## Thursday, 21 February 2019

### Reading Assignments - Split-Plot Design, Magnitude-Based Inference

This semester, I'm teaching a new (to me) course that's heavy into design of experiments and biostatistics, which means I needed some new reading assignments. First, a survey of applications of split-plot designs for fisheries. Next, a seminal paper on magnitude-based inference, written for physiologists. Non-paywalled links to the papers included.

#### Split Plot Designs

To answer the following questions, read the article "Use of a Split-Plot Analysis of Variance Design for Repeated-Measures Fishery Data", by Maceina, Bettoli, and DeVries, found at

1)    What are the three assumptions of ANOVA?

2)    What is one way in which these assumptions are commonly violated when dealing with fisheries data?

3)    What is the name of the proposed design for handling multiple measurements over time at the same sampling station?

4)    What are the different sources of variation that this model accounts for?

5)    In the trapnet example, on page 16, why were year and station considered main plot effects, while day was considered a sub plot effect? (Hint: A sub plot is a smaller factor that happens with a main plot)

6)    In Figure 2, there is a potential problem with the regression line, shown by the dotted line. Explain what the problem is (Hint: Two points).

7)    In the Cove-rotenone example, on page 17, the biomass of bass are log-transformed. Why?

8)    On page 18, what problem did the ANOVA in the Cove-rotenone example have and how was it fixed?

9)    What must be recognized in order to use the repeated measures split-plot ANOVA correctly?

#### Magnitude-Based Inference

The following questions pertain to the Batterham, A. M. and Hopkins, W. G. (2006) 'Making meaningful inferences about magnitudes', International Journal of Sports Physiology and Performance, 1 (1), pp.50-57, found at https://tees.openrepository.com/tees/bitstream/10149/58195/5/58195.pdf

Questions directly related to the reading:

1) What was R.A. Fisher’s rationale for choosing 0.05 as the original significance threshold for the p-value?

2) Instead of knowing whether there is an effect or not, as the p-value does, what is the more relevant issue (according to the paper)?

3) Does a large (more than 0.05) p-value imply that there is no effect (i.e. that the null hypothesis is true?) If not, what else could explain the large p-value?

4) What are the three possible inferences you could make using only the confidence interval and a value (e.g. a null hypothesis value) that marks the difference between a negative and positive effect?

5) What are different effect size ranges in a 3-level scale of magnitude?

6) How many different inferences could you make from data using a 3-level scale of magnitude?

7) What are two different ways to interpret an observed effect in the ‘beneficial’ range, but a confidence interval that spans the both the beneficial and neutral range?

8) What additional information could be reported to further explain the results using a 3-level scale of magnitudes? (Hint: See Figure 3)

9) What is one drawback to magnitude-based inference that some researchers may use to argue against it?