Take-home assignment: Linear Mixed Models

 Task: Like the unit, this assignment consists of two parts: In the first part, you will reflect on the meaning of test statistics and how to interpret them. In the second part, you will perform, report, and interpret a series of statistical analyses, taking your conclusions from Part 1 into account. Part 1: Critically evaluate the following statement from Benjamin et al. (2017): The default P-value threshold for statistical significance for claims of new discoveries should be changed from 0.05 to 0.005. Explain why the authors believe such a change is necessary at this point in time, and give several arguments for and against the proposal. Your statement should reflect your own position on the issue, and should indicate whether you are planning to use the 0.005 pthreshold for your own research (or apply it to existing literature). Your words should be completely your own, and must not overlap with either Benjamin et al. (2017), blog posts and internet commentary, or other students’ work (although you may of course consult these sources and talk to your fellow students). (1000 words maximum) Part 2: Conduct and report the appropriate statistics for the data set you are given based on the scenario below as one would for an academic journal. Be sure to report the means, group sizes, and standard deviations of the discrete variables in a table and to make a plot of all the significant effects. Scenario: A group of researchers (although the data are made up, this is based on a real study that was just published in Psychological Science: Joel, Teper, & MacDonald, 2014) wants to investigate how likely people are to agree to date unattractive people out of pity. In order to do this, they asked 40 heterosexual female participants (raters) to rate 20 male confederates (rated) of different attractiveness. The confederates were also present in the lab and were introduced as participants in the same study. Participants rated the confederates in terms of how likely they would be to go on a date with each man (on a scale from 0 = extremely unlikely to 100 = extremely likely). For half of the rated confederates, the confederate had left the room when participants gave the rating to the experimenter (absent condition). For the other half of the rated confederates, the confederates were present in the room and listening when the participants gave the rating to the experimenter (present condition). In order to see if attractiveness played a role, the researchers also obtained attractiveness ratings (from 0 = extremely unattractive to 10 = extremely attractive) for the 20 photographs from a different group of participants. Instructions: Conduct and report the appropriate statistics using the data provided as one would for a Results section an academic journal. References are not necessary. Be sure to report the means, group sizes, and standard deviations of the discrete variables in a table and to make a plot of all the significant effects. Perform and report three sets of analyses, each testing all of the three relevant null hypotheses about the fixed effects (There is no main effect of rating condition; there is no main effect of attractiveness; there is no interaction between rating condition and attractiveness): 1. Two repeated-measures Analysis of Variance, one over raters (F1) and one over rated individuals (F2) with rating condition and attractiveness as discrete predictors. 2. A standard multiple regression model with rating condition as a discrete predictor and attractiveness as a continuous predictor (ignoring the random effects of rater and rated individual). 3. A linear mixed model with rating condition as a discrete predictor and attractiveness as a continuous predictor and random intercepts for both participant and rated person (as we want to be able to generalise the results beyond the 40 raters and the 20 rated individuals). Are the results of the three analyses similar? If not, explain (in non-technical terms) why not. Which analysis is more appropriate to the data? In layperson (non-academic) language describe the results and summarise the answers to the following questions referring to the three hypotheses tested: Does the knowledge that the rated person will hear their rating (and perhaps be hurt) lead participants to give higher (or lower) ratings (pity effect)? Is the date rating affected by the attractiveness of the rated person? Does the pity effect disappear (or maybe get stronger) for very attractive people? Explain how the results of these analyses affect your interpretation. (2000 words maximum) Data: Each student will receive an individual data set. The data will be available in the file labelled Assignment2_yourname.csv on Brightspace, where “yourname” is your surname. Perform the analyses on all the data points provided and do not remove outliers or transform the data. Please make sure that you analyse your correct data set, as a submission using an incorrect data set will be given a mark of 0%. Reading: Core materials: Dienes, Z. (2008). Understanding Psychology as a Science. Basingstoke: Palgrave Macmillan Fox (2015). Applied Regression Analysis and Generalised Linear Models (3rd edition); Learning Outcomes Assessed: This individual assignment contributes to the assessment of the following Intended Learning Outcomes: • Knowledge of advanced statistical analyses (including linear mixed models etc.); • Ability to critically evaluate the use and interpretation of a test for the specific research design; • Knowledge of, and ability to screen for, common errors made using inferential statistics and their causes • Ability to perform these tests using statistical software; • Ability to disseminate the results from the statistical tests in an appropriate written format.