PSYC51A

Report #2 – t tests & ANOVA

INSTRUCTIONS

Learning Goals:

· Perform. and interpret your first inferential statistical tests om grouped data.

o Conduct 1-sample t tests, both manually and with JASP, to compare levels of an independent variable to chance.

o Use JASP to conduct t tests comparing two levels of an independent variable to each other.

o Use JAPS to conduct one-way ANOVA, to compare multiple levels of an independent variable

o Synthesize results across all analysis to deduce broad conclusions about non-verbal perception.

· Illustrate your analysis with the descriptive statistics and plots obtained in Report #1, revised and improved, if necessary, on the basis of critiques provided by the grading of Report #1.

· 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.

· Analyze the strengths and weakness of your conclusion.

Background Information: You will answer the research questions posed below which pertain to the experiment studying interpersonal perception experiment 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 with objectively definable qualities; 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 scene (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

Procedures:  

All JASP procedures The procedure 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.

Where you are asked to provide descriptive statistics for this report, you may use results from Report#1.  However, before copying them, you should improve them, if necessary, by consulting the grading feedback and the posted answer key for Report #1.

Research Question 1. You will manually perform. a 1-sample t-test of whether performance for each of the 3 types of social judgments studied (dominance, affiliation, deception) differs from chance (guessing, without any information about the IPT scenes). The number of questions expected correct by chance (guessing) in a large population is μ= n*p, where n is the number of questions and p is the probability of getting each question correct by chance. For Research Question 1, n=3 because there are 3 questions and p=1/3 because all IPT scene questions had 3 possible answers, so μ= n*p= 1/3 * 3 = 1 question correct by chance. The sub-parts of Question 1 lead you through the manual calculations.

Research Question 2. Requires using JASP to conduct 1-sample t test of whether performance for each information channel (Transcript, Audio-visual) differs from chance guessing.  Again, the number expected correct by chance (guessing) is μ= n*p, where, n=9 because all subjects answered 9 questions and p=1/3 because all IPT scene questions had 3 possible answers, so μ= n*p= 1/3 * 9 = 3.

Research Question 3. Requires using JASP to conduct an independent groups t test to compare the two information channels to each other (rather than comparing each to chance, like in Question 2).

Research Question 4.  Requires using JASP to conduct a one-way, within-subjects (repeated measures) ANOVA to compare the performance on the three types of social interactions

When done answering the assigned questions, remove these 2 instruction pages and all the red rubric information interspersed with th 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.) Re-read the report at this point 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 (21 pts) As explained in the Background Information, all subjects in both information channel conditions answered 9 IPT questions, so the theoretical population mean number correct by chance (guessing) is μ_Chance=3.  This research question asks:  Do the observed sample means for each information channel – Transcript. and Audio-visual – differ from chance (guessing); the desired false positive error probability is p=0.05.

1.1 (1pt) Insert the table of descriptive statistics from Report 1 for the two information channel conditions.  Be sure to label them adequately (JASP variable names alone are not sufficient), and make any other changes called for by the grading of Report#1.  

· -1 pt if N, M, s missing or wrong for either channel

· -.5 if only JASP variable names used as labels

· Note: policy for labels is that full IV, level, and DV labels must appear either in every individual table/plot or as some kind of a legend associated with the plot

1.2 (2 pt) What are the statistical hypotheses, for each channel?

Transcript.

Audio-visual: -1 pt per missing/wrong hypothesis (deduct if not FULLY correct)

1.3 (3 pt) What is are the critical α level,  directionality, and degrrees of freedom for each channel?

Transcript. α=______, _______-tailed, df=_________

Audio-visual: α=______, _______-tailed, df=_________

· -.5 pt per missing/wrong value

1.4 (2 pt) What are the critical t values, for each channel?

Transcript. t_Obs=______

Audio-visual: t_Obs=______

· -1 pt per channel missing/wrong

1.5 (1 pt) What is the decision rule (same for both channels)

Decision rule: ___t__

· -1 pt if missing/wrong

1.6 (3 pt) What are the mean and standard error for the sampling distributions for chance (guessing) performance, for each channel? Show the formula and result.

Transcript. μ_M=; s_M=  

Audio-visual: μ_M=; s_M=   

· -.5pt per μ_M value missing/wrong

· -.5 pt per channel if s_M formula OR values inserted in formula missing/wrong

· -.5 pt per channel if answer missing/wrong

1.7 (3 pt) Insert histograms for each channel (Make sure to label conditions).  Place the red line representing the sample mean on each histogram.  Scale the normal curve template and superimpose on the histograms to represent the sampling distribution for chance.

· -1 pt if BOTH histograms not present and if missing/wrong

· -.5 pt per sample mean ref line not place properly

· -.5 pt per sampling distribution not scaled/placed properly

· Note: policy for labels is that full IV, level, and DV labels must appear either in every individual table/plot or as some kind of a legend associated with the plot

1.8 (2 pt) What is the observed t value for each channel?  Show the formula and result.

Transcript. t_{Obs_____}_

Audio-visual: t_Obs_____

· -.5 pt per channel if formula OR values inserted in formula missing/wrong

· -.5 pt per channel if answer missing/wrong

1.9 (2 pt) What is the decision, for each channel?

Transcript. Decision:_ _____

Audio-visual: Decision:_ _____

· -.1 pt per channel if missing/wrong

1.10 (2 pt) What is the effect size for each channel? Show the formula and result.

Transcript. Cohen’s d____

Audio-visual: Cohen’s d____

· -.5 pt per channel if formula OR values inserted in formula missing/wrong

· -.5 pt per channel if answer missing/wrong

Research Question 2 (15 pts) This research question is the same as Research Question 1:  Do the observed sample means for each information channel – Transcript. and Audio-visual – differ from chance (μ_Chance=3), with a desired false positive error probability of p=0.05. In this question the test will be performed with JASP rather than manually.

2.1.  (6 pts) Perform. 1-sample t tests for each information channel compared to chance, in JASP.  Be sure to request the effect size, descriptive statistics, and bar plots with 95% confidence intervals.   

In order to perform. these analyses separately on each information channel condition, you will have to create new JASP variables with just the Transcript. IPT_Tot values in one column and just the Audio-visual IPT-Tot values in another column.   Do this by copy-paste operations for each set of values from the original IPT_Tot column to the new columns (as we will demonstrate in class).  Be sure to set up the analysis consistent with the directionality of the research question.

Provide i) the t test output table including effect size (Cohen’s d) (2 pts), ii) a descriptive statistic table (2 pts), iii) bar plots for both conditions with 95% confidence intervals (2 pts).  Put all tables/plots on one page.

If your results do not match what you had found manually in Research Question 1 then you need to examine both procedures and resolve whatever errors caused the discrepancies. 

● -2 if any value in the t table missing/wrong

● -.5 if t table not labelled fully comprehensibly

● -2 if any value in the descriptives table missing/wrong

● -.5 if descriptives table not labelled fully comprehensibly

● -1 pt per missing/wrong bar plot

● -.5 if plots not labelled with full name of conditions, y-axis, and type of error bar

● Note: policy for labels is that full IV, level, and DV labels must appear either in every individual table/plot or as some kind of a legend associated with the plot

2.2 (6 pt) Using the information from your manual and JASP analyses, write one APA report about the primary research question encompassing both channels, including all essential elements.

2.3 (3 pt) Write a non-statistical, newspaper-style. report about the results.

· 1 pt – general description of the non-effect of verbal and positive effect of non-verbal info relative to chance (in other words, a clear reference to the research question)

· 1 pt – some statement conveying significance, in common language

· 1 pt – statement conveying functional impact, in common language

Research Question 3 (17 Pts) This research question compares the effects of Transcript. (written verbal information plus a small amount of non-verbal information) and Audio-visual (audible verbal information with a large amount of non-verbal audible/visible information) channels on the accuracy for perceiving social interactions (number of IPT questions correct).  

It is important to understand that the scenes read/viewed are natural scenes in which 1) the participants did neither knew what aspect of the interaction experimental subjects would be asked judge nor intentionally conveyed information, 2) the verbal content of the Transcript. and Audio-visual conditions give no clues to the correct interpretation of the aspect of the scenes which the subjects had to judge, and 3) chance performance is what would result if subjects guessed the interpretation of the scenes without being exposed them.

3.1 (2 pts) Taking into account analyses of both previous research questions, is a directional or non-directional research hypothesis justified for a direct comparison between conditions? Explain your choice citing previous analyses.

 Keep in mind that a one-tailed hypothesis is more powerful (more likely to find a difference if there really is one, or, equivalently, less likely to produce a false negative conclusion) than a two-tailed hypothesis, so one-tailed should be used if it is justified by previous analyses.

· -1 if directional is missing/wrong

· -.1if explanation does not cite previous results OR is logically inconsistent with results cited

3.2  (1 pt) Convert the research hypothesis to a statistical hypothesis

· -.5 for each member of the paired hypotheses missing or not fully correct

3.3 (8 pts) Do the analysis in JASP and insert i) the t test output including effect size (Cohen’s d) (2 pts),  ii) tables for the assumptions of normality and equal variance (Levene) (2 pts), iii) a descriptive statistic table ( 2 pts), and iv) a bar plot showing both conditions (channels) with 95% confidence intervals (2 pts).  Be sure to set up the analysis to be consistent with your research hypothesis.  Be sure to get all tables/plots on one page.

● -2 if any value in the t table missing/wrong

● -.5 if t table not labelled fully comprehensibly

● -1 for each assumption table missing/wron

● -2 if any value in the descriptives table missing/wrong

● -.5 if descriptives table not labelled fully comprehensibly

● -2 pt if  missing bar plot

● -1 pt of plot present but dat wrong

● -.5 if plots not labelled with full name of conditions, y-axis, and type of error bar

● Note: policy for labels is that full IV, level, and DV labels must appear either in every individual table/plot or as some kind of a legend associated with the plot

3.5 (6 pts) Write an APA-style. report about Research Question 3. The report should contain a final sentence stating weakness in the analysis.

Research Question 4 (22 pts)  In the nonverbal person perception experiment outlined in the Backgroud section, every respondent answered 3 IPT questions about each of 3 aspects of social interactions: the relative dominance (status) of the interacting people, their affiliation (kinship) relations, and their deceptiveness.  The primary research question here is whether the type of interaction judged affects the accuracy of non-verbal interpersonal perception.  The secondary question is how the accuracy for different type of interactions differ.

4.1 (1 pt) Insert the table of descriptive statistics for the three types of social interactions from Report#1.  Be sure to label itadequately (JASP variable names alone are not sufficient), and make any other changes called for by the grading of Report#1.  

· -1 pt if N, M, s missing or wrong for any type of social interaction

· -.5 if only JASP variable names used as labels

4.2 (2 pt) Describe the four steps through the Decision Tree we have been using in class to determine that a 1-way repeated measures ANOVA is the appropriate way to analyze the primary research question.

 Decision Tree Question Answer

-.5 for any question if answer either missing or wrong

4.3 (2 pt) What are the formal null and alternative hypotheses for the primary research question?

-1 for each hypothesis missing or not fully correct

4.4 (8 pts) Perform. a 1-way repeated measures ANOVA in JASP for the primary research question.  When setting up the analysis, be sure to provide descriptive labels for the levels of the IV in the “Repeated Measures Factors” box (this will ensure adequate labeling of the output).  The analysis options should include an estimate of effect size (η²), the a check of the sphericity (equality of variance) assumption and the Greenhouse-Geisser correction if the assumption is violated, a bar plot of the levels of the IV, and post-hoc comparisons among the levels of the IV using the Bonferroni correction for multiple comparisons.  These setup options will have been discussed in class.

Insert i) the Within-subjects ANOVA table, ii) the sphericity check, iii) the bar plot, iv) the post-hoc test table.

· -2 pts if Within-subject ANOVA table missing or if any value is wrong

o -.5 if present but not labeled correctly

· -2 pts if sphericity table missing or if any value is wrong

o -.5 if present but not labeled correctly

· -2 pts if bar plot missing or if any value is wrong

o -.5 if present but not labeled correctly

· -2 pts if post-hoc table missing or if any value is wrong

o -.5 if present but not labeled correctly

· Note: policy for labels is that full IV, level, and DV labels must appear either in every individual table/plot or as some kind of a legend associated with the plot

4.5 (1 pt) Do the ANOVA results indicate a significant effect of the type of interaction judged on the IPT accuracy (1 pt)?  What value from the table backs up your claim?  (1 pt).

· -.5 if “ significant” is missing/wrong

· -.5 if p<.001 is missing/wrong (G-G correction does not have to be mentioned)

4.6 (1 pts) What percent of variance in interpersonal perception accuracy is accounted for by the independent variable (1 pt).  Is this a small/medium/large effect (1 pt)?

· -.5 if η² missing/wrong.  

· -.5 if “medium” missing/wrong

4.6 (1 pt)  Does the ANOVA result justify interpretation of the pairwise contrasts?  Why?  (1 pt)

· -.5 if “Yes” answer is missing/wrong

· -.5 if not say why - because need a significant ANOVA first

4.7 (6 pts) Write an APA report about the results.  It should significance of the overall ANOVA as well the difference between levels.