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homework assignment 4 – Experiments – Due Tuesday April 6, 11:59 PM
Version History:
Released 2020/3/
This assignment is due Tuesday April 6, 11:59 PM.
Create your homework repository in github classroom: https://classroom.github.com/a/fwYDiNIL. At the time of submission, it should
contain a PDF, Markdown, or html file with the bulk of your answers and a JS or Python file to accompany the last question. Both files
should be named HA4 with the appropriate extension and have your name at the top. You may include other files, e.g., a spreadsheet file,
as supplementary material.
In your PDF, MD, or HTML file, please complete the following problems below. Each problem will specify what should be shown. If your
solution requires multiple calculations and you are using a spreadsheet or other program to help, please clearly label what is going on in
each step in a way that can be seen without interacting with the program.
Example 1: If you use a spreadsheet, each sub-result should have a label next to it explaining what the sub-result is and how it was
calculated, visible in the PDF/MD/HTML, even if you include the spreadsheet file. I should not have to open the spreadsheet file to see what
it is.
Example 2: If you use a script, each sub-result should have a comment above it explaining what it is and what the code does to generate it.
Section A: Experiment Design
For each of the scenar ios A.1 and A.2, describe an experiment that tests the idea in question. Describe:
the independent variables and their conditions in the experiment and your justification/explanation for each (3 pts)
dependent variables and your justification/explanation for each (3 pts)
control variables, random variables, and confounding factors and your justification/explanation for each (5 pts)
the population, how participants would be drawn from it, how many would participate, and how they would be assigned to trials (3 pts)
the type of tasks the participants would perform, where the differences in trials would arise from (e.g., what changes in data?), and
what order the trials would be given in (4 pts)
your data analysis procedure including whether you would prune data points (and why) and what statistical tests you would use to
analyze the collected data (and why) (3 pts)
the limitations of your study, why may it not apply to someone else's similar problem? (4 pts)
If there are multiple possible criteria / interpretations to the scenario, choose one that you think is among the most important, describe what
it is, explain why it is important, and design the rest of the experiment (e.g., tasks, variables) with that particular criteria / interpretation in
mind.
In some cases, your answer may be dependent on information you do not know but could discover in piloting. In those cases, note where
you would pilot and what you would determine from the pilot for your answer.
See lecture slides list statistical tests that can be used for greater than two conditions.
A.1 Preview Text on a Tutorial Site
How much text should be shown to preview an article on a tutorial site?
A.2 "Sweets"
Suppose you're a product manager at a social media company. Your company has just launched a new feature called "sweets" which are
special posts designed for sharing content about your meals. To encourage users to try this new feature, you add a new icon too the default
posting UI. One icon is shaped like candy, the other shaped like a case slice. Which icon is better for encouraging users to try the new
feature?
A.3 Number of Participants (EXTRA CREDIT: 10 pts)
Suppose you are planning a within subjects experiment to determine if there's a meaningful difference in speed between using a finger or a
stylus on a touch interface for a mobile game. You plan to give participants some tutorial-type actions to do on screen. From piloting, you
estimate that drawing with a finger takes an average of 9 seconds to perform the task with a standard deviation of 1.5 seconds. From this
data you are also comfortable with assuming the distribution is normal. You consider a difference in order time of 20% meaningful. How
many participants do you need for your experiment assuming the commonly accepted level of significance and power? How many
participants would you need if a difference of 10% was meaningful?
You may calculate this yourself or use a tool (including online). If you calculate this by hand, include any reference material you used and
describe each step in the calculation. If you use a tool, explain why you chose the tool, what settings you used, and why. Include
screenshots. Also, include the URL if the tool is online. In either case, if you had guidance (e.g., StackOverflow post), cite that guidance.
Section B: "By-Hand" Statistical Analysis
For Problems B.1 & B.2:
1. State what statistical test should be used. (3 pts)
2. Calculate the test statistic. Show your work (10 pts):
evidence/argument of meeting test assumptions
significance (alpha)
degrees of freedom where applicable
the test statistic to be compared again
major intermediary calculation where applicable, e.g., sample mean, sample standard deviationns, observed outcomese, expected
outcomes.
3. State where there is a statistically significant difference. (2 pts)
You may use an existing tool to calculate the sample mean and sample standard deviation (if required), as well as per for m any basic
arithmetic operation (addition, subtraction, multiplication, division, square root, etc.)
Yo u m ay n o t u s e a t o o l g e a re d t owa rd s d o i n g t h e e n t i re s t a t i s t i c a l t e s t fo r yo u. You may however verify your result using a program that
performs the test directly. If you choose to do this, you must still include the sub-results as described above. Note that in class, we used the
Student's t test for both paired and independent unequal variance samples. The latter is often replaced by the Welch's t test in practice, and
thus stats programs may perform the latter. You may choose to do the latter by hand when applicable but if you do so, please make it clear.
The experiments and data described in this section are fictional and for educational purposes only.
B.
A manufacturer of third party gaming controls runs an experiment to compare their new software-assisted button-press detection to the
more traditional standard button-press detection. In the experiment, 20 participants were asked to play a simple test game. The controller
switched between standard mode and software-assisted mode between rounds of the game. The order of trials was randomly set per
participant. Through a series of tasks, a measure of time per round in the game was recorded as follows:
Standard: [27.9, 21.2, 21.4, 19.8, 25.6, 16.1, 28.2, 20.7, 24.0, 22.3, 27.4, 16.8, 22.0, 21.8, 26.4, 19.7, 22.5, 20.4, 23.1, 24.7]
Software-Assisted: [22.7, 29.4, 28.7, 27.5, 28.7, 23.9, 25.6, 23.2, 25.2, 27.6, 23.9, 24.8, 23.9, 23.5, 24.0, 26.0, 22.6, 26.7, 31.0, 28.2]
Is there a significant difference in how long participants took each round between the two modes?
B.2 Email Reading
An HR department is testing the use of emoji in subject lines. The department wants to know if adding an emoji to the subject line results in
more employees opening the email. They randomly select 800 employees for an experiment, 400 of which receive the normal email with a
smile emoji and 400 will receive without. In post-processing the data, a few users weer removed because they left the company during the
experiment period. The data kept indicated that 141 people opened the email of the 395 who saw the emoji and 159 people opened the
email of the 398 who did not see the emoji
Is there a significant difference how people who saw the emoji behaved versus those who did not?
B.3 Bootstrap Confidennce Intervals: Navigation
Designers ask participants to rate how much they like each of three styles for browsing a photo app: Album, Bento-grid, and Carousel. The
tasks were completed by 20, 17, and 21 participants respectively. The following ratings were recorded:
Album: [9.2, 7.1, 7.2, 6.7, 8.5, 5.6, 9.3, 7.0, 8.0, 7.5, 9.0, 5.8, 7.4, 7.4, 8.7, 6.7, 7.5, 6.9, 7.7, 8.2]
Bento: [5.1, 8.0, 7.7, 7.2, 7.7, 5.6, 6.3, 5.3, 6.2, 7.2, 5.6, 6.0, 5.6, 5.4, 5.6, 6.5, 5.0]
Carousel: [5.4, 7.5, 6.1, 4.7, 3.7, 3.9, 7.5, 5.1, 4.0, 5.3, 8.2, 5.2, 5.9, 5.5, 4.5, 3.3, 4.5, 4.7, 5.9, 6.3, 6.4]
a) Calculate 95% bootstrap confidence intervals as described in class. Use 5,000 resamples. You may use javascript or Python, but you
may not use a library method that directly calculates them for you. (You may use libraries for randomization, taking the mean, percentiles,
etc.) Include your code in a separate file. This code does NOT have to follow any specific architecture like MVC. (12 pts)
Tip: If you use Python, use a seed function (e.g., numpy.random.seed ) to set a seed value for the random number generator. This allows
you to get reproducible results even with random calls, making things easier to debug. Unfortunately, no such functionality exists for
Javascript's Math.ranndom()
b) What are the confidence intervals of the conditions (in interval format)? (3 pts)
c) Plot the confidence intervals. (3 pts)
d) What can be inferred from these intervals? (2 pts)
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