and Y3=opacity – were measured at two levels of the factors, X1=rate of extrusion and X2=amount of additive. The measurements were repeated n=5 times at each combination of the factor levels. The data are contained in the file Plastic Film.JMP.
a) Conduct appropriate analyses to compare the mean of each response separately across for the two rate of extrusion levels. You can do this by selecting Fit Y by X and putting all three responses in the Y box and rate of extrusion in the X box. If you hold down the Ctrl key while selecting the analysis options for tear resistance (Y1), it will do the same for the other two responses as well. Briefly summarize your findings. (6 pts.)
b) Repeat part (a) but this time, consider the potential effect of the amount of additive. Does amount of additive seems to have any effect on these plastic film properties? (6 pts.)
c) Use Rows > Color or Marker by Column to color code the points by amount of additive. The use Fit Y by X to plot gloss (Y) vs. tear (X) and then select Group By… from the Bivariate Fit pull-down menu and finally select Density Ellipse > .90 from the same pull-down menu. Explain how the resulting plot shown below, created using the procedure above, that the amount of additive actually might impact both tear resistance and gloss. (3 pts.)
d) Conduct a two-way MANOVA to determine if rate of extrusion and/or amount of additive effect the responses. Summarize your findings. (6 pts.)
Problem 4 – Fatty Acid Concentrations of Italian Olive Oils
This is an open ended problem, think of it like a mini-midterm (a week or so late). Researchers are interested in characterizing differences in the fatty acid content of olive oils made from olives grown in different regions of Italy. There are two geographic classifications in these data. The first classification is nine individual growing areas in Italy (Area Name) – East Liguria, West Liguria, Umbria, North-Apulia, South-Apulia, Sicily, Coastal Sardinia, Inland-Sardinia, and Calabria. A broader classification is the growing region in Italy (Region Name) – Northern, Southern, and Sardinia. The map below should help in your understanding of where these areas/regions are located in Italy.
The fatty acids measured are as follows:
Palmitic C16H32O2
Palmitoleic C16H30O2
Stearic C18H36O2
Oleic C18H34O2
Linoleic C18H32O2
Eicosanoic C20H40O2
Linolenic C18H30O2
Molecular formulae taken from Wikipedia, so if these are wrong it is not my fault. I don’t understand how small differences in the number of carbon and hydrogen molecules make distinct fatty acids. Chemistry is weird!
Research Question/Problem:
Use any/all descriptive and inferential methods you think are appropriate to characterize the differences in the amino acid content between the olive oils produced in each growing region/area in Italy. Summarize your findings for the researchers. Be sure to include all relevant plots and analysis summaries in your report. (20 pts.)