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Assignment 4: Statistical Analyses

• statistical
• descriptive
• inferential
• correlations
• hci.cs.wisc.edu

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<strong>Assignment</strong> 4: <strong>Statistical</strong> <strong>Analyses</strong><br />

<strong>Assignment</strong> Description<br />

In this assignment, you will practice methods you learned in class for descriptive and<br />

inferential statistical analyses. You will use the data you collected and the scales you<br />

constructed in the previous assignment (<strong>Assignment</strong> 3; Scale Construction) as a basis<br />

for your analysis. The methods I would like you to practice in this assignment are<br />

calculating descriptive statistics for the populations you are studying, correlations<br />

among your scales, and inferential analysis using appropriate t-tests or analyses of<br />

variance. Finally, you will report the findings from your analyses following APA<br />

guidelines. The lecture slides on statistical analysis also provides examples of how to<br />

report results of a correlation or inferential test. The handout provides the list of R<br />

functions that you will need to use to complete the assignment. You can choose to<br />

use JMP to complete the assignment. Please refer to the last two lectures on statistics<br />

for descriptions and example uses of the JMP functions that correspond to those<br />

provided here.<br />

The expected outcome of this assignment is a one-page write-up of the process you<br />

followed in and findings from your analysis following the APA guidelines. Please attach<br />

to your report the .csv data file and R functions you used and their outputs in a .txt<br />

file. If you used JMP, please provide the .jmp data file and the model output as an .rtf<br />

file as attachments. To save the model output in JMP, select Edit > Journal and File ><br />

Export into an .rtf file. Send your submission following the naming convention<br />

“<strong>Assignment</strong>4-StudentLastName.zip.” Further directions are provided on the last page<br />

of this handout.<br />

Resources<br />

The following resources might be useful in completing your assignment.<br />

Related Lectures:<br />

Descriptive Statistics, Correlations, Unpaired and Paired T-tests<br />

Analysis of Variance, Contingency Analysis<br />

R Project Website, Reference Guide, Descriptive Statistics, Correlations, T-tests, ANOVA<br />

JMP Website, Getting Started in JMP, Tutorials<br />

Quick reference to APA guidelines for reporting results from statistical analyses<br />

APA formatting and style guide<br />

<strong>Assignment</strong> submission template<br />

CS/Psych-770 <strong>Assignment</strong> 4 – <strong>Statistical</strong> <strong>Analyses</strong> Page 1 of 7

Step 1. Descriptive Statistics<br />

The first set of analyses you will do with your data is what is called descriptive<br />

statistics. The goal of this form of analysis is to create quantitative summaries of your<br />

dataset. Descriptive statistics inform us on average measurements of a scale or item,<br />

how much these measurements vary across observations, the range of<br />

measurements, and other aspects you might want to know about your data. This form<br />

of analysis also includes creating visual representations of your data as box plots, bar<br />

graphs, pie charts, histograms, and scatterplots. Visual tools help the researcher identify<br />

anomalies, outliers, and trends in data.<br />

R provides a host of methods to conduct descriptive statistics and create visual<br />

representations of your data. The following method from the “psych” package<br />

provides a full list of descriptive statistics for a given dataset.<br />

library(psych)<br />

describe(mydata_scales)<br />

describe.by(mydata_scales, mydata_conditions)<br />

R also provides a host of visualization options. Below are methods for creating some<br />

of the most common forms of descriptive visualizations. You can copy the graphs you<br />

create in R simply by copying them in R and pasting them in your Word Processor.<br />

boxplot(mydata_scales)<br />

hist(mydata_scales\$scale)<br />

plot(density(mydata_scales\$scale))<br />

barplot(table(mydata_scales\$scale))<br />

barplot(table(mydata_conditions, mydata_scales\$scale))<br />

barplot(table(mydata_conditions, mydata_scales\$scale), beside=TRUE)<br />

Step 1 – Study your dataset using descriptive statistics and visualization methods in R or<br />

JMP. Note down any anomalies, outliers, or extreme skews or multimodalities in your<br />

distributions that you can identify using these methods.<br />

CS/Psych-770 <strong>Assignment</strong> 4 – <strong>Statistical</strong> <strong>Analyses</strong> Page 2 of 7

Step 2. Correlations<br />

Next you will study how the scales and items in your data might correlate with each<br />

other. The goal of looking at correlations is to identify relationships between your<br />

measurements and suggest possible causal relationships. For instance, you might have<br />

measured how much people trust a particular kind of technology and how often they<br />

shop online. You might find that these two measures are highly correlated, suggesting<br />

that shopping online and trusting technology might have some relationship or might<br />

be affected by a shared latent variable. These suggestions inform further studies or<br />

analyses of your data. For instance, you might split your population into two groups as<br />

frequent online shoppers and infrequent online shoppers and conduct inferential<br />

statistics to test whether how much people shop has an effect on how much they<br />

trust technology.<br />

The most common measure of correlation between variables is “Pearson's<br />

correlation” calculated by dividing the covariance between the two measures by the<br />

product of their standard deviations. This operation creates an r-value (Pearson<br />

product-moment correlation coefficient), ranging from -1 to 1 where -1 represents a<br />

strong negative relationship, 0 represents no relationship, and 1 represents strong<br />

positive relationship between the two variables. However, we cannot make a<br />

conclusive statement on the relationship between these variables simply by looking at<br />

the r-value, because the r-value is extremely sensitive to the data distribution and<br />

population size. We can, however, conduct a significance test to whether a correlation<br />

is significant given its data distribution and population size. Significant tests produce<br />

reliable results with sample sizes above 50.<br />

R provides methods to calculate correlations and significance tests. Below are<br />

commands that will help you calculate r-values and p-values for significant-testing.<br />

cor(mydata_scales, use="complete.obs", method="pearson")<br />

library(Hmisc)<br />

rcorr(as.matrix(mydata_scales), type=”pearson”)<br />

Step 2 – Identify correlations among your scales using R or JMP. Report high correlations<br />

with r-values and p-values.<br />

CS/Psych-770 <strong>Assignment</strong> 4 – <strong>Statistical</strong> <strong>Analyses</strong> Page 3 of 7

Step 3. Inferential Statistics<br />

The final step in this assignment is to test hypotheses about your data using inferential<br />

tests. You will be using these tests to identify how your categorical variables affect your<br />

scales or response variables. As we discussed in class, what inferential test you should<br />

be using will depend on your experimental design. The decision map below will help<br />

you choose the appropriate test for your purposes.<br />

One-way ANOVA<br />

One-way repeated<br />

measures ANOVA<br />

Unpaired t-test<br />

Paired t-test<br />

2+ independent<br />

samples<br />

2+ dependent<br />

2 independent<br />

2 dependent<br />

Single-<br />

Factor<br />

Design<br />

Factorial<br />

Within<br />

participants<br />

Mixed-model<br />

Between<br />

Multi-way repeated<br />

ANOVA<br />

Multi-way<br />

The first step in conducting your inferential analysis is to determine your null and<br />

alternative hypotheses. A null hypothesis suggests that your independent variables do<br />

not have any effect on your dependent variables or response variables. An alternative<br />

hypothesis suggests an effect. In your analysis, you will have to identify the “direction”<br />

of the effect suggested by your alternative hypothesis. For instance, if you have a<br />

univariate design with 2 independent samples, your alternative hypothesis has to<br />

identify whether the treatment condition in your independent variable will cause an<br />

increase, decrease, or simply a change in your dependent variable. If the alternative<br />

hypothesis suggests an increase, this analysis will use a one-tailed unpaired t-test.<br />

R provides all the tools you will need to conduct inferential tests. Below is a list of<br />

functions that you can use to conduct these tests. Alternatively, you can use JMP.<br />

Examples of the use of these functions and descriptions and examples of<br />

corresponding JMP tests are provided in the related lectures. If your experiment has a<br />

multivariate design (i.e., more than one factors), you also need to conduct post-hoc<br />

analyses to make pairwise comparisons across conditions.<br />

Unpaired, one-tailed t-test — Use to compare two between-participants conditions<br />

where the alternative hypothesis suggests that the treatment condition causes an<br />

increase in the dependent variable:<br />

t.test(mydata_scales~mydata_conditions, alternative="less", paired =<br />

FALSE, var.equal=TRUE, conf.level=.95)<br />

Paired, one-tailed t-test — Use to compare two within-participants measurements<br />

(e.g., before stimuli and after stimuli) where the alternative hypothesis suggests that<br />

the stimuli causes an increase in the dependent variable:<br />

t.test(mydata_scales\$measurement1, mydata_scales\$measurement2,<br />

alternative="less", paired=TRUE, conf.level=0.95)<br />

One-way, between-participants ANOVA — Use to compare more than two<br />

between-participants samples. Tukey’s HSD test can be used to conduct pairwise<br />

comparisons between conditions.<br />

model = aov(mydata_scales~mydata_conditions, data=dataFile)<br />

summary(model)<br />

TukeyHSD(model)<br />

CS/Psych-770 <strong>Assignment</strong> 4 – <strong>Statistical</strong> <strong>Analyses</strong> Page 4 of 7

One-way, within-participants ANOVA — Use to compare more than two withinparticipants<br />

samples. Tukey’s HSD test can be used to conduct pairwise comparisons<br />

between conditions; in this case, using “generalized linear models.”<br />

model = aov(mydata_scales~mydata_conditions+Error(Subject/<br />

mydata_conditions), data=dataFile)<br />

Step 4. Reporting Using APA Guidelines<br />

The APA (American Psychological Association) provides a style guide for academic<br />

writing in social sciences and HCI research follows these guidelines. In this assignment,<br />

you will write a report of your findings that resembles the “Results” section of an<br />

empirical paper and follow these guidelines. The “Resources” section of this handout<br />

provides links to APA style guides. The lecture slides on statistical analysis also provides<br />

examples of how to report results of a correlation or inferential test.<br />

Step 4 – Write up your results from all three sets of analyses you applied to your data.<br />

Follow APA guidelines for reporting statistical results and creating graphics.<br />

CS/Psych-770 <strong>Assignment</strong> 4 – <strong>Statistical</strong> <strong>Analyses</strong> Page 6 of 7

Final Step. Write-Up<br />

Write a one-page report of your results. This report should resemble the “Results”<br />

section of an empirical paper and follow the assignment template. For examples on<br />

reporting statistical tests and results, you can refer to the links provided on the first<br />

page of this handout, the slides for lectures on statistics, and the papers we have<br />

discussed in class as examples. Be sure to follow in your submission the naming<br />

convention “<strong>Assignment</strong>4-StudentLastName.zip” and include the following:<br />

In your write-up as a .docx file;<br />

• Results from descriptive analyses,<br />

• Results from correlational tests,<br />

• Results from inferential tests,<br />

• Tables or figures supporting descriptive and inferential tests,<br />

As appendices included in the .zip file;<br />

• If you use R, the .csv data file and a .txt file with a list of the R commands you<br />

ran and the outputs.<br />

• If you use JMP, the .jmp data file and a single .rtf file with the outputs from your<br />

tests.<br />

E-mail your assignments to [email protected].<br />

Grading Criteria (5 points total)<br />

Calculating descriptive statistics (0.5/0.5)<br />

Calculating correlations (0.5/0.5)<br />

Conducting inferential tests (2/2)<br />

Determining the appropriate test for the required analysis (0.5/0.5)<br />

Conducting appropriate tests, pairwise comparisons, and model simplification<br />

(if necessary) (1/1)<br />

Creating graphics to visually support the results (0.5/0.5)<br />

Following APA guidelines in reporting all results (1/1)<br />

Quality of the report (1/1)<br />

CS/Psych-770 <strong>Assignment</strong> 4 – <strong>Statistical</strong> <strong>Analyses</strong> Page 7 of 7

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<strong>Assignment</strong> 4: <strong>Statistical</strong> <strong>Analyses</strong> <strong>Assignment</strong> Description In this assignment, you will practice methods you learned in class for descriptive and inferential statistical analyses. You will use the data you collected and the scales you constructed in the previous assignment (<strong>Assignment</strong> 3; Scale Construction) as a basis for your analysis. The methods I would like you to practice in this assignment are calculating descriptive statistics for the populations you are studying, correlations among your scales, and inferential analysis using appropriate t-tests or analyses of variance. Finally, you will report the findings from your analyses following APA guidelines. The lecture slides on statistical analysis also provides examples of how to report results of a correlation or inferential test. The handout provides the list of R functions that you will need to use to complete the assignment. You can choose to use JMP to complete the assignment. Please refer to the last two lectures on statistics for descriptions and example uses of the JMP functions that correspond to those provided here. The expected outcome of this assignment is a one-page write-up of the process you followed in and findings from your analysis following the APA guidelines. Please attach to your report the .csv data file and R functions you used and their outputs in a .txt file. If you used JMP, please provide the .jmp data file and the model output as an .rtf file as attachments. To save the model output in JMP, select Edit > Journal and File > Export into an .rtf file. Send your submission following the naming convention “<strong>Assignment</strong>4-StudentLastName.zip.” Further directions are provided on the last page of this handout. Resources The following resources might be useful in completing your assignment. Related Lectures: Descriptive Statistics, Correlations, Unpaired and Paired T-tests Analysis of Variance, Contingency Analysis R Project Website, Reference Guide, Descriptive Statistics, Correlations, T-tests, ANOVA JMP Website, Getting Started in JMP, Tutorials Quick reference to APA guidelines for reporting results from statistical analyses APA formatting and style guide <strong>Assignment</strong> submission template CS/Psych-770 <strong>Assignment</strong> 4 – <strong>Statistical</strong> <strong>Analyses</strong> Page 1 of 7

• Page 2 and 3: Step 1. Descriptive Statistics The
• Page 4 and 5: Step 3. Inferential Statistics The
• Page 6 and 7: Step 4. Reporting Using APA Guideli

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