misterhay / math-20-2

Math 20-2 Statistical Research Project

Part of the requirements of the Math 20-2 course is a research project. The project is connected to the Statistics section of this course and will count towards your final grade.

For this project, you will collect numerical data about a topic that interests you. Then you will perform a statistical analysis of your data and report on your findings. You will be expected to present your findings and your predictions using a Jupyter notebook, plus be prepared to explain your results when asked questions. There are a number of starter notebooks in the AccessingData folder.

For more background on statistics, check out this Introductory Statistics Textbook, this online course, or these class notes.

Part 1: Creating an Action Plan

Create a research question on a statistical topic you would like to answer.

Think of some subjects that interest you. Then make a list of topics that are related to each subject. Once you have chosen several topics, do some research to see which topic would best support a project. Of these, choose the one that you think is the best.

Some questions to consider when selecting a topic:

• Does the topic interest you?
• Is the topic practical to research?
• Can you find enough numerical data to do a statistical analysis?
• Is there an important issue related to the topic?
• Will your audience appreciate your presentation?

You may choose a topic where you collect the data yourself through surveys, interviews, and direct observations (primary data) OR where you find data that has already been collected through other sources such as websites, newspapers, magazines, etc. (secondary data).

Primary Data

• To make sure that you have an adequate amount of information with which you can perform a statistical analysis, you must collect at least 100 data values.

Ideas for Primary Data Topics:

Feel free to choose a topic that is not in this list, but keep in mind that you need to be able to find enough data.

• People's: height, shoe size, etc.
• Family size, number of children in a family, the time separation between siblings, age difference between mother and father
• Number in a household of: pets, TV’s, books, mobile devices, vehicles, etc.
• Number of mobile devices that a person has owned
• Number of hours of television watched in a day or week
• Number of songs on a person’s playlist
• Number of hours on the phone in a day or week
• Number of text messages sent in a day or week
• Mass of apples or any other type of produce
• The number of items of your favourite product sold in a day (contact local retailers)
• The length (time or distance) of a person's commute to school or work
• The length of a poet’s poems (either by lines or words)
• The size of classes
• The number or percentage of each gender in classes
• How long people can keep their eyes open or stand on one foot
• Number of people on the different school clubs or sports teams

Secondary Data

If you choose this type of data, please make sure your research question is well-defined. To make sure that you have an adequate amount of information with which you can perform a statistical analysis, you must find at least 100 data values.

You may want to do a comparison (e.g. compare climate in provinces, compare career stats of two or more hockey players, etc.) in order to get enough information to perform a statistical analysis.

Ideas for Secondary Data Topics:

You can use the starter notebooks in the AccessingData folder. Feel free to choose a topic that is not in that list, but keep in mind that you need to be able to find enough data.

Creating Your Research Question or Statement

A good question requires thought and planning. A well-written research question or statement clarifies exactly what your project is designed to do. It should have the following characteristics:

• The research topic is easily identifiable and the purpose of the research is clear.
• The question/statement is focused. The people who are listening to or reading the question/statement will know what you are going to be researching.

Evaluating Your Research Question or Statement

• Does the question or statement clearly identify the main objective of the research?
• Are you confident that the question or statement will lead you to sufficient and approprate data to reach a conclusion?
• Can you use the statistical methods you learned in class to analyze the data?
• Is the question or statement interesting? Does it make you want to learn more?

Your Turn:

A. Write a research question for your topic. B. Use the above checklist to evaluate your question. Adjust your question as needed. C. Be prepared to discuss with your teacher your research question and your plan for collecting or finding the data.

Part 2: Carrying Out Your Research

A. Decide if you will use primary data, secondary data, or both. Explain how you made your decision. B. Make a plan you can follow to collect your data. C. Collect the data. There is a sheet at the back of this booklet for you to record your data.

• If using primary data, describe your data collection method(s).
• If using secondary data, you must record detailed information about your source(s), so that you can cite them in your report.
• Consider the type of data you need and ensure that you have a reliable source (or sources) for that data, especially if you are using secondary data.

Part 3: Analyzing Your Data

Statistical tools can help you analyze and interpret the data you collect. You need to think carefully about which statistical tools are most applicable to your topic. Some tools may work well; others may not be applicable with your topic. Keep in mind that you will be marked on the thoroughness of your statistical analyis, so don’t try to scrape by with the bare minimum!

Tools

• Data Table
• Visualization(s) (e.g. Histogram, Frequency Polygon, Scatterplot)
• Measures of Central Tendency (Mean, Median, Mode) ** Which is the most appropriate for measuring the “average” of your data?
• Measures of Dispersion: Range and Standard Deviation ** Comment on the dispersion of your data.
• Outliers ** Are there outliers in your data? Do these skew the results? Would it be more appropriate to remove the outliers before calculating measures of central tendency or dispersion?
• Normal Distribution ** Does your data approximate a normal distribution? Explain why or why not.
• Z-Scores ** Find the z-score of a number of significant data points. If your data is normally distributed, find the percentage of data that is below or above a significant data point.

Your Turn:

A. Determine which statistical tools are appropriate for your data. B. Meet with your teacher to evaluate your plan for analyzing your data. Be prepared to explain why you chose the statistical tools you did. Modify your plan as necessary. C. Use statistics to analyze your data.

• Your analysis must include a table and a graphical display (histogram or frequency polygon) of the data you collected. Make sure these are neat and labeled on a scale large enough to display to the class.
• Include all appropriate measures of central tendency, measures of dispersion, and outliers.
• Comment on trends in your data. Interpret the statistical measures you used. What conclusions can you draw?
• If you have collected data on more than one group, person, time frame, or region, comment on the differences between them. What conclusions can you draw?

Example Projects

Income Per Person

Soccer Data

Part 4: The Final Product and Presentation

Your final presentation should be more than just a factual written report of the information you have found. To make the most of your hard work, select a format for your final presentation that will suit your strengths, as well as your topic. You will be presenting the results of your research topic via video (approximately 3 to 5 minutes), and must include visuals.

Evaluating Your Own Presentation

Before giving your presentation, you can use these questions to decide if your presentation will be effective:

• Did I define my topic well? What is the best way to define my topic?
• Is my presentation focused? Will my audience (classmates and teacher) find it focused?
• Did I organize my information effectively? Is it obvious that I am following a plan in my presentation?
• Does my topic suit one presentation format better than others?
• From which presentation format do I think my audience will gain the greatest understanding?
• Am I satisfied with my presentation? What might make it more effective?
• What unanswered questions might my audience have?

Your Turn:

A. Choose a format for your presentation, and create your presentation. B. Meet with your teacher to discuss your presentation plans and progress. C. Present your topic via video. D. Submit your statistical analysis and written conclusions.

Statistical Research Project Scoring Rubric

Criteria	4 Excellent	3 Proficient	2 Adequate	1 Limited	Insufficient or Blank
Data Collection	pertinent and from reliable and documented sources	relevant and from substantially reliable and documented sources	suitable but from questionable or partially documented sources	unsuitable	no data collected
Process and Reflection (Checkpoints)	prepared to discuss topic, plans, and methods insightfully	prepared to discuss topic, plans, and methods	partially prepared to discuss topic, plans, and method vaguely	unprepared to discuss topic, plans, and method with difficulty or incorrectly	no discussion
Statistical Calculations	thorough statistical analysis with accurate calculations	adequate statistical analysis with essentially correct calculations	superficial statistical analysis with partially correct calculations	minimal statistical analysis with flawed calculations	no statistical calculations performed
Interpretation	astute and insightful	credible and understandable	rudimentary and minimal	incomplete or flawed	no interpretation of the data and statistical measures
Organization and Presentation	purposeful and compelling	logical and effective	reasonable and simplistic	disorganized and ineffective manner	no organization or presentation