Assessment 2

PS923 - Methods and Analysis in Behavioural Science

Autumn Term 2020 (updated: 2020-12-17)

      •   This assessment counts for 36% of your overall grade.

      •   Submission Instructions: Submit your solution as one html or pdf document containing both R code, R output, figures, and written out text (i.e., full sentences) to Tabula as “Assessment 2” until Wednesday, 10th February 2021 at 12:00 midday (noon).

      •   Please use RMarkdown to create the document.

      •   Important: Your document should be called YOUR-STUDENT-ID_a2 (followed by the correct file ex-tension). Please also add your student ID to the top of the document. To help ensure anonymous marking, please refrain from using your name in either the document, script, or the file name.

      •   Your text does not need to contain references (i.e., references to scientific papers).

General Guidelines

Please complete the following questions. Your answer to each question should have two separate sections for each question, one immediately after the other.

In the first section, write out your answers using complete sentences, as you might for the results section of a paper. Include descriptive statistics in the text, or in tables or figures as appropriate. Tables and figures should be of publication quality (i.e., fully labelled, etc.). Integrate inferential statistics into your description of the results. Your answers might be short. Given the correctness/appropriateness of the statistical analysis, the first section will play the main role for your mark.

The second section should include the complete R code that you used and its output. Add comments (after a #) to explain what the code does. The code should show all of the commands that you used, enough for me to replicate exactly what you did (I will be copying and pasting code to run it, so make sure that works). You can include figures here that you used to explore the data that you do not wish to include in the first section. I will use the second section to help identify the source of any mistakes. For practical reports and papers you would only submit the first section in the main manuscript.

For an example of such a solution, see the Assignment 1 sheet.

Task 1

People differ in the extent to which they choose risky options (even in important matters like health; be-havioural responses to covid being an example). In this task, we’ll look at monetary choices where the risks differ. In everyday life, while some people choose a standard savings account (reliable but with a low rate of interest), others invest in the stock market (with a greater expected rate of interest, but the where value is more stochastic). It is not that one choice is right or wrong; different people have different perceptions of risk. At a basic level, we might wonder about the extent to which these differences are inherent to individ-uals, or largely (or entirely) formed through experience. This task addresses the question of whether recent experiences influence risk preferences.

The file risk_choices.csv contains experimental data, where each participant was randomly assigned to one of three sets of Treatment: gain, lose or mixed. Each participant was given a series of trials. In each trial, they chose between two lotteries (each of which had two possible outcomes, and where each outcome had a 50% probability of occurring). The two lotteries had the same expected value but the variances of the lotteries differed. For instance, the participants may have a choice between lottery 1, with a 50% chance of gaining £20 and a 50% chance of gaining £40, or lottery 2, with a 50% chance of gaining £10 and a 50% chance of gaining £50. Thus each lottery has the same expected value (£30). The lottery with the higher variance is regarded as the risky choice (lottery 2 in this example). To encourage the participants to express real risk preferences, the choices were incentivized: each lottery was played out after each choice and each participant’s reimbursement was tied to the money they won.

Each participant had to make 48 choices; these are broken into 3 blocks, each of 16 choices. The lottery choices were identical across the 3 treatments in the first and third blocks (though the order within a block was randomised for each participant). In half of the trials in the first and third blocks, the lotteries were between positive values, so the participants won money on those trials. In the other half, the lotteries were between negative values, so they had to lose money in those trials.

The difference between the treatments came in the second block of 16 choices. In the gain treatment, each participant only had choices between positive (win) lotteries in the second block. In the lose treatment, they only had choices between negative (loss) lotteries. In the mixed treatment, half were win lotteries, and half were loss lotteries. The order of trials in each block was randomized separately for each participant, so each individual saw the trials in an order that was uniquely created for them.

The file risk_choices.csv provides the results for 82 participants, in wide format (i.e., one row per partici-pant). The first three characters of the response columns specify the block (b1 is block 1, etc); the remaining characters specify the gamble within a block. Each risky (higher variance) lottery choice is coded as a 1 in the data; the less risky choice is coded as a 0.

Your task is to analyse the data with an ANOVA and address the research question of whether a series of positive (win) or negative (loss) experiences (in the second block) affects the probability of choosing a risky lottery. In other words, are risk preferences stable or affected by recent experiences?

Task 2

How individuals judge the morality of actions is a complicated topic, covering numerous domains, so it is not surprising that different people judge things differently (including whether something is a moral transgression or not). Although many moral transgressions cause suffering to others, some actions only directly affect the individual committing the action (e.g., self-harming), which may affect judgements about the actions. Another complication is that some actions have a greater severity (in magnitude or frequency). In this task, we consider whether the severity of an action combines with the domain of the transgression to influence moral judgements.

It seems intuitive that as the severity of harm to others increases (e.g., bullying more forcefully, or more often), the transgression should be judged more harshly. The extent to which this is true of moral transgressions involving only the one individual is perhaps less clear. For example, if an individual chooses to drink their own urine, does it much matter how much they drink, or how often? One idea is that transgressions that hurt others are judged increasingly harshly as the severity of the action increases in frequency or magnitude, whereas judgements of transgressions that involve only the one individual may not alter as sharply with increased severity.

To test this idea, for each of a series of statements, participants were asked: “How bad was the action?” Responses were provided on a scale of 0 (not bad at all) to 100 (extremely bad). Each statement related to one of two domains of moral transgression (against self or other), and each either had a high or low level of severity (SeverityLevel) relating to the SeverityType (i.e., frequency or magnitude). The examples below show a transgression in each of the cells of the design, with the manipulation of severity shown in square brackets [ ]. Note that participants provided more than one response per cell of the design.

      •   Other & Magnitude: Someone steals a [small/large] amount of money.

      •   Other & Frequency: Someone bullies [one person/several people].

      •   Self & Magnitude: Someone deliberately burns their own leg [lightly/deeply] with a poker.

      •   Self & Frequency: Someone chooses to drink their own urine [once/several times].

The focal hypothesis is that the effect of SeverityLevel is stronger, or only present, for transgressions against others than transgressions against self. The file judgement.csv contains simulated judgement scores (score) of how wrong each of the particular actions were judged to be (each row providing the response of one individual to one question).

Please analyse the data with a repeated-measures (within-subjects) ANOVA. The SeverityType mainly serves as a control variable but should also be considered.

In addition to the statistical analysis, please identify what, if any, caveats you would add to the analysis, in terms of whether these findings are trustworthy, or how future studies of this topic might improve upon this study in addressing the research question (of whether altering the severity of transgressions has the same effect across these two domains).