How far can you go with transformations? For instance, can I transform data using square root, arcsin, and then natural log? If I shouldn’t, why not?

Discussion  6 TQ:1 How far can you go with transformations? For instance, can I transform data using square root, arcsin, and then natural log? If I shouldn’t, why not?

Discussion 7 TQ4: A freshwater biologist was studying the effects of increased light intensity on the rate of photosynthesis of a species of phytoplankton from Lake Hume on the Murray River in Australia. A mesocosm set-up located near the lake was used. There were two large ponds used for the experiment. In one pond, shade-cloth was used to reduce light intensity. In the other pond, light intensity was not altered. At the end of the experiment, a random sample of ten replicate aliquots of phytoplankton was removed from each pond and the rate of photosynthesis measured on each aliquot. Boxplots and related tests indicated that the assumptions of parametric tests were met and a one-way ANOVA was used to test the null hypothesis of no effect of light intensity on the rate of photosynthesis.

Critically evaluate this story in terms of generating an ANOVA; will the design meet the conditions required of an ANOVA? How about any of the non-parametric methods? Or should the researchers just go home?

 

Discussion 8 TQ:3 If one level of a two-level nested ANOVA proves not to be significantly different among another level of that same nested ANOVA, could I then re-design the study to eliminate that level, turning the analysis into a one-factor ANOVA?

Discussion 9 TQ:2 An ecologist studying a rocky shore at Phillip Island, in southeastern Australia, was interested in how clumps of intertidal mussels are maintained. In particular, he wanted to know how densities of adult mussels affected recruitment of young individuals from the plankton. As with most marine invertebrates, recruitment is highly patchy in time, so he expected to find seasonal variation, and the interaction between season and density – whether effects of adult mussel density vary across seasons – was the aspect of most interest. The data were collected from four seasons, and with two densities of adult mussels. The experiment consisted of clumps of adult mussels attached to the rocks. These clumps were then brought back to the laboratory, and the number of baby mussels recorded. There were 3-6 replicate clumps for each density and season combination.

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