2024 RMHI/ARMP Problem Set 2

Hello everyone! This is the description for the assignment, which is due on Canvas on Monday May 13, 2024 before 8:00am Melbourne time. You’ll need to submit a Word-knitted version of the completed R Markdown file found in this zip file, according to the following instructions:

1. Rename the document called pset2.Rmd as studentID-pset2.Rmd. (Replace studentID with your student ID number). This is your R Markdown file, where you’ll be putting your code and answers.

2. Replace “Your name and ID goes here” in the header of the R Markdown file with your name and student ID. (Keep the quotes or it won’tknit properly).

3. While we encourage collaboration in tutorials and learning in general, you should not be collaborating with anybody AT ALL for this assignment. That means sharing code privately or publicly; even talking in the abstract about problems will effectively be collusion. You should be completing it independently, with no help from any other person in any capacity. Of course, as always, you are free to use any of the resources from the class to help you, and you're also free to google or look anything up that you like (as long as you aren't asking anybody, including discussion boards or AIs, questions related to this assignment). Note that we do look at places like chegg and will follow up if anything from this problem set is posted there.

4. Plagiarism check is enabled and you can check the similarity report on your submission. In previous years we have found people who tried to cheat, so please don’t risk it! That said, understand that we will not be naively looking at the overall % figure: with this sort of assignment a certain amount of overlap is inevitable, so don’t worry if you get what looks like a high % score as long as you know you didn’t plagiarise or collude. With this sort of assessment, that % overlap is higher than essays and the like. We will be using the plagiarism check for the parts of the assignment where we'd expect some variability, and to give a general sense of the overall gestalt.

5. Complete all of the problems below in the R Markdown document. Do not remove any of the arguments to the code chunks, like the names of the code chunks or where it says message=FALSE or whatever. If a problem asks you to display a tibble or variable so it shows up in the knitted version, make sure that you do as the marker cannot evaluate it without seeing it, and if they can't see it then they won’t be able to award you points for it! Remember that to display a tibble (or any variable) you just type its name on a line of its own within the R chunk.

6. As much as possible, questions do not build on each other (often even parts of questions). That means that if, say, you can't get Q5 then you can still get Q6. Try to do all of them.

7. Go for partial credit! Many of these questions have some form of partial credit possible. If it    is asking for some R code, breakdown the problem into pieces. Even if you can only do some of the pieces, or do them part of the way, that will be worth something. [Note that there is no question-by-question rubric available because designing one would mean giving away the answers. In general we will give full credit for responses that correctly address all of the parts of the question.] Short answer questions (SAQs) can also be given partial credit and are generally asking for some thoughtful interpretation. If it is based on a previous graph or test you've done, if you did the first part wrong but discuss it well, you can still get most or all points for the SAQ part. If your code does not run but you want to include it for possible partial credit, just comment it out (using the # sign) so that it shows up in the knitted document but R does not try to run it. If some of your commented-out code is correct and some isn’t, we will not give you credit for the correct code; put the thing in there that you think is the closest to the correct answer, don’t just include everything.

8. We don’t care much what decimal place you round answers to and you will not lose credit for decimal places unless you round so much that your answer is impossible to discern (e.g., don’t round p-values to the nearest integer!). Similarly, you will not lose points for trivial presentation things like using parentheses instead of commas around statistical references, as long it’s clear. That said, for those who want a guideline, I’ll suggest that you follow APA format or round p-values to three decimal places, degrees of freedom to one, and test statistics and probabilities to two.

9. Some questions specify a word count. In that case you need to either calculate it from the knitted document or type up your answer in Word and then cut and paste it into the R Markdown file.

(Please put your answer in between the word ANSWER and [Word count: XX]; those two bits do not count towards your word count). The word counts specified in each question are designed to give you a guideline about the maximum number of words you should need answer completely and correctly. So don’t feel like you must use all of the words; if you can answer it fully with less, that’s fine. In fact, the total word count for the solution set we wrote up is around 1320, so it’s possible to fully answer the questions while going substantially under the word limit. That said, it is okay to go over the word limit for individual questions as long as the total word count for all of the questions combined is fewer than 1760 words (i.e., fewer than 1600+10%, with the standard penalty if it is 1600+10% or over. See the student manual for details on word count penalties).

10. There is no word count for code chunks. Word count only applies to the short answer questions  that have [Word count: N] attached and suggested word counts given. Remember to report your total word count for the assignment as a whole at the top of the document. Your total word count is  the sum of the word counts where those are reported.

11. You'll be turning in the knitted output of your R Markdown file. We prefer that you knit to Word but if you can't get Word to knit then html is okay. In the worst case, you can turn in the completed  Rmd file. We highly, highly recommend that you knit as you go: (a) knitting can identify problems in your code that you would have otherwise missed; and (b) you do not want to get close   to the deadline and think you’re done only to find that you’re having trouble knitting. Save yourself the panic and knit often.

12. Similarly, you can turn in the assignment multiple times before the deadline, so we strongly encourage you to submit it even before it’s perfectly polished. That will save you last-minute panic or computer issues. Also, take a screenshot for proof of having turned it in just in case you need it. If you run into last-minute computer issues and can’t even succeed in uploading an Rmd, email us ([email protected]) your assignment as soon as possible to demonstrate that it was done at that time. We cannot make promises about whether you will receive any late penalties if you do this, but if you don’t, you almost certainly will get penalised because we have no way to know if the problems were genuine.

*** IMPORTANT NOTE ***

Making figures is an important part of doing your data analysis, and in many of these problems creating the appropriate figure will help you understand what is going on with your data. Deciding out what figure is necessary and when is also a key skill.

What this means is that even if a problem does not explicitly say you should make a figure or what it should look like, you may benefit from making one anyway! As a result, all of the code chunks include options for figure sizes regardless of whether one is necessary; you can leave the code chunk as is even if you don’t make a figure. If a question doesn’t tell you to make a figure, you will always be evaluated on the correctness of your analysis only, and if you can understand and explain the data without creating a figure that is fine. However, much of the time a figure will help understand and explain the data, and you will never be penalized for making a figure that you don’t need (unless you interpret it wrong or something). So if you do not understand something about your data or analysis, make figure(s) or tables! If you do make one, you won’t be evaluated on its beauty but if it is unclear then you will not benefit from making it.

Q1a. 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.

Q1b. 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. [Suggested word count: 90]

Q1c. 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. [Suggested word count: 80]

Q1d. 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.   [Suggested word count: 40]

*   *   *

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.

Everyone looks at each other awkwardly.

LFB and Foxy are both feeling a little calmer now that it appears nobody is going to try to kill them on sight. Still, the Others seem rather suspicious (not that that is surprising, really).

Everyone introduces themselves: the bear is called Super Size, the unicorn is Rainbow, the hippo is Hugo, the owl is Wol, the penguin is Little Blue, the snake is Sissily, and the guitar is Kevin.

“What are your names?" Super Size asks them.

"LFB," says LFB, trembling.

"What kind of name is LFB?" asks the guitar.

LFB bites her tongue and narrowly avoids asking what kind of guitar is named Kevin, and just says "It stands for Lovable Fluffy Bunny. My mum named me."

The unicorn – Rainbow – shakes her tail and says "It's a lovely name. I like it," and glares at Kevin.

“How about hers?” the snake hisses, pointing at Foxy.

“She can answer for herself,” Foxy says, bristling a bit. “My name is Foxy. Because I am a fox.”

“Okay, okay,” says Hugo the hippo. “That’s fine. Are you okay? We didn’t mean to hurt you when we captured you, we just didn’t want to let you get away.”

Mollified, Foxy nods. “Head hurts a bit but I’m okay.”

"What are you doing here?" the giant owl interrupts.

Trading back and forth, LFB and Foxy tell everyone the whole story -- how they fear they are running out of food, and they wanted to see if the Others were stealing it (at this point LFB

trembled a little bit more, and Foxy gave her a reassuring hug) or were having similar problems. As they get into the story, they can't help but notice that most of their listeners seem stunned. The

penguin whispers to the unicorn and the giant bear several times during the explanation. When they stop, there is a long silence.

"How do we know you're telling the truth?" the snake, Sissily, finally asks.

"I... don't know," LFB says. “We are, I swear."

After a pause, Little Blue (the penguin) raises her wing. "I have an idea," she says. "We can separate them and then ask them each a bunch of questions. If the answers agree with each other, that’s an    indication that they aren’tlying.”

“What kind of questions?” asks the unicorn curiously.

“All sorts,” says Little Blue. “A lot of them would be details about their story which they haven’t   already shared with us – like small details about who was with them or what time they set out or whatever – which if they are telling the truth they would agree on.”

Oh dear, thinks Foxy. This sounds very stressful.

“I can take the test,” LFB volunteers. “I mean, I know that we’re telling the truth and I’dlike to demonstrate that.”

Foxy pauses, and then says, “I can take it as well.”

Kevin bursts out suspiciously, “How do we know they won’t cheat?”

LFB bristles, but Rainbow the unicorn just smiles. “Don’t worry,” she says. “We’ll separate them right now so they can’t coordinate in advance. And we’ll have them take it at the same time, in     separate rooms, so there is no way to overhear each others’ answers.”

After a moment, Kevin nods, mollified, and the rest of the Others join in. It seems to be settled.

I hope this works, Foxy thinks nervously. I know I’m telling the truth, but what if I mess this up? What if their test isn’t very good after all?

But there is no choice – she can’t think of anything else that would persuade them better, so she nods and tries to look confident. She can’thelp but notice that LFB and Little Blue look nervous also, but everyone gets up and the two of them go to separate rooms to take the test.

The tibble d1, which has been loaded for you in the R Markdown document, contains the results of the test. It is described in Table 2 below.

Q2 [16% of total mark]

Q2a. The Others are very interested in knowing if there is a correlation between LFB’s and Foxy’s answers. Based on the data in d1, 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. [Suggested word count: 40]

Q2b. 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? [Suggested word count: 120]

Q2c. Calculate and report the standardised coefficient for the linear regression in part Q2b.

Q2d. 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? [Suggested word count: 100]

Q2e. 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). [Suggested word count: 80]

*   *   *

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.

“Sorry for our suspicion. We have been having food problems ourselves," she confides quietly. "We haven't known what to do about it, and are pretty worried."

“Maybe we could help?" LFB offers. "I mean, I don't know much, but perhaps if we compare   problems we'll be able to figure out what's going on. We can tell you what we know about our situation too.”

Foxy nods and they all share the survey data we saw in previous weeks. The Others share their food data that you went over in the tutorials, and everyone agrees that there is a problem.

“The thing is,” Super Size observes (everyone is now very companionable and speaking frankly), “I  fear that this is having a lot of bad indirect effects on everything else. People are more irritable and fighting more, they’re sick more often, and things like that.”

“Do you have any data about that?” LFB asks, curious.

Little Blue thinks, and then nods finally. “We do have a dataset for crime statistics – specifically    thefts – from this year and last year. It’s our New Year in a few days so that gives us two complete years, pretty much.”

Sissily frowns. “I don’t understand what data about crimes like stealing would show us.”

“Let’s see,” Little Blue says. Everyone pauses while she shows the dataset to everyone.

“Hmmm,” says Foxy, examining it. “It’s counting how many thefts of different things – like food or vehicles or whatever – there were in each year. I suppose if food shortages are really a problem,

you’d expect to see more food thefts than other kinds of stealing.”

Kevin leans over to have a look. “What does the category ‘other’ mean?” he asks. “My friend Kevin Clark is a string and got kidnapped a few months ago as a prank. Would that count as ‘other’?”

“Wait, there’s a sentient string in Otherland?” LFB asks incredulously.

Kevin looks up, miffed. "Yes. He’s my best friend,” he says. "What, do you think a string can't be intelligent? Or a guitar, for that matter?"

"No, no, just curious," LFB backpedals hastily. "All good."

Rainbow whispers to her, "We don't understand it either. Just go with it."

Super Size clears his enormous throat. "I don’t think we need to worry too much about the interpretation of what ‘other’ means,” he says tactfully. “The main question is about the food. As long as this dataset is representative then it might be useful.”

“It certainly is,” Little Blue assures everyone.

The data is in the tibble called dc, which has been loaded for you. It is described in Table 3 below.