Homework VIII

1. ( 16 points ) The data below are blood pressure measurements for hamsters as a function of Age and Sex.

   	Sex
   Age	Male	Female
   Adolescent	108	110
   	110	105
   	90	100
   	80	90
   	100	102
   Mature	120	110
   	125	105
   	130	115
   	120	100
   	130	120
   Old	145	130
   	150	125
   	130	135
   	155	130
   	140	120

   1. ( 5 points ) Analyze these data as a two-way factorial Model I ANOVA in SPSS to determine the effects of Age, Sex and the Age  Sex interaction on blood pressure. Report and explain the ANOVA table from SPSS in your results.
   2. ( 5 points ) Below is a profile plot (e.g. Figures 12.1 and 12.2) of means by treatment. Diagram the mean effect of Age and of Sex. How does age affect blood pressure? Does the Figure suggest there is an interaction between Sex and Age? If so indicate what on the graph suggests this and explain.

1. (12 points ) The file predator-prey size ratio.sav contains data on the ratio of the body mass of predators to that of their prey ( ratio : the ratio on the arithmetic scale; logratio : common log of ratio). Two explanatory variables are also included:

Habitat (3 levels): freshwater, marine, terrestrial.

Predator Type (3 levels): ectotherm vertebrate, endotherm vertebrate, invertebrate.

c. ( 5 points ) Analyze logratio with Model I ANOVA, the factors being habitat and predtype and interpret the ANOVA table. Is there a significant difference in predator-prey size ratio among habitats? How about among predator types? Is there a significant interaction?

d. ( 5 points ) Use SPSS to create profile plots. Diagram the mean effect of Predator Type and the mean effect of Habitat. Also generate box plots for logratio by habitat and predtype using the Graphs, Boxplot menu. Interpret the results.

e. ( 2 points ) What do these results suggest biologically ?

1. (16 points) Consider a two-factor Model I ANOVA in which the first factor ( A ) has three levels and the second factor ( B ) has two levels. Graph profile plots (i.e. like figure 12.2) illustrating the following circumstances (put factor A on the horizontal axis and diagram the mean effect of factors A and B in each graph):
   f. (4 points) Strong effect of factor A, moderate effect of factor B and no interaction, with , where j indexes the levels of factor B .

1. (4 points) No effect of factor A, Strong effect of factor B and an interaction A  B , with and .

Hint. Draw the table for this experiment and label the cell, row and column means. And, if you get stuck, try making up some data and generating profile plots in SPSS (the data in each cell must have some variability − all values can’t be equal − or the error MS will be 0 and SPSS won’t calculate F statistics).

1. (15 points ) The file grasses.sav contains data on the yield (growth) of five grass varieties selected at random from several hundred. The three varieties were treated with three different seed promotion methods.

j. (5 points ) Are Variety and (seed promotion) Method fixed or random factors? What type of ANOVA model (I-III) should be used to analyze the yield data?

k. (5 points ) Analyze the data using the model you selected in part a . Report and intrepret the ANOVA table from SPSS in your results.

l. (5 points ) Generate a profile plot (i.e. like figure 12.2) using SPSS and interpret the results.

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