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To investigate the impacts of sexual activity on the fruitfly longevity, Partridge and Farquhar (1981), measured the longevity of male fruitflies with access to either one virgin female (potential mate), eight virgin females, one pregnant female (not a potential mate), eight pregnant females or no females. The pool of available male fruitflies varied in size and since size is known to impact longevity, the researchers also measured thorax length as a covariate.
Open the partridge1 data file. HINT.
Fit the linear model and produce an ANOVA table to test the null hypotheses that there no effects of treatment (female type) on the (log transformed) longevity of male fruitflies adjusted for thorax length. Note that as the design is inherently imbalanced (since there is a different series of thorax lengths within each treatment type), Type I sums of squares are inappropriate. Therefore Type III sums of squares will be used.
Constable (1993) compared the inter-radial suture widths of urchins maintained on one of three food regimes (Initial: no additional food supplied above what was in the initial sample, low: food supplied periodically and high: food supplied ad libitum. In an attempt to control for substantial variability in urchin sizes, the initial body volume of each urchin was measured as a covariate.
Open the constable data file. HINT.
There is clear evidence that the relationships between suture width and initial volume differ between the three food regimes (slopes are not parallel and a significant interaction between food treatment and initial volume). Regular Ancova is not appropriate.
Each column represents the number of plants per 100m2 for 9 quarters before and 11 quarters after the impact.
In the previous question, we analysed the data from the nuclear power station example, using either a ttest or a one-way ANOVA, with the dependent variable as the difference in kelp density between Control and Impact locations (i.e., a BACI analysis). Now, we will revisit that analysis, using instead the full ANOVA model. The advantage of the full model is that we can deal with situations in which there are multiple control and/or impact locations.
Open the songs data file. HINT. Notice that the TIME variable contains only numbers. Make sure that you define this variable as a factor (HINT)
Note that the main test of interest is the interaction. You might not expect to find any difference in the density of kelp between control and impact sites before the impact (power station), but you might expect that there would be a difference after the impact - hence an interaction between before-after and control-impact. Note also that the test of this interaction gives the same degrees of freedom, F-ratio and P-value as is achieved via the simple ANOVA from Q3 above!