## Doing Factorial ANOVAs

Qn20. Download the file socialvalue.csv from the course materials. This file describes a study of people viewing a positive or negative film clip before going onto social media and then judging the value of the first 100 posts they see there. The number of valued posts was recorded. Examine the data and indicate what kind of experiment design this was.

``````- A 2x2 between-subjects design with factors for clip (positive, negative) and social (Facebook, Twitter).
-A 2x2 within-subjects design with factors for clip(positive, negative) and social (facebook, Twitter).
-A 2x2 mixed factorial design with a between-subjects factor for clip (positive, negative) and a within-subjects factor for social (Facebook, Twitter).
- None of the above
``````

Qn21. How many subjects took part in this experiment?

Qn22. To the nearest hundredth (two digits), on average how many posts out of 100 were valued for the most combination of clip and social?

Qn23. Create an interaction plot with social on the X-axis and clip as the traces. Do the lines cross?

``````Yes
No``````

Qn24. Create an interaction plot with clip on the X-axis and social as the traces. Do the lines cross?

``````Yes
No``````

Qn25. Conduct a factorial ANOVA to test for any order effects that the presentation order of the clip factor and/or the social factor may have had. To the nearest ten-thousandth (four digits), what is the p-value for the ClipOrder main effect? Hint: Use the ez library and its ezANOVA function. Pass both ClipOrder and Socialorder as the within parameter using a vector created with the “c” function.

Qn26. Conduct a factorial ANOVA on valued by clip and social. To the nearest hundredth (two digits), what is the largest F statistic produced by such a test? Hint: use the ez library and its function. Pass both clip and social as the within parameter using a vector created with the “c” function.

Qn27. Conduct two planned pairwise comparison using paired-samples t-tests. The first question is whether on Facebook, the number of valued posts was different after people saw a positive fil clip versus a negative film clip. The second question is whether on Twitter, the number of valued posts was different after people saw a positive film clip versus a negative film clip. Assuming equal variances and using Holm’s sequential Bonferroni procedure to correct for multiple comparisons, what to within a ten-thousandth (four digits) is the lowest p-value from these tests? Hint: use the reshape2 library and its dcast function to make a wide-format table with columns for subject and the combination of social* clip, and then do a paired-samples t-test between columns with the same social level.

Qn28. Which of the following conclusions are supported by the planned pairwise comparisons just conducted? (Mark all that apply)

``````On Facebook, people valued significantly more posts after seeing a positive film clip than a negative film clip
On Facebook, people valued significantly more posts after seeing a negative film clip than a positive film clip.
On Twitter, people valued significantly more posts after seeing a positive film clip than a negative film clip,
On Twitter, people valued significantly more posts after seeing a negative film clip than a positive film clip.
``````

Qn29. Continue using the file socialvalue.csv from the course materials. Conduct a nonparametric Aligned Rank Transform procedure on Valued by Clip and Social. To the nearest hundredth (two digits). What is the largest F statistic produced by this procedure?

``````Hint: use the ARTOOL library and its art function with the formula.
Valued ~ Clip * Social + (1|Subject)``````

The above formular expression indicates that subject is to be treated as a random effect.

Qn30. Pairwise comparisons among levels of clip and among levels of social could be conducted using the following code, but these are unnecessary after our main effects tests because each of these factors only has two levels.

``````library(lsmeans)
lsmeans(artlm(m,”clip”), pairwise ~ Clip)
lsmenas(artlm(m, “social”), pairwise ~ social)``````

True
False

Qn31. Conduct interaction contrasts (i.e difference-of-differences) to discover whether the difference in the number of valued posts after viewing a negative clip vs. a positive clip on Facebook was itself different that that same difference on Twitter. To the nearest hundredth (two digits), what is the chi-square statistic from such a test? Hint: use the phia library and its testInteractions function with the artlm function.

Qn32. The difference in the number of valued posts after people saw negative film clip vs positive film clips in the Facebook condition is significantly different from that difference in the Twitter condition. An interaction plot makes it clear that the difference in valued posts was much greater in the Facebook condition than in the Twitter condition, with positive film clips resulting in more valued posts.

## Doing factorial ANOVA Coursera quiz answers

Qn1. Download the file avatars.csv from the course materials. This file describes a study in which men and women were shown a virtual human avatar that was itself either male of female, and asked to craft a persona and write a day-in-th0life scenario for that avatar. The number of positive sentiments in either description were summed by a blind panel of judges. Examine the data and indicate what kind of experiment design this was.

• A 2 x 2 between-subjects design with factors for sex (M,F) and Avatar (M,F)
• A 2 x2 within-subjects design with factors for ex (M,F) and Avatar (M,F).
• A 2 x 2 mixed factorial design with a between-subjects factor for sex (M,F) and a within-subjects factor for Avatar (M,F).
• None of the above

Qn2. How many subjects took part in this experiment?

Qn3. To the nearest hundredth (two digits), on average how many positive sentiments were expressed for the most positive combination of sex and avatar?
Qn4. Create an interaction plot with Sex on the X-axis and Avatar as the traces. Do the lines cross?

``````Yes
No
``````

Qn5. Create an interaction plot with Avatar on the X-axis and Sex as the traces. Do the line cross?

``````Yes,
No
``````

Qn6. Conduct a factorial ANOVA on positives by sex avatar. To the nearest hundredth (two digits), what is the largest F statistic from such a test? Hint: Use the ez library and its exANOVA function. Pass both Sex and Avatar as the between parameter using a vector created with the “c” function.

Qn7. Which effects are statistically significant in the factorial ANOVA of positives by sex and avatar? (Mark all that apply)

``````Main effect of sex
Main effect of Avatar
Sex * Avatar interaction
None of the above
``````

## Planned Pairwise Comparisons

Qn8. Conduct two planned pairwise comparisons using independent samples t-tests. The first question is whether women produced different numbers of positive sentiments for male avatars versus female avatars. The second question is whether men produced different numbers of positive sentiments for male avatars versus female avatars. Assuming equal variances and using Holm’s sequential Bonferroni procedure to correct for multiple comparisons, what to within a ten-thousandth (four digits) is the lowest corrected p-value from these tests? Hint: You will need conjunctions with ampersands (&) to select the necessary rows for your t.test functions.

Qn9. Which of the following conclusions are supported by the planned pairwise comparisons just conducted? (Mark all that apply.)

``````Women made significantly more positive sentiments about male avatars that they did female avatars
Women made significantly more positive sentiments about female avatars than they did male avatars
Men made significantly more positive sentiments about male avatars than they did female avatars
Men made significantly more positive sentiments about female avatars than they did male avatars
None of the above
``````

Qn10. Download the file notes.csv from the course materials. This file describes a study in which iphone and Android smartphone owners used their phone’s built-in note-taking app and then switched to an add-on third-party app, or vice-versa. The number of words they wrote in their notes apps over the course of the week was recorded. Examine the data and indicate what kind of experiment design this was

``````A 2 x 2 between-subjects design with factors for phone (iPhone, Android) and Notes (Built-in, Add-on).
A 2 x 2 **within-subjects design with factors** for Phone(iPhone, Android) and Notes (Built-in, Add-on)
A 2 x2 mixed factorial design with a between-subjects factor for Phone (iPhone, Andoid) and a within-subjects factor for Notes (Built-in, Add-on).
None of the above``````

Qn11. How many subjects took part in this experiment?

Qn12. To the nearest hundredth (two digits) on average how many words were record with the most heavily used combination of phone and notes?

Qn13. Create an interaction plot with Phone on the X-axis and Notes as the traces, Do the lines cross?

``````Yes
No``````

Qn14. Create an interaction plot with notes on the X-axis and Phones as the traces. Do the lines cross?

``````Yes
No
``````

Qn15. Conduct a factorial ANOVA to test for any order effect that the presentation order of the Notes factor may have had. To the nearest ten-thousandth (four digits), what is the p-value for the order factor from such a test? Hint: use the ez library and its ezANOVA function, passing one between parameter and Order as the withing parameter.

Qn16. In our test of possible order effects, Mauchly’s test of sphericity is irrelevant because our within-subjects factor only has two levels, which cannot present a sphericity violation.

``````True
False
``````

Qn17. Conduct a factorial ANOVA on words by phone and Notes. To the nearest hundredth (two digits), what is the largest F statistic produced by such a test? Hint: use the ez library and its ezANOVA function, passing one between parameter and on within parameter.

Qn18. Conduct two planned pairwise comparisons using paired-samples t-tests. The first question is whether iPhone users entered different numbers of words using built-in notes apps versus the add-on notes app. The second question is whether Android users entered different numbers of words using the built-in notes app versus the add-on notes app. Assuming equal variances and using Holm’s sequential Bonferroni procedure to correct for multiple comparisons, what to within a ten-thousandth (four digits) is the lowest p-value from these tests? Hint: use the reshape2 library and its dcast function to make a wide-format table with columns for subject, phone, Add-on, and Built-in, and then within each phone type, do a paired-samples t-test between the Add-on and built-in columns.

Qn19. Which of the following conclusions are supported by the planned pairwise comparisons just conducted? (Mark all that apply)

``````Android users entered significantly more words using the built-in notes app than theadd-on notes app.
Android users entered significantly more words using the add-on notes app than the built-in notes app.
iPhone users entered significantly more words using the add-on notes app than the built-in notes app.
None of the above

``````

## Understanding Factorial Designs

Qn1. Interaction effects explore which of the following?

``````-How the response changes as factors change
- How the response is affected by levels of a factor
- How the response is differently affected by levels of one factor based on levels of another factor.
- How the response is differentially affected by levels of one factor depending on the different levels of the factor can take on
- None of the above
``````

Qn2. Which of the following is a description of a 3x2 factorials design?

• Comparison of task completion times using each of three drawing tools while at a standing desk and a sitting desk
• Comparison of task completion times while working at one of three desk types with one of the two drawings tools.
• Comparison of task completion times using drawing tool at a desk
• Comparison of task completion times using a drawing tool at a standing or sitting desk three times
• Comparison of task completion times using a drawing tool at a standing or sitting desk

Qn3. Parallel lines on an interaction plot often indicate the presence of a statistically significant interaction effect

• True
• False

Qn4. Assuming small variances in comparison to means, which effects are most likely present given the following interaction plot?

• A significant main effect of Numbers
• A significant main effect of letters
• A significant numbers x Letters interaction

Qn5. Assuming small variances in comparison to means, which effects are mostly likely present given the following interaction plot

• A significant main effect of numbers
• A significant main effect letters
• A significant numbers x letters interaction

Qn10. The aligned rank transform (ART) generally refers to which procedure?

• For each main and interaction effect, align the data and conduct an ANOVA
• For each main and interaction effect, rank the data and conduct ANOVA
• For each main and interaction effect, align the data, rank it, and conduct an ANOVA

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