Report #3, Correlation & Regression

INSTRUCTIONS

Learning Goals:

· Conduct correlation and regression analyses with JASP, to quantify bivariate associations and predictions, respectively.

· Perform. descriptive and inferential bivariate statistics

· Illustrate your analysis with bivariate descriptive statistics and plots.

· Write your conclusions in both APA format and “newspaper” format, which is described, in your text, in posted lectures, and in the posted Hypothesis Testing Guides.

Background Information: The research questions posed below pertain to the experiment studying interpersonal perception presented in class, outlined as follows:

Population: All humans

Sample: Students in PSYC51A

Study Design:

· All subjects are presented 9 IPT scenes which depict real social interactions; all subjects answer a multiple-choice question (3 options) about each social interaction (0-9 correct).  

· Subjects are randomly assigned to either view an audio-visual movie of the social interactions (verbal + lots of non-verbal information) or to read a transcript. (verbal + a tiny bit of non-verbal information)

· All subjects, in both presentation modes, judged scenes with 3 types of social interactions – affiliation, deception, dominance (0-3 correct per type of interaction)

Data: The data file is posted in the Moodle module “Data Analysis Reports – Instructions and Assignments” in a link entitled “IPT Data-REAL”. DO NOT use “IPT Data-PRACTICE” by mistake.

Research questions:

Report #2 analyzed the judgments about about the three types of social interactions - dominance, affiliation, or deception as three levels of one independent variable in a repeated measures design.  The figure on the right is from Report#2, which found that interpersonal p erception accuracy differed significantly for different types of social interactions, F(1.88, 184.07)= 30.406, p <.001, (Greenhouse-Geiser adjusted).  Perceptual accuracy was significantly better for judgments of deception than of dominance and affiliation (post-hoc Bonferroni pairwise comparisons, both p<.001); dominance and affiliation not differ from each other.  

Report #3 treats the same study as an observational design, in which dominance, affiliation, and deception are 3 dependent variables measured for every subject.  Research Question 1 asks whether there is an association between accuracy of social perception (# of IPT questions correct, 0-3) across different types of judgments. The research hypothesis is that better accuracy on one type of social interaction is associated with better accuracy on the other two.   Research Question 2 asks whether people are self-aware of their non-verbal social perception capability, and, if so, can systematic predictions be made?  

Procedures:  

All JASP procedures will have been demonstrated in class (an Echo recording of which is available in case you missed the class), and it is also described in the Achieve Using Statistical Software: A Guide to SPSS, R, JASP, and jamovi , as well as in the online JASP User Guide  link provided in the Moodle “Data Analysis Reports - Instructions and Assignments” module.

When done answering the assigned questions, remove these 2 instruction pages and all the red rubric information interspersed with the questions below, so your report will look like a coherent, systematic investigation of the research questions, rather than like a question-by-question response.  Do not delete the questions. Proofread the report to make sure all the answers are quantitatively consistent, grammatically correct, and use consistent, prose terminology for all constructs and statistical elements.

Convert the finished report to a PDF, upload it to Gradescope, and assign pages.

Research Question 1 (28 Pts): Research Question 1 asks whether there is an association between accuracy of social perception (# of IPT questions correct, 0-3) across different types of judgments. The research hypothesis is that better accuracy on each type of judgment is associated with better accuracy on the other two.  

1.1 (3 pts) List the bivariate associations which must be quantified for Research Question 1.

1.2 (3 pts) List the statistical hypotheses required to address Research Question 1.

1.3       (3 pts) Present JASP scatterplots of the bivariate relationships for Research Question 1. The raw JASP scatterplots are not adequate for full credit, because the visual association of axis labels and graphs is poor.  Note: if you choose to replot the data in another application, the default fit line which JASP includes is not necessary.  

1.4       (3 pts)  How many data points are in the sample?

  How many points appear in the plots?

Why do you think the previous two answers differ?

1.5 (3 pts) Present JASP tables showing the bivariate descriptive statistics for Research Question 1, and their significance levels.  Be sure to select the correct hypothesis test directionality.

1.6      (3 pts) What percent of variance does the association between variables explain, for each pair?

1.7 (10 pts) Write an APA report describing the results.

1.8 Extra Credit (2 pts).  Our survey of non-verbal social perception at the beginning of the semester defined different modalities and types of non-verbal information.  A few examples of non-verbal cues in the text modality include i) ellipsis marks indicating hesitation and ii) the frequency with which speakers directly engage each other.  The audio-visual modality includes information about i) contact between agents via touch or gaze and ii) tone of voice, and other cues.  Report #2 showed that the type of social interaction being judged affects the accuracy of social perception. This can be interpreted as a cause-effect relationship in which different kinds of non-verbal cues affect the accuracy of perception of different types of social interactions, though a weakness of this causal interpretation is that a non-experimental, repeated measures design was used, permitting potential confounding variables to exert an influence.  With this background, how do you explain the pattern of correlations Report #3 found in Research Question 1?  Your answer should take into consideration that correlations never proves causation, but it can help refine a model of causation which has already been statistically supported.

Research Question 2 (21 Pts): Research Question 2 asks whether people are self-aware of their non-verbal social perception capability, and, if so, can systematic predictions be made?  This research question makes the first use of the IPT Confid variable (last column of the JASP data file).  This variable was obtained by asking each subject, after rating 9 IPT scenes, to rate how many of the 9 they thought they had answered correctly.  Our statistical approach is to determine 1) whether there is an association between the actual scores (IPT_Tot ) and the confidence (IPT_Confid), 2) to develop a prediction of  the actual scores from the confidence scores, and 3) to assess the confidence interval of such predictions.

2.1       ( 4 pts) a)  Paste a bar plot of mean actual and self-estimated  IPT scores, with 95% confidence interval error bars in the space below.  Use the  bar plot option in the JASP t test menu. (2 pts))

b)  Paste a scatterplot of actual IPT scores (y-axis) versus IPT confidence ratings (x-axis) in the space below; Make sure the range for both axes is the same, and that the plot area is approximately square.  Note: Like in Research Question 1, there are fewer points on the graph than there are subjects in the sample. (2 pts)

2.2      (4 pts)  Use JASP to perform. a t test to determine if the mean actual and self-estimated IPT scores differ, and fill in the following blanks (no JASP output needed):

A ___-tailed,  _____ t test showed that the actual (M_actual =____) and self-estimated (M_Estimated=____) number of questions correct in the IPT non-verbal social interaction perception test  _are/are not     significantly different, t(df=____)=______, p=_____.

2.3       (3 pts) Use JASP to compute the association between IPT scores and IPT confidence ratings. The statistical hypothesis test should be based on information provided by the scatterplot in question 2.1.  Fill in the following items (no JASP output needed):

A _____ correlation coefficient describing the association between the actual and self-estimated number of IPT questions correct was r (df=___)= ____, which  is/is not    significantly______than zero, p=____.

2.4       (2 pts) Use JASP to compute the regression coeeficients for predicting accuracy of dynamic social perception (IPT_Tot) from the subjective confidence (IPT_Confid).  Then fill in:

The regression equation is: = ____ * IPT_Confid + __.

The standard error of the estimate for predicting IPT_Tot from IPT_Confid ()= ___.

The percentage of variance in  IPT_Tot accouted for by  IPT_Confid= _____  %.

2.5       (3 pts) Use the regression equation to manually compute the predicted values of IPT_Tot for the extreme values of  IPT_Confid (1 and 7) Note: you are not required to show the computation process. (2 pts).  Use the predictions to place the dashed line template onto the scatterplot in question 2.1. (1 pt).  

If IPT_Confid= 1, then IPT_Tot=_______ (1ps)

If  IPT_Confid= 7, then IPT_Tot=  ______(1ps)

2.6       (3 Pts) Compute the 95% confidence intervals around the predicted values of the endpoints of the regression line computed in question 2.5, using: . (2 pts) Note: you are not required to show the computation process. Place the vertical error bar templates on the scatterplot in question 2.1,  in the proper location and resized to represent the 95% Cis (1 pt).

Starting point: CI:  X= 1, 95% CI for Y____to____

Ending point:  CI:  X= 7, 95% CI for Y=____to____

2.7 (2 Pts) Provide a statistical result from this report which supports each of the following statements:

a) Individuals are self-aware of their non-verbal person perception accuracy.

b) On average, people estimate their actual non-verbal person perception accuracy pretty well.