Feasible Inferential Statistics Projects for Introductory Statistics

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Feasible Inferential Statistics Projects for
Introductory Statistics

• Kenneth M. Brown, PhD, Department of Mathematics,
  College of San Mateo, San Mateo, California
• Cheryl P. Gregory, MEd, Department of
  Mathematics, College of San Mateo, San Mateo,
  California

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Projects in Elementary Statistics provide
students with the opportunity to

• use statistics in an authentic setting.
• demonstrate organization skills (time, concepts,
  and expression)
• express statistical results in words.
• integrate the material for multiple units within
  the course.
• work in a team.
• develop a portfolio entry that is evidence of
  quantitative literacy
• reflect on the process of producing a
  quantitative paper

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Essentials for Projects

• Good data
• A good statistical software package with which
  students are familiar
• Good prompts, good scaffolding of the assignment
  with interim deadlines

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Essentials for Projects 1Good Data

• Data Collection is not laborious
• Data has a variety of quantitative and
  categorical variables
• Data can be understood by students

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Descriptive Statistics Project 1st Writing
Project (Default used car data)

• A mixture of quantitative and categorical data
• Data available in table format
• Data require cleaning before they can be
  analyzed
• Students use statistical package to analyze
  cleansed data

• Used car data from www.cars.com (shown in Fathom)

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Essentials for Projects 2

• A good statistical software package with which
  students are familiar
• Our experience We use Fathom in connection with
  Rossman-Chance-Locke Workshop Statistics

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Essentials for Projects 3

• Good prompts, good scaffolding of the assignment
  with interim deadlines
• Prompts (a new word?) clearly stated assignment,
  but not too general or too specific
• Scaffolding Provides structure and interim
  deadlines with penalties for missing the
  deadlines
• (Organization and time management tend to be
  students weak points)

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An Example scaffolding-deadlines

• Interim Due Dates
• Name of team members and market to be researched
  (week 1)
• Raw data set due by email (week 1.5)
• Cleaned data due by email (week 2)
• Rough draft due by email (week 3)
• Final draft due by email and hard copy (week 5)
• Reflection paper (week 5)
• Worksheets and in-class examples that relate to
  parts of the paper (scattered through 5 week
  period)
• Writing Lab support available to students

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Descriptive Statistics Projects are somewhat
straightforward

• Descriptive Data Sets are easy to find
• Census at School Data from various countries (but
  not California)
• Sports data (NFL, NHL, Major League baseball)
• Nutrition data for fast food restaurants
• Data on the backgrounds of political figures
• Real Estate data
• Cautions (questions to be answered)
• Can data be formatted to read into a statistical
  package program without taking up a week (or so)
  of student time with retyping
• What are the observational units? Are the data
  aggregated (e.g. state or country or year)?
• Can meaningful research questions be answered
  with the data chosen?

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Inferential Statistics Projects are less
straightforward

• Our introductory texts emphasize having simple
  random samples or simple random allocation in
  experimental settings.
• Finding data sets that are clearly SRS of a
  reasonably well defined population is not easy.

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Inferential Statistics

• One Challenge What is the population?
• Used car data are at best cluster samples, and
  may vary systematically by season.
• Sports data are generally censuses (although one
  could make random sub-samples).
• Find a fairly large population, and sample from
  it.

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Real Estate Data for San Mateo County

• The data on real estate sales are public data
  that are published -- in bits and pieces -- in
  newspapers, and hence on-line as well.
• The manner in which it is published on the web
  makes it very difficult to up-load to spreadsheet
  form.
• The data are available to real estate agents
  however in a convenient form. One of us begged a
  real agent friend to let us have the data for the
  5600 homes sold in San Mateo County from June
  2005 to June 2006

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Real Estate Data what they look like in Fathom

• There is a mixture of quantitative and
  categorical data.
• However, the variable Region is our creation
  the original data had zipcode, town and a more
  specific region indicator.
• For the most part the data are meaningful for
  students.
• So how did we handle this project?

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What we did, and why . . .

• Using Rossman-Chance-Locke Workshop Statistics we
  cover all of the inferential material for
  categorical data first-- that is for proportions,
  and then basically repeat the topics for
  quantitative data.

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What we did, and why . . .

• The inferential project was assigned after
  students had been tested on the basic inferential
  concepts (for proportions) and their application.
• We experimented! -- and replaced the last test on
  inferences for quantitative variables with the
  inferential statistics project
• Students were responsible for this material on
  the Final Exam, and on bi-weekly small quizzes.
• In class worksheets modeled the process
• Again . . .The prompt is quite important . . .

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Looking at the prompt . . .

• The prompt is a contrived but realistic
  situation.
• The questions asked cover most of the techniques
  covered in inference for quantitative variable
  one and two variable analyses and ANOVA.
• Students are expected to determine whether the
  technical conditions for the analyses are met.
• For some of the samples the technical conditions
  are met, and for some the equal variances rule of
  thumb (largest s lt 2 smallest s) fails.
• The total sample size is large, but for some of
  the variables the data are not at all normal.

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The Prompt
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The Prompt (cont.)
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The Prompt (cont.)
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The Prompt (cont.)
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The Prompt (cont.)
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The Prompt (cont.)
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Fewer specific deadlines were used, but

• This was the second paper and students had
  already
• Completed a descriptive statistics project
• Reflected, in writing, on their process what
  worked, what didnt and what they would do
  differently for the second project
• Received instructor feedback on the first project
• Students were required to have a rough draft
  ready for a peer evaluation. Peers used the
  instructors marking rubric.

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So how did it work?

• Following are excerpts from student papers

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So how did it work?
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So how did it work?
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So how did it work?
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So how did it work?
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So how did it work?
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What we learned . . .

• We think the timing was fairly good the timing
  is somewhat constrained by having ANOVA as the
  last topic to be covered.
• Students found the feedback from their peers
  helpful, also a few energetic groups wanted
  instructor feedback and had material ready early
  for review.
• Using the Fathom software students get the
  calculations right.

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Student Reflection and Feedback Quotes

• The real estate project is quite different from
  the car project and it gave us a chance to
  practice something new. Group work makes it
  easier for us to break project into parts and
  then independently work on it. Group work is
  helpful if you have a good partner and I am lucky
  that I got a partner like A.. for this project.
  We had no trouble contacting each other and
  finding time to work on the project. We both
  finished our parts over the weekend, which made
  it easier for us to make changes in our project
  to improve it and to e-mail it to Ms. Gregory on
  time. I learned that it is always good to finish
  work before time, so I plan to continue doing
  that for my future projects. I really liked that
  Ms. Gregory guided us through this projects by
  worksheets and also explained us what we are
  supposed to do. It wouldve been better of we had
  worked on this project before and not in the last
  week of the semester. I wouldve liked to study
  for the final instead of working on the project.
  Everything else was good, I had no problem with
  the due dates, electronic edits, etc.

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Student Reflection and Feedback Quotes
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Student Reflection and Feedback Quotes

• Real Estate Analysis Project Reflection
• Once again I seemed to do all of the work on this
  project. Were this time there were better
  intentions by my different partner, he still fell
  short in doing his fair share. We chose to work
  together because we both had similarly rough
  experiences with our last partners on the last
  project. We thought we would finally have a
  decent partnership, but life comes at you fast
  and if one thing goes wrong then most likely they
  all will. That is exactly what happened. However,
  this time was defiantly better than the last. I
  think that once again finding the right partner
  is key, but one must also be able to deal with
  what they are dealt. I would maybe add one more
  check in date for the groups, but overall I
  really think that the lead up work and the peer
  editing was so useful and really helped us get a
  finished project that we can be proud of.

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Contact Information brownkm_at_smccd.edu gregory_at_smcc
d.edu Slides posted on www.smccd.edu/accounts/csmw
s
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Readable Fathom Case Table
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Readable Fathom Case Table