R Question

Question 1

Assume you are going to run a Two-Way independent ANOVA on the memory.csv data. Answer the question is the data balanced?

Question 2
Without doing any analyses, what kinds of results do you expect to see for the main effects? i.e., what are your predictions?

Question 3
Assume the researchers anticipated a moderate effect size ( = 0.13) for a main effect of strategy, delay, and their interaction. Does the study have a reasonable sample size to achieve a power level of at least 0.8 to assess those effects? What is the minimum total sample size (N) they would need for each, (round to an integer)?

Question 4
Plot the classical means and their 95% confidence intervals for this dataset. Based on the plot, does the pattern suggest an interaction between strategy and delay? Give the plot interesting colours.

Question 5
Calculate the total sum of squares and its associated degrees of freedom.

Question 6
Calculate the models sum of squares and the models degrees of freedom.

Question 7
Calculate the sum of squares for a main effect of Strategy and its degrees of freedom.

Question 8
Calculate the sum of squares for a main effect of Delay and its degrees of freedom.

Question 9
Calculate the sum of squares for a possible interaction and its degrees of freedom.

Question 10
Calculate the sum of squares for the residuals/error and its degrees of freedom.

Question 11
Calculate the mean squares for the effect of Strategy, Delay, the interaction between Strategy and Delay, and the mean square error/residuals.

Question 12
Calculate the F-ratios for each main effect and the interaction. Also report the associated degrees of freedom and p-value.

Question 13
Use one of Rs cheat codes (i.e., functions) to quickly check and see if your results in questions 5 – 12 are correct. Make sure your output displays the degrees of freedom, sum of squares, F-Ratios, and p-values.

Question 14
In plain English, what do the results of the ANOVA you ran tell you?

Question 15
Pretend the memory.csv data is unbalanced and the researchers dont want to violate the principle of marginality. Re-run question 13 in a way that does not violate this principle.

Question 16
Pretend the memory.csv data is unbalanced. Re-run question 13s analyses using Type-III sum of squares.

Question 17
The significant interaction suggests that it would be useful to examine some simple effects. Conduct a simple effects analyses that allows you to evaluate the effect delay has on each type of strategy. i.e., compare delay (5m vs 2d) across each type of strategy. Display the summary output and list the comparisons you made that are classified as simple effects and state which ones are significant.
e.g., Generated 5m vs Generated 2d: significant.

Question 18
How does delay impact the three different strategies, if at all, and what strategy seems best overall.

Question 19
Write R code to verify that the contrasts used for the simple effects analysis are centered.

Question 20
Write R code to verify that the contrasts used for the simple effects analysis are orthogonal.

Question 21
Instead of doing a simple effects analysis, a bunch of t-tests could have been conducted across the 6 combinations of levels. If you took that approach, how many pairwise comparisons would you be making? Find an automated way of determining this in R.
Hint: combinations, not permutations, are what you want

Question 22
Given the previous question, if you are making 15 pairwise comparisons, what would your familywise error be if you are using = 0.05? In plain English what does this mean?

Question 23
In the lectures I have said repeatedly that an ANOVA is just multiple linear regression. Consequently, it has all the same assumptions. For the model Recall ~ Strategy + Delay + Strategy:Delay does it look like the residuals are homoscedastic? Use of lm() is permitted.
Make the plot an interesting set of colours.

Question 24
Are the residuals normally distributed?
When you create the Q-Q plot, be sure to include a line to help visualize how well the points conform to a straight path. By default, the line ignores the bottom and top 25% of the data when fitting. It does this to give strong protection against outliers. Pretend you believe that is too conservative for the line. Figure out a way to change behaviour that so it only ignores the bottom and top 10%.

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