Assignment 1 Brief
MATH3831: Statistical Methods for Social and Market Research
UNSW Sydney
Term 2, 2025
Last updated: June 8, 2025
Summary of Information
Assessment Title: Estimating the Size of Your Vocabulary
Weighting: 10%
Due Date: Monday of Week 7, 5:00 PM
Type: Project
Group work: No
Length: No more than 3000 words.
Feedback Details: Feedback will be given in the form of marks and comments from
academic staff.
Aligned CLOs: 1, 2, 3
Assessment Description
Rationale
In this assignment, you will practice sampling design and analysis techniques.
Task Description
Use survey sampling methods to estimate the size of your vocabulary using a dictionary.
There is more than one way to do this. For example, if you know the number of words
in the dictionary N , you can use survey sampling techniques to estimate the proportion
of words in the dictionary that you know pˆ. Then, an estimate of the number of words
that you know is Npˆ. Alternatively, you could sample pages, not words – estimating the
average number of words you know per page y¯, then calculating the number of words you
know as Np y¯ where Np is the total number of pages in the dictionary. Note that for each
of the above approaches, there is more than one survey sampling technique that might
be suitable (for estimating pˆ or y¯).
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The dictionary
You should use a modern, large, printed dictionary or equivalent, which states (at least
approximately) how many words are in the dictionary. It is important that you choose
a dictionary that is sufficiently large so that it is reasonable to assume that (nearly)
all the words that you know are in the dictionary. You are welcome to measure the
size of your vocabularies in any language you speak, provided you are able to obtain a
printed dictionary. For English, the dictionary should contain at least 100 000 words.
For other languages, you may refer to e.g., https://en.wikipedia.org/wiki/List_of_
dictionaries_by_number_of_words for guidance on appropriate dictionary size. You
do not have to use the largest dictionary in your chosen language, merely large enough
to contain all words you know.
Many such dictionaries are available in UNSW library.
Electronic dictionaries You may not use an electronic word list or any dictionary
that enables random sampling of words. You may use a paginated document, e.g., a
dictionary in a PDF file or an electronic library loan. Regardless of the precise format,
the sampling procedure must be one that can be used for a printed dictionary. In practice,
this means that you cannot sample words directly but must sample pages (directly or
indirectly), then words within pages.
Assignment components
1. Answer the following preliminary questions.
(a) Briefly describe the dictionary you will use, how many words are in it, and
why you chose to use it.
(b) Describe how you intend to test yourself on whether or not you know a word.
Include sufficient details that someone else would be able to use the same
method.
2. Making use of survey sampling methods we have discussed in lectures, construct
three different strategies that could be used to estimate the size of your vocabulary.
(Same sampling scheme with different sampling units or different target variables
or with and without auxiliary variables can be considered as different strategies of
estimation.) For each strategy, describe:
(a) The sampling procedure and the estimation method. Include sufficient details,
including calculation formulas, so that someone else would be able to estimate
their own vocabulary size by following your procedure and instructions.
(b) Some potential advantages and disadvantages of using this approach, as com-
pared to the other two approaches you consider. (Your discussion should be
specific to the context of estimating vocabulary using a printed dictionary).
3. Choose one of the above methods, which you will use to estimate the total number
of words that you know.
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(a) Briefly explain why you chose the method you chose rather than the alterna-
tives considered in question 2.
(b) Estimate the sample size required to achieve a pre-determined level of accuracy
in estimating the number of words that you know.
(c) Sample from your dictionary in order to estimate the total number of words
that you know. Use your results for question 3b as a guide for sample size, but
also note that you are not expected to spend longer than an hour sampling.
(d) Showing all working, estimate the number of words you know knows, with a
confidence interval.
(e) If you were to make recommendations to future MATH3831 students con-
cerning a good sampling method to use for this project, what would be your
recommendations? Why?
4. Compile all of the above into a report.
Important skills to demonstrate in this assignment
• Demonstrated understanding of the applicability of different survey sampling schemes,
for the given problem.
• Identification of appropriate sampling strategies.
• Correct usage of methods for determining sample size.
• Correct method for estimating key population parameters, and their measures of
uncertainty, for a given sampling strategy.
• Clear and concise presentation.
Marking notes
• Sampling effort is not one of the marking criteria, in the sense that you will not
be treated more (or less) favourably if you spend longer than two hours sampling
words.
• Note that this assignment has a word limit. Responses in excess of this word limit
will not be marked.
Submission Details
You will be required to submit the following components:
1. The report, as an RMarkdown notebook HTML file, to be uploaded to the provided
Turnitin space.
2. A file containing the raw data from your sampling. This will most likely be a table
with the following columns:
• the word tested
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• whether or not you knew the word
• any random numbers generated in order to select the word, e.g., the page
number.
You must use a common format, such as CSV, TSV, Excel, or ODS. Other formats
may be used with instructor’s permission only.
3. The RMarkdown file used to generate it.
Note that between Items 2 and 3, I should be able to reproduce Item 1.
Permitted resources and collaboration
This is an individual assessment. You may not receive help on this assessment from
anyone except for the instructor, and you must not communicate this assessment to
anyone. An exception is that you are permitted to collaborate on and share dictionaries.
You may use any static resources, but you must attribute them whenever this use is
nontrivial. (For example, you do not need to individually cite every R command’s help
or vignette, unless you have borrowed a significant amount of code from it.)
Static resources include, but are not limited to, R help files, vignettes, lecture and lab
notes, code, and solutions, published books and manuals, and any web pages available
to the public or with a UNSW subscription. This does include Q&A sites such as Stack
Overflow; but you may only read what is already there; you may not post questions about
this assessments or solicit answers.
If in doubt, ask the instructor first.
Generative AI Permission Level: Simple Editing Assistance
In completing this assessment, you are permitted to use standard editing and referencing
functions in the software you use to complete your assessment. These functions are
described below. You must not use any functions that generate or paraphrase passages
of text or other media, whether based on your own work or not.
If your Convenor has concerns that your submission contains passages of AI-generated
text or media, you may be asked to account for your work. If you are unable to satisfac-
torily demonstrate your understanding of your submission you may be referred to UNSW
Conduct & Integrity Office for investigation for academic misconduct and possible penal-
ties.
For more information on Generative AI and permitted use please see https://www.
student.unsw.edu.au/assessment/ai .
Declaration
The University regards plagiarism as a form of academic misconduct, and has very strict
rules regarding plagiarism. See UNSW policies, penalties, and information to help you
avoid plagiarism, as well as the guidelines in the online ELISE tutorials for all new
UNSW students. Note, in particular, the policies on Contract Cheating: sharing your
assignment, and, in general, publicly or privately soliciting or obtaining help with it in
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ways not expressly authorised by the instructor is not permitted and will be investigated
and punished. The information can be found at the following links:
• https://subjectguides.library.unsw.edu.au/elise/check
• https://www.student.unsw.edu.au/plagiarism
• https://www.unsw.edu.au/assurance-integrity/conduct-integrity/conduct-unsw/
cheating
By submitting this assessment item, you declare that this assessment item is your own
work, except where acknowledged, and acknowledge that the assessor of this item may,
for the purpose of assessing this item:
• Reproduce this assessment item and provide a copy to another member of the
University; and/or
• Communicate a copy of this assessment item to a plagiarism checking service (which
may then retain a copy of the assessment item on its database for the purpose of
future plagiarism checking).
• You certify that you have read and understood the University Rules with respect
to Student Conduct.
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