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ATHK1001 Assignment 1
Assignment
Late penalties of 5% per day apply.
• Online submission: All submissions are to be
made online via the ATHK1001 Canvas website.
Submissions will be checked for plagiarism. You
may not use AI tools to assist you.
• Word length: 750 words across all questions
(except references in Question 13). Penalties will
apply to papers that exceed this limit by more
than 10%.
• Total marks: 60 (15% of total grade for class)
Background to Assignment 1
• A useful skill when dealing with data is being able
to estimate plausible answers to questions you
don’t know the answer to.
• A strategy for doing this is embodied by what are
known as “Fermi problems.”
– A common example is “How many piano tuners are
there in Chicago?”
– Most people have no idea, but perhaps they can
answer if we turn it into a Fermi problem.
Fermi problems
• Could breakdown “How many piano tuners are there in
Chicago?” into a series of sub-question you may be
better at estimating:
– How many people are there in Chicago? How many
families? What proportion of families have a piano?
How often does a piano have to be tuned? How long
does it take to tune a piano? How many days a year
would a piano tuner work?
• Ärlebäck & Albarracín (2019) reviewed evidence that
Fermi problems are used in science education, but
found no studies testing if they led to better estimates.
• We tested this in the experiment you did in Week 2.
Our experiment
• You answered nine question setup as Fermi problems
(i.e., with sub-questions) and nine as Non-Fermi
problems.
• Two sets of questions were used each with a Fermi
problem version (i.e., target question with sub-
questions) and a Non-Fermi version (i.e., target
question with no sub-questions).
– A “multiplicative” set of questions in which multiplying the
sub-questions helps answer the target question (e.g.,
“How many piano tuners are there in Chicago?”)
– An “additive” set of questions in which adding the sub-
questions helps answer the target question (e.g., “What is
the total military budgets of the members of the UN
Security council (USA, Russia, China, UK, France), in
millions of $US?”)
Two groups
• Participants were randomly assigned to one of two
conditions:
– The “Multiplicative condition” in which participants’ Fermi
problems came from the multiplicative set of questions,
and their Non-Fermi problems came from the additive set
of questions.
– The “Additive condition” in which participants’ Fermi
problems came from the additive set of questions, and
their Non-Fermi problems came from the multiplicative set
of questions.
• So everyone answered both sets questions, had both Fermi
and Non-Fermi problems, and the control group for each
condition came from the other condition.
• We also randomly varied the order of questions, but we did
not analyse the effects of order.
What a trial looked like
Hypotheses
• Hypothesis 1: Mean accuracy for Fermi problems will be
different than for Non-Fermi problems. We predict accuracy will
be greater for Fermi problems.
• Hypothesis 2: Mean accuracy for Fermi problems will not differ
between “Multiplicative condition” and the “Additive
condition”.
• Hypothesis 3: Mean accuracy for Non-Fermi problems will not
be differ between “Multiplicative condition” and the “Additive
condition”.
• Hypothesis 4: Accuracy for Fermi problems will correlate with
accuracy for Non-Fermi problems.
• How we test such hypotheses will be covered in lectures in
Week 4 and 5, and in Week 5 tutorials.
Participants
• A number of students who did the experiment
are not part of the data set.
– Some students did not have their data
correctly recorded.
– Some students did not complete enough of
the experiment.
– Some students did not consent to having
their data included.
• This left a data set of 197 ATHK1001 students.
Results
• Data file “Assignment1_dataset.xls” has been put on our
Canvas website. Each line represents a participant.
• First column “id number” is an arbitrary ID number
generated by the computer.
• The second “condition” column represent an
independent variable
– 1 indicates “Multiplicative condition”
– 2 indicate “Additive condition”.
• The column “Accuracy for Fermi problems” is the
participant’s accuracy on their Fermi problem questions.
• The column “Accuracy for Non-Fermi problems” is the
participant’s accuracy on their Non-Fermi problem
questions.
How is accuracy calculated
• How the two dependant variables are calculated is critical.
• We do not expect Fermi problems to lead people to estimate the
exact right answer, often the goal is just to estimate the answer to
the right order of magnitude (power of 10).
– E.g., any answer between 100 and 999 has an order of magnitude of 2.
• For each students’ set of Fermi problems how many answer had
the right order of magnitude was counted and divided by the
number of Fermi problems they answered.
– This is “Accuracy for Fermi problems” and is a proportion between 0.0 and
1.0.
• For each students’ set of Non-Fermi problems how many answer
had the right order of magnitude was counted and divided by the
number of Non-Fermi problems they answered.
– This is “Accuracy for Non-Fermi problems” and is a proportion between 0.0
and 1.0.
Your task
• Use Excel (or similar program) to analyse this data and
determine if the hypotheses have been supported.
• There are 13 questions to answer, each worth a
specified number of marks.
• Answer these questions with complete sentences
(except where a graph is requested), but do not repeat
the questions themselves. Don’t use tables.
• Some questions ask you to give interpretations, just try
to use your judgement and the tools you have been
given in the course to answer as well as you can.
– There are not necessarily single correct answers to such
questions.
Readings
• You should read at Ärlebäck and Albarracín (2019) so
as to understand what Fermi problems are and how
they have been used.
– This article can be found in the library but will be available
on the “Reading list” accessible from ATHK1001’s Canvas
page.
• You do not need to read anything else on this topic in
order to be able to write an excellent assignment.
– You can read more widely if you wish. However, if you use
words or ideas from something you read then you must
properly cite it.
Formatting recommendations
• Our preference is that you use the font “Times
New Roman”, 12-point size, and double-space
all the lines.
– Indent the beginning of each paragraph using one
tab space.
• You should use APA style referencing and
citations, but we will accept other styles.