The Story of LFB and Foxy Doggie Flopsy Assignment

Assignment Task

The story of LFB and Foxy

For this assignment, we're going to go back to meet up with LFB and Foxy and hear their story. As you'll recall, a few weeks ago they, Doggie, and Flopsy went on a mission to Otherland to steal some of their data. The mission was successful but LFB and Foxy went missing! In your assignment, we get to see what happened to them.

LFB and Foxy are acting as lookout as Doggie and Flopsy enter the building. Standing on one side of the building, LFB is squinting through the darkness trying to see when she hears a rustle. Then another one, then another one, coming ever closer. Not wanting to raise the alarm prematurely, LFB holds still, but when she hears another rustle only meters from where she is, she whistles, giving the signal.

Foxy dashes around the building as quickly as she can, just in time to see the bushes near LFB part. She catches a hasty glimpse as three very large shapes -- bears? dogs? something else? -- jump out at LFB. Startled, LFB whistles as loud as she can, but it is abruptly cut off by one of the animals covering her mouth.

Forgetting her normal shyness, Foxy shouts "stop!" as loud as she can and charges at the two creatures. She growls at them, surprising herself, and they turn. She trembles: one of them is the largest bear she has ever seen, but it's too late to go back now. She growls again, and then the bear rushes at her and hits her and she is knocked unconscious.

After a short and frightening journey through the dark, LFB and Foxy are put into a small, bright room. LFB is relieved to see Foxy start to stir after a moment — she hasn’t been hit that hard — and the two of them cuddle together in fear. The room they are in looks like a library, but it has very large chairs and books. LFB has to jump just to get down from the high sofa and reach the door handle. It is locked. There is a small window in the door, too high for either of them to reach.

Eventually they notice that different people keep looking through the window; it appears that the people are taking turns watching them. The monitoring shifts are shared between three people: a bear who is so large that only one eye fits in the window at a time, a horse (or possibly unicorn?) of some sort, and what might be a hippo or rhinoceros. Not having anything better to do, Foxy and LFB keep track of how long each person spends watching them before the next person takes over.

Questions

1. After 60 shifts (20 from each person), LFB wonders if there is a difference between the three people in the amount of time they spend watching on average per shift.

a. Create a bar plot showing the mean length of time spent watching per shift: there should be three bars, one corresponding to each person. Each bar should be outlined in black and have error bars corresponding to the standard error. The colour of each bar should be semi-transparent and be different for each person, using a sensible palette of your choice. Individual data points should be included and follow the same colour scheme as the corresponding bar, and both bar and individual data points should be visible. There should be no legend. Title and label the axes appropriately (you don’t need a subtitle). Make sure your figure shows in the knitted document.

b. There are two main assumptions you need to test before implementing the analysis in Q1c below that addresses LFB’s question. Evaluate each of these assumptions and report the results. (It does not matter what order you test them in). For each assumption, be sure to explicitly state what assumption you are testing, the name of the test you did to evaluate it, the results including the stats reference, whether the assumption was violated, and how you could tell.

c. Based on your results in Q1b, run the appropriate statistical test to evaluate whether there is a significant difference between the three people in the length of time spent watching. Report your results. Be sure to mention which statistical test you used and why (given your results in Q1b), the predictor and outcome variable(s), the appropriate stats reference, and its interpretation in terms of the research question. You should also report and interpret effect size

d. Regardless of whether your results in Q1c are significant or not, run post-hoc tests. Report on the result, clearly indicating which differences are significant (if any) along with their corresponding p-value and an interpretation of what that means in terms of the research question.

After some hours, the door finally opens and seven people come in. The first is the bear, who is even bigger than he looked – he is larger anybody LFB has ever seen, and she suspects that is the main person who subdued them. He is followed by the horse (who it turns out is actually a gorgeous unicorn with a rainbow mane), the hippo, an owl, and a cute penguin carrying a snake. The entire group is trailed by what looks, to their astonishment, to be a sentient guitar (that's right, a musical instrument that can walk and talk). This is a very strange place, thinks LFB.

2 a. The Others are very interested in knowing if there is a correlation between LFB’s and Foxy’s answers. Based on the data in dl, what would you tell them? In your answer, explain which statistical test you used and why, include the appropriate stats reference, and interpret what this result means about the nature and/or presence of a relationship between these two variables

b. Instead of using a correlation to answer the question in Q2a, use a linear regression with LFB’s answers as the outcome measure and Foxy’s answers as the predictor. You do not need to report it; instead, use it to answer the following questions. (i) You should see that the degrees of freedom is the same for the correlation and the linear regression; what other two parameters are also identical? (ii) What parameter of the linear regression is the correlation coefficient r related to, and how is it calculated? (iii) What two additional pieces of information does the linear regression give us about the answer to our research question that were not evident from the correlation?

c. Calculate and report the standardised coefficient for the linear regression in part Q2b.

d. The code chunk calculates two new variables called lfbZnorm and foxyZnorm. Based on the code, explain what it is calculating and what the purpose is. Rerun the analysis in Q2a but use these new variables instead. Is the answer the same or different? Why or why not?

e. Re-run the linear regression from Q2b on the new variables created in Q2d. The slope and intercept parameters are different from the answer in Q2b. Report them, explaining how and why they are different. (You don’t need to report the entire regression, just discuss those parameters)

The Others confer a bit and realise that regardless of the results of the test, over the course of working and talking with LFB and Foxy they have realised that the two are at least reasonably trustworthy. Following a long, whispered conference amongst each other, Rainbow the unicorn steps forward and unties them

3 a. Using the tibble called dcPlotTable provided in the code chunk, make the figure above. Hint: the geom used is one you have already been taught, but with different arguments; part of the purpose of this question is to evaluate your ability to figure this kind of thing out by using the help files and google. For full credit, your figure should have all the components with everything in approximately the same places. The colours have no transparency. Use the Set1 palette.

b. Considering the current year only, perform the analysis that would answer LFB and Little Blue’s question. Be sure to explain what test you did on what variables, include the stats reference, and interpret the result in terms of the research question. You don’t need to present the descriptive statistics since they are in the figure. Don’t worry about effect size either.

c. Compare the thefts from the current year to the previous year using the appropriate statistical test. Be sure to explain what test you did and why, include the stats reference, and interpret the result in terms of the research question. As before, you don’t need to present the descriptive statistics since they are in the figure. Don’t worry about effect size either.

d. Use the code chunk to display the adjusted residuals from the test in Q3c. What do they suggest about what crime types, if any, are significantly different between the current and the previous year? In your answer be sure to explain why they suggest that.

4 a. There is one main assumption you need to test before implementing the analysis that would answer Super Size’s question. Test that assumption and report the results. Be sure to include the assumption, the name of the test you did, the variable(s) involved, the results including stats reference, whether the assumption was violated, and how you could tell.

b. Given the answer in Q4a, use the appropriate statistical test to implement the analysis that would answer Super Size’s question. Report on the results. Don’t worry about descriptive statistics, but include the predictor and outcome variable(s), the effect size and its interpretation, and the results including stats reference. You should also explain which statistical test you used and why as well as interpret the result in terms of the research question.

5 a. Create a figure that you can use to display the information Super Size wants to see. Part of the purpose of this question is for you to determine about what kind of figure is best given this specific aim and these specific variables, so you must decide which geom(s) to use, what variables to include, and how to design everything. Your mark will be based on whether your figure displays the information Super Size wants to observe in a way that is both clear and informative.

b. Run the appropriate statistical test to evaluate whether income category or exercise category are significant predictors of health rating, including whether there is an interaction. You do not need to test any assumptions and can act as if none have been violated. In your report, don't worry about including descriptive statistics but do include an explanation of which statistical test you used, the stats reference(s), the predictor and outcome variable(s), and the interpretation of this data in terms of the research question. Don’t worry about effect size or post-hoc tests.

6 a. Do as LFB suggests: run the appropriate statistical test to evaluate whether exercise and/or income are significant predictors of health rating. Don’t include an interaction term. You do not need to test any assumptions and can act as if none have been violated. In your report, don't worry about including descriptive statistics but do include an explanation of which statistical test you used, the stats reference(s), the predictor and outcome variable(s), the effect size of the model as a whole, and the interpretation of this data in terms of the research question. Include a description and interpretation of any significant unstandardised coefficients but don’t worry about standardised ones or the intercept.

b. Run the same analysis as in Q6a but this time include an interaction term. (i) Report the results of the interaction term only, including its stats reference as well as interpretation in terms of the research question. (ii) Compare the effect size of this model to the one in Q6a. What does this mean about which model, if any, fits the data better? (iii) Describe how the unstandardized coefficients for each of the two predictors have changed, and explain why. Include an interpretation of these predictors in terms of the research question.

c. Does your analysis in Q5b and Q6b lead to the same qualitative conclusion about which factors are significantly associated with health rating? If so, explain on what basis one should decide which analysis to report. If not, explain why the two are different

7 a. For each of (i), (ii), and (iii) in the table below, indicate which of the two statistical references (A or B) is not possible. Use your knowledge about each test statistic and how it is related to degrees of freedom and/or p-values to answer this. You don’t need to do any coding or calculations.

b. For each answer in Q7a, explain it by describing intuitively what the test statistic captures and thus why you chose the answer you did. Be sure to make reference to the degrees of freedom, test statistic, and/or p-value as appropriate to justify your answer

8. These marks are free as long as you say anything! Who is your favourite character in the Bunnyland story, and why? (This can be anyone, whether from Bunnyland or Otherland or whatever. There is no word limit here, say as much or as little as you want)

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