Please answer the following questions in essay format. There is no word limit, but your answers do not need to be long. Your answers should be comprehensible to a layperson who does not know anything about hypothesis testing but is familiar with general concepts such as sample, population, probability, probability distribution, degrees of freedom, mean, standard deviation, effect, predictor, variance, continuous and discrete variables, correlation, etc. If it helps, feel free to use concrete examples to aid your explanation. 1. The p-value is a probability, but what exactly is it the probability of? Why do we care if it is below .05 or not? 2. What does it mean with regards to the sample and the population when researchers say that an effect is “not significant”? 3. Why do we need to test if certain assumptions are met for statistical tests? 4. In a non-technical manner, explain the concept of “Type I”, “Type II”, and “Type III” sums of squares in multiway ANOVA and multiple regression. Under which circumstances will the different sums of squares tests yield different results? 5. Dr XY is interested in the hypothesis that looking at cat pictures improves a person’s mood. He has set up an experiment comparing participants’ mood ratings before and after viewing either a cat picture or a control picture. In order to minimise the number of participants needed for the experiment, Dr XY runs a one-way ANOVA with cat picture as a predictor as soon as he has 2 participants. He then re-runs the analysis after each new tested participant and checks if the cat picture effect is significant. After 20 participants, the effect finally comes out significant. Dr XY now writes the data up for publication and sends them to Psychological Science. Is this acceptable? Why/why not? Part 2 – Data analysis 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 who were also present in the lab and were introduced as participants in the same study in terms of how likely they are 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. Does the knowledge that the rated person will hear their rating (and perhaps be hurt) lead participants to give higher ratings? What role does the attractiveness of the rated person play? Does the pity effect disappear for very attractive people? 1Assignment 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 two analyses: 1. A standard multiple regression model with rating condition as a discrete predictor and attractiveness as a continuous predictor 2. 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 two analyses similar? If not, explain (in non-technical terms) why not. Which analysis is more appropriate to the data? Finally, in layperson (non-academic) language describe the results and summarise the answers to the two following questions also given at the end of the scenario paragraph: Does the knowledge that the rated person will hear their rating (and perhaps be hurt) lead participants to give higher ratings? What role does the attractiveness of the rated person play? Does the pity effect disappear for very attractive people? Due date This assignment is due on January 29th at 12 pm and should be submitted as a Word document via myBU (using TurnitinUK).