MATH3831 Statistical Methods for Social

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 p?. Then, an estimate of the number of words that you know is Np?. Alternatively, you could sample pages, not words – estimating the average number of words you know per page yˉ, then calculating the number of words you know as Np yˉ 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 p? or yˉ). 1 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. 2 (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 3 ? 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 4 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: 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