Connecting Data Analysis,
Design, and Statistical
Inference
Daren Starnes
The Lawrenceville School
dstarnes@lawrenceville.org
CMC South Oct 2015
AP Statistics Teachers Meeting
• In this room at 12:30.
• Grab a bite to eat and come join us for a
panel discussion and some fabulous giveaways from the publishers.
Why are we here?
• Examine the statistical problem solving process:
ask a question, collect data, analyze data,
interpret results.
• Explore three applets that make the connection
between data collection, data analysis, and
inference explicit.
• Discuss how to use these applets to deepen
students’ statistical understanding.
• Use simulation as a tool for performing inference.
I. Analyzing categorical data
Who Watches Survivor?
Television executives and companies who advertise on
TV are interested in how many viewers watch particular
shows. According to Nielsen ratings, Survivor was one
of the most-watched television shows in the United
States during every week that it aired. An avid Survivor
fan (and textbook author) claims that 35% of all U.S.
adults have watched Survivor. A skeptical editor
believes this figure is too high. He asks a random
sample of 200 U.S. adults if they have watched
Survivor; 60 say “yes.”
I. Analyzing categorical data
Who Watches Survivor?
http://www.cbs.com/shows/survivor/
• Design: How were the data produced?
Random sample of 200 U.S. adults
• Data Analysis: What is appropriate for one
categorical variable?
– Graph
– Numerical summaries
www.tinyurl.com/SPAapplets
I. Analyzing categorical data
Who Watches Survivor?
• Inference: Testing a claim about a
population proportion
– Via simulation
– Using traditional inference methods
What conclusion should we draw?
II. Comparing distributions of quantitative data
Does sleep deprivation linger?
Researchers have established that sleep deprivation
has a harmful effect on visual learning. But do these
effects linger for several days, or can a person “make
up” for sleep deprivation by getting a full night’s sleep
on subsequent nights?
A recent study (Stickgold, James, and Hobson, 2000)
investigated this question by randomly assigning 21
subjects (volunteers between the ages of 18 and 25)
to one of two groups: one group was deprived of
sleep on the night following training and pre-testing
with a visual discrimination task, and the other group
was permitted unrestricted sleep on that first night.
II. Comparing distributions of quantitative data
Does sleep deprivation linger?
Both groups were allowed as much sleep as they
wanted on the following two nights. All subjects
were then re-tested on the third day. Subjects’
performance on the test was recorded as the
minimum time (in milliseconds) between stimuli
appearing on a computer screen for which they
could accurately report what they had seen on the
screen.
The computer task
a
b
c
After display of the mask (c), subjects must report first on
whether the letter ‘T’ (for example, in a) or ‘L’ (b) was
displayed at fixation, and then whether the three diagonal
bars were arrayed horizontally (a) or vertically (b).
II. Comparing distributions of quantitative data
Does sleep deprivation linger?
The sorted data presented here are the
improvements in those reporting times between
the pre-test and post-test (a negative value
indicates a decrease in performance):
Sleep deprivation (n = 11):
-14.7, -10.7, -10.7, 2.2, 2.4, 4.5, 7.2, 9.6, 10.0,
21.3, 21.8
Unrestricted sleep (n = 10):
-7, 11.6, 12.1, 12.6, 14.5, 18.6, 25.2, 30.5, 34.5,
45.6
II. Comparing distributions of quantitative data
Does sleep deprivation linger?
• Design: How were the data produced?
Completely randomized experiment with 21
volunteer subjects
• Data Analysis: What is appropriate for one
quantitative variable and two groups?
– Graph
– Numerical summaries
www.tinyurl.com/SPAapplets
II. Comparing distributions of quantitative data
Does sleep deprivation linger?
• Inference: Testing a claim about a
difference between two means
– Via physical simulation
– Via computer simulation
– Using traditional inference methods
II. Comparing distributions of quantitative data
Does sleep deprivation linger?
Question: Based on the data, is it plausible that there’s really no
harmful effect of sleep deprivation, and random chance alone
produced the observed differences between these two groups?
Let’s re-do the random assignment many, many times…
• If no treatment effect, then values will be the same as in the
original study.
• Write each of the 21 data values on a separate card.
• Place all of the cards (subjects) in a bag.
• Mix your cards well and deal two groups—one with 10 cards
(unrestricted sleep) and one with 11 cards (sleep deprived).
• Calculate the difference in mean time improvement for the two
groups (unrestricted – sleep).
• Write value on sticky note and bring to me.
II. Comparing distributions of quantitative data
Does sleep deprivation linger?
What conclusion should we draw?
III. Challenges students face in
tackling inference questions
1. Which inference method to choose
• Estimating or testing a claim?
• Means, proportions, relationships between
categorical/quantitative variables?
2. Conditions for using each inference method,
and why they are important
• Random sampling or random assignment
• Normal/Large Sample or Large Counts
• Independence (of measurements/samples)
III. Challenges students face in
tackling inference questions
3. Different inferential thinking in sampling and
experiments: Scope of inference
– Random selection in sampling settings allows
inference about a population
– Random assignment in experiments allows
inference about cause-and-effect
III. Challenges students face in
tackling inference questions
4. Communicating effectively
• Using notation and statistical terminology
correctly
• Stating technically correct conclusions in
context
5. Distinguishing among samples,
populations, statistics, and parameters.
6. Using technology as a tool: The “Do” step
IV. A resource!
Larry Green’s Web site
at Lake Tahoe Community College
www.ltcconline.net/
greenL/java/Statistic
s/catStatProb/categ
orizingStatProblems
JavaScript.html
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How Did We Do?
• Questions and answers
• Parting thoughts
E-mail me with comments or questions:
dstarnes@lawrenceville.org