Posted: February 28th, 2023

Statistics

Math 125, Paper One
Spring 2023

(5% of Final Grade)

Overview

For this paper, you will investigate biased questions. After you create your own neutral and

biased questions, you will gather data to examine if the wording you used had an effect on how

people answer.

Here are examples of two different biased questions.1

• According to research from The Journal of the American Medical Association, “stronger

gun policies were associated with decreased rates of firearm homicide, even after

adjusting for demographic and sociologic factors.”2 Do you support or oppose stricter

gun control laws in the United

States?

• The United States Constitution says, “the right of the people to keep and bear Arms, shall

not be infringed.” Do you support or oppose stricter gun control laws in the United

States?

Both questions ask about the person’s ideas about gun control, but they position them

differently. (People are likely to have strong opinions on gun control already; I suggest you

choose a less contentious topic.)

A more neutral version would be “do you support or oppose stricter gun control laws in the

United States?” (Note that this is still a little bit biased. There is a small bias because of the word

order – support is first – so in a real-world situation it would be best to change the order

randomly when you asked people, putting support first half the time and oppose first half the

time. Using the word “stricter” will also potentially influence people’s responses. It’s nearly

impossible to write a perfectly neutral question; you’re just going to do the best you can.)

1 Other examples can be found at: https://www.qualtrics.com/blog/writing-survey-questions/ and

http://danielsroar.weebly.com/uploads/5/3/1/4/5314494/pg_46_biased_or_unbiased_practice_answers

2 From Firearm Laws and Firearm Homicides: A Systematic Review | Firearms | JAMA Internal Medicine | JAMA
Network Information downloaded 6/12/202
(Found via On gun violence, the United States is an outlier | Institute for Health Metrics and Evaluation)

https://www.qualtrics.com/blog/writing-survey-questions/

http://danielsroar.weebly.com/uploads/5/3/1/4/5314494/pg_46_biased_or_unbiased_practice_answers

https://jamanetwork.com/journals/jamainternalmedicine/article-abstract/2582989?utm_campaign=articlePDF&utm_medium=articlePDFlink&utm_source=articlePDF&utm_content=jama.2018.10060

https://jamanetwork.com/journals/jamainternalmedicine/article-abstract/2582989?utm_campaign=articlePDF&utm_medium=articlePDFlink&utm_source=articlePDF&utm_content=jama.2018.10060

https://www.healthdata.org/acting-data/gun-violence-united-states-outlier

Math 125, Paper One
Spring 2023

(5% of Final Grade)

Your paper should include:

A discussion of the questions

Pick a topic that interests you and come up with a neutral yes/no question about it. (If you’d

prefer your question could be support/oppose or another binary choice.)

Give the neutral version and explain why you picked it. You should also explain why you think it is

neutral. (Please pick a question where you think the probability of a “yes” is between 25% and

75%. It’s okay if you turn out to be wrong, but you should aim for that – our statistical methods

work best if the probabilities aren’t close to 0% or 100%.)

Rephrase the question to be biased toward a “yes” or “no” response. (It does not need to be the

case that more than half the people choose that answer; it just needs to be that you think they

would be more likely to choose it than they were before.)

Make sure your question is still about the same basic situation. Discuss:

1) how you developed the biased questions,

2) why you think the question is biased, and

3) what answer it is supposed to be biased towards.

You will get feedback from me and your fellow classmates in the second discussion forum.

A discussion about populations & sampling

Note: Even if you are not going to actually ask people the questions (another option is

given below), pretend that you are for this section. Discuss what population you’d like to

get information from, what type of sampling you’d use, and how you would create such

samples.

Describe the population that you are interested in asking these questions to and why you chose

it. Be sure to use the same population for both questions. This population could be an online one

(for instance, you can use social media). Or it could be a population you interact with at work,

etc.

Math 125, Paper One
Spring 2023

(5% of Final Grade)
Create two separate samples, with 35 people in each. You should be sampling the same

population both times.

Identify the type of sampling technique you selected and explain why you chose it. You should

also discuss whether your sampling technique is likely to give you useful data. Are there any

potential problems with your technique?

Data collection

• Option One (preferred and also more interesting): gather some real-world data.

Ask the people your questions. Thirty-five people should answer your neutral question (this is

your first set of data); thirty-five people should answer the biased question (this is your

second set of data). These should be different people. Record your raw data and include the

raw data in the paper.

• Option Two: work with computer-generated data. In this case, since you’ll have less work

with data gathering, I want you to analyze three sets of data.

Go to https://www.random.org/sequences/ and generate a sequence with smallest value 1

and largest value 50. Look at the first thirty-five responses. Assume all even numbers are

“yes” responses and all odd numbers are “no” responses. Record these responses as your

first set of data and include them in the paper.

Then go to https://www.random.org/integers/ and generate of sequence of thirty-five

numbers where each integer has a value between 1 and 150. Assume all multiples of three

are “yes” responses and all other numbers are “no” responses. Record these responses as

your second set of data and include them in the paper.

Go to https://www.random.org/integers/ Generate a different sequence of thirty-five

numbers where each integer has a value between 1 and 150. Assume all even numbers are

“yes” responses and all odd numbers are “no” responses. Record these responses as your

third set of data and include them in the paper.

https://www.random.org/sequences/

https://www.random.org/integers/

https://www.random.org/integers/

Math 125, Paper One
Spring 2023

(5% of Final Grade)

Presentation of Data

Calculate the percentage of “yes” and “no” responses for each set of data. Give your results in a

relative frequency distribution table.

Pick at least one appropriate way to represent the data sets visually. You can represent each

data set with its own image or combine them into one image, depending on the type of visual

you select. Please do not use a frequency distribution here – you already did that – but any other

appropriate method is fine.

I would suggest using Excel to create your images, since you can cut and paste them into a Word

document. However, you can use other software, if you’d prefer. I’ve used Desmos and

WolframAlpha to create some of the examples in the slides; there are links to other options on

Brightspace. You could also draw one by hand and insert an image of it.

Extra Credit: Include additional appropriate visual representations of your data.

Conclusion

• If you chose Option One: Do you think that the different wording influenced the results?

Explain, based on your data. Either answer could be fine, as long as you explain why your

data support that.

• If you chose Option Two: Do you think that “yes” responses were equally likely in all three

sets of data? Do you think they were equally likely in any pairs of data sets? Explain your

reasoning. There is not necessarily a correct answer, as long as you explain why your data

support your reasoning. You won’t be able to talk about the wording of your questions, since

you didn’t actually gather data based on those questions.

Throughout the paper, you try to show mathematical understanding of the situation.

http://www.desmos.com/calculator

http://wolframalpha.com/

Math 125, Paper One
Spring 2023

(5% of Final Grade)

Other things I will look for when grading:

Spelling/Grammar/Formatting

Your paper should be typed & double-spaced. There is no minimum or maximum length,

provided you include all parts of the assignment.

This is a short paper; use full sentences and proper grammar. If you have any concerns about

these, I suggest you work with the writing tutors, who are available from the Academic Support

Center (https://prepare.ccc.edu/mxvss/).

If you use any outside resources/information, you should cite them. Otherwise you are

technically stealing and may earn a zero on the paper. More information regarding citations can

be found here Plagiarism_one_pager (purdue.edu) and here Plagiarism Overview // Purdue

Writing Lab.

Timeliness/Feedback

This paper will be done in a few parts

Discussion Board 2 Initial Post due, 2/10

You will come up with potential questions and get feedback on them.

First Paper draft due, 2/21

First Paper comments returned, 3/3

Revised First Paper due, 3/10

Your final paper will lose 5 points for every day it is late.

Please upload the draft and final paper to Brightspace by 11:59 PM.

There are links under MODULE TWO → Module Two Discussions & Paper Assignments or you

can go to Assessments → Assignments.

https://prepare.ccc.edu/mxvss/

https://owl.purdue.edu/owl/avoiding_plagiarism/documents/plagiarism_one_pager

https://owl.purdue.edu/owl/avoiding_plagiarism/index.html

https://owl.purdue.edu/owl/avoiding_plagiarism/index.html

Math 125, Paper One
Spring 2023

(5% of Final Grade)

Paper One Rubric

Missing
Not There

Yet
Almost
There

Completely
There

The Questions

Neutral version of question, why it
was chosen, and why it’s neutral

0 3 7 10

Biased version of question, why it’s
biased, in what direction it is
biased

0 5 10 15

Sampling & Data
Description of what the population
is and why it was chosen

0 0 5 10

Correctly identified sampling
technique(s).
Explanation of sampling technique
choice, including rationale.

0 3 7 10

Raw Data 0 0 8 15

Presentation of
data

Percentages correctly calculated 0 0 0 5

Data is represented visually using
an appropriate graph or graphs (up
to 5 additional extra credit point
possible)

0 5 10 15

Conclusion

Did wording appear to have an
influence/did it seem as though
the percentages were different?
Explanation should fit with the
data presented.

0 3 7 10

Draft
Submitted draft on time.
Incorporated comments from draft
into final version.

0 3 7 10

Late work penalty
Loss of 5 point per day for every
day late.

100 points possible