Implementation and Order of Topics at Hope College

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Implementation and Order of Topics at Hope
College
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In the beginning

• We start the course with an overview of the
  statistical investigative process (we have seven
  steps) from asking a question to communicating
  the results.
• We then focus on the inference part of this
  process and begin using randomization during the
  first week of the course.

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In the beginning

• Our first example is a test for a single
  proportion.
• We start out modeling the null hypothesis through
  coin flipping.
• We had been using the study involving babies
  preferences for nice versus naughty toy. In that
  example, 14 of 16 babies picked the nice toy.
• We will now be using a dolphin communication
  study example where 15 of 16 trials two dolphins
  successfully communicated.

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In the beginning

• Both these examples are very significant and we
  can put off talking about specifics of the
  p-value for a little while and focus on the
  process of randomization.
• As an initial example, we like the dolphin study
  over the naughty or nice toy study.
• The dolphin study boils down to a single dolphin
  pushing one of two buttons and then repeating
  this process 16 times.
• Flipping a single coin 16 times, nicely models
  this process if the dolphin is just guessing.

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Tactile Methods

• We begin with tactile methods of randomization.
• Coin flipping for single proportion
• Playing cards (red/black) shuffled into two piles
  for comparing two proportions
• Playing cards (red/black) shuffled to mix up
  categorical variable while the quantitative
  variable stays in the same order when comparing
  two means.
• Cards with numbers on them for testing
  correlation.

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Technology

• We use an applet to simulate coin flipping.
• We have used Fathom for the other randomized
  methods.
• We are in the process of converting our materials
  so that applets are used instead of Fathom.
• We also use SPSS for some of the traditional
  methods and projects.

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Order of Topics (Last two years)

• One proportion
• Comparing Two Proportions
• Comparing Two Means
• Correlation and Regression
• Correlation and Regression
• Comparing Means
• Comparing Proportions
• Single Mean and Proportion

Randomization Methods
Traditional Methods
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Other topics

• Descriptive statistics are interspersed
  throughout in a just in time approach.
• Power is discussed in a very intuitive way and
  how it relates to sample size, difference in
  sample statistics, etc.
• The differences between analyzing a process,
  sampling from a finite population, and an
  experiment are discussed early.
• Confidence intervals are introduced as a range of
  plausible values for the population parameter.

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Key Features

• We do little lecture and lots of activities.
• We meet in a computer classroom.
• We focus on the entire statistical investigative
  process.
• We look at real studies in our examples,
  activities, homework, case studies, and research
  papers.
• Students complete two research projects, one in
  the middle of the semester and one at the end.

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How we got started using a randomization-based
course at Hope College
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How we began

• In 2008, Hope College was awarded a 1.4 million
  grant from the Howard Hughes Medical Institute.
  Part of that grant was earmarked for the creation
  of a computer classroom devoted to teaching
  statistics.
• Nathan Tintle lead the effort to get the lab and
  start redesigning the curriculum.

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How we began

• We used part of the HHMI grant as well as a few
  other small ones to begin development of a new
  curriculum.
• Early in 2009, we began by converting
  randomization-based modules that were previously
  written by Allan Rossman and Beth Chance into a
  complete text.
• Three of us were doing the writing (Nathan
  Tintle, Jill VanderStoep, and myself).
• We held a workshop during the summer for the
  other instructors.
• In the Fall of 2009 we had a text completed that
  would be used in all our sections of introductory
  statistics.

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Institutional support/resistance

• The college and the department have historically
  been very supportive of curricular changes.
• Nathan spoke with groups from all the client
  departments about the changes that we were
  making. He found no resistance, in fact they
  were excited about the changes.
• Other instructors of statistics are supportive of
  this method, though they arent too excited about
  the constant changes we make.

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The times they are a-changin

• We are in the process of rewriting the entire
  curriculum by
• Changing the order of topics
• Making it as flexible as possible (lecture or
  activity)
• Having the best possible research examples
• Etc.
• For the last year, we have been working with Beth
  Chance, Allan Rossman, Soma Roy, and George Cobb.

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Is it worth it?

• Yes! We believe that this is how introductory
  statistics should be taught. Students gain a
  clearer and deeper understanding of the process
  of inference using a randomization-based approach
  than with a traditional approach.

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Assessment I (JSE March 2011)

• The Comprehensive Assessment of Outcomes in
  Statistics (CAOS)
• Students in our randomization course took this
  pre- and post-test in the Fall of 2009 (n 202).
  These results were compared with students that
  took our traditional course in the Fall of 2007
  (n 198) and those from a national
  representative sample (n 768).
• Overall, learning gains were significantly higher
  for students that took the randomization course
  when compared to either those that took the
  traditional course at Hope or the national
  sample.

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Questions where the new curriculum faired
significantly better

• Understanding that low p-values are desirable in
  research studies (Tests of significance)
• Understanding that no statistical significance
  does not guarantee that there is no effect (Tests
  of significance)
• Ability to recognize a correct interpretation of
  a p-value (Tests of significance)
• Ability to recognize an incorrect interpretation
  of a p-value. Specifically, probability that a
  treatment is not effective. (Tests of
  significance)

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Questions where the new curriculum faired
significantly better

• Understanding of the purpose of randomization in
  an experiment (Data collection and design)
• Understanding of how to simulate data to find the
  probability of an observed value (Probability)

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Questions where the new curriculum faired
significantly worse

• Ability to correctly estimate and compare
  standard deviations for different histograms.
  (Descriptive statistics)

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Assessment II (Submitted to SERJ)

• Four Month Retention
• Students again took the CAOS test four months
  after the end of the course.
• In 2007 the overall mean decreased by about 4
  percentage points from December to April.
• In 2009 the overall mean decreased by about 0.5
  percentage points from December to April.

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Assessment II

• Significant differences between 2007 and 2009
  were found in questions involving
• Data Collection and Design
• Tests of Significance

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Contact Information

• swansont_at_hope.edu
• http//www.math.hope.edu/isi/