COnducting Planned Comparisons Coursera Quiz
Qn5. Download the file hwreco.csv from the course materials. This file describes a study of three handwriting recognizers (A,B,C) and subjects who were either right-handed or left-handed. The response is the number of incorrectly recognized handwriting words out of every 100 handwritten words. The research questions are how each recognizer fared overall and whether a given recognizer performed better for right-handed or left-handed writers. How many subjects took part in this study?

Qn6. Create an interaction plot with Recognizer on the X-axis and Hand as the traces. How many times, if any, do the two traces cross?

Qn7. Fit Poisson distributions to the Errors of each of the three Recognizer levels and test those fits with goodness-of-fit tests, To the nearest ten-thousandth (four digits), what is the lowest p-value produced by these tests? Hint: To fit a Poisson distribution, use the fitdistrplus library and its fitdist function. Then test the fit with the gotstat function.

Qn8. Use Poisson regression to examine Errors by Recognizer and Hand. To the nearest ten-thousandth (four digits), What is the p-value of the recognizer * hand interaction? Hint: Create a model with glm using family – poisson. Then use the car library and its Anova function with type = 3. Prior to either, set sum-to-zero contrasts for bot recognizer and Hand.

Qn9. Conduct three planned comparisons between left-and right-handed recognition errors within each recognizer, Adjust for multiple comparisons using Holm’s sequential Bonferroni procedure. What is the lowest corrected p-value form such tests? Hint: use the multcomp and lsmeans libraries and the lsm formulation of the right glht function. Because we only have three planned pairwise comparisons, use “non” for the initial multiple comparisons adjustment to avoid correcting for all possible pairwise comparisons. Instead, just find the three planned and as=ye uncorrected p-values and pass them manually to p.adjust with method=”holm”.

Qn10. Which of the following conclusions are supported by the analyses we performed on hwreco.csv? (Mark all that apply)

The handwriting counts seemed to be Poisson-distributed.
There was a significant main effect of Recognizer on Errors
There was a significant main effect of hands on Errors
There was a significant Recognizer * Hand interaction
For recognizer ‘a’ there were significantly more errors for right-handed writers that left handed writers.
For recognizer B, there were significantly more errors for left-handed writers than left-handed writers.
For recognizer C, there were significantly more errors for right-handed writers than left-handed writers. 

Doing Generalized Linear Models
Qn1. Download the file deviceprefssex.csv from the course materials. This file describes the same study as in our deviceprefs.csv file, but now augmented with a column for sex (M,F). It also still contains a column for disability (1,0). The research question is how preference for either touchpads or trackballs differs by disability status and sex. How many subjects took part in this study?

Qn2. Use binomial regression to examine Pref by Disability and sex. To the nearest ten-thousandth (four digits), what is the p-value f the Disability * Sex interaction? Hint: Create a model with glm using family=binomial. The use the car library and its Anova function with type = 3. Prior to either, set sum-to-zero contrasts for both disability and sex.

Qn3. Multinomial regression generalizes binomial regression to dependent variables with more than two categories, so it can handle just two categories as well. Use multinomial regression to examine Pref by Disability and Sex, To the nearest ten-thousandth (four digits), what is the p-value of Disability * Sez interaction? Hint: use the nnet library and its multinom function, The use the car library and its Anova function with type = 3. Prior to either, set sum-to-zero contrasts for both Disability and Sex.

Qn4. Let us examine whether there was a significant preference for touchpads or trackballs within each Disability Se combination. Conduct such exploration using post hoc binomial tests. Adjust for multiple comparisons using Holm’s sequential Bonferroni procedure. What is the lowest corrected p-value produced by such an exploration? Hint: Conduct four separate tests with binm.test. The four tests correspond to the four combinations of Disability and Sex. For each combination, test the sum of rows preferring “touchpad” against all rows having that same Disability Sex combination. Since there are only two devices, a test for touchpad is implicity a test for trackball, and vice versa.

Qn1. What do generalized linear models (GLMs) generalize?

The linear model, which encompasses the ANOVA
The linear model, which is a subset of the ANOVA
The general model, which supersedes the ANOVA
The general model, which is a subset of the ANOVA
None of the above

Qn2. Generalized linear models (GLMs) handled only between-subjects factors.

True
False

Qn3. Poisson regression is an example of a generalized linear model (GLM) with a Poisson distribution for the response and a log link function.

True
False

Qn4. Which of the following is not an example of a generalized linear model (GLM)?

Poisson regression
Binomial regression
Gamm regression
Ordinal logistic regression
All are GLMs

Qn5. The link function in a generalized linear model (GLM) most precisely relates what to what?

Factors to each of the responses
Factors to the  mean of the response
Factors to the distribution of the response
Factors to the error in the response
None of the above

Qn6. Nominal logistic regression is also known as multinomial regression

True
False

Qn7. Multinomial regression with the cumulative logit link function is also know as:

Nominal logistic regression
Ordinal logistic regression
Poisson regression
Binomial regression
   None of the above

Qn8. Poisson regression is often appropriate for analyzing which kind of data?

Error rates
Success percentages
Logarithmic distributions
Rare event counts
None of the above

Qn9. Exponential regression is a special case of which generalized linear model (GLM)

Poisson regression
Binomial regression
Ordinal logistic regression
Gamm regression
None of the above

Qn10. The generalized linear model (GLM) can be used in place of the linear mode (LM) for between-subjects designs.

True
False

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.

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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