Transcript An Active Approach to Statistical Inference using

Implementation and
Order of Topics at
Hope College
In the beginning …
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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.
In the beginning …
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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.
In the beginning …
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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.
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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.
Tactile Methods
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We begin with tactile methods of
randomization.
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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.
Technology
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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.
Order of Topics (Last two years)
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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
Other topics
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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.
Key Features
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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.
How we got started using a
randomization-based course
at Hope College
How we began
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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.
How we began
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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 randomizationbased 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.
Institutional support/resistance
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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 aren’t too excited about the
constant changes we make.
The times they are a-changin’
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We are in the process of rewriting the entire
curriculum by
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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.
Is it worth it?
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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 randomizationbased approach than with a traditional
approach.
Assessment I (JSE: March 2011)
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The Comprehensive Assessment of Outcomes in
Statistics (CAOS)
Students in our randomization course took this preand 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.
Questions where the new curriculum
faired significantly better
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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)
Questions where the new curriculum
faired significantly better
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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)
Questions where the new curriculum
faired significantly worse
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Ability to correctly estimate and compare
standard deviations for different histograms.
(Descriptive statistics)
Assessment II (Submitted to SERJ)
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Four Month Retention
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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.
Assessment II
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Significant differences between 2007 and
2009 were found in questions involving
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Data Collection and Design
Tests of Significance
Contact Information
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[email protected]
http://www.math.hope.edu/isi/