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Day 1
Introduction to the Course
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What is Statistics?
Statistics is the art and science of decision making. That is, the art and science of using
data to answer research questions.
Explore the following research question: Is Rock-Paper-Scissors a fair game?
o How can we decide if Rock-Paper-Scissors is a fair game?
o What assumptions are made?
o Model the Statistical Process:
 Define Research Question
 Collect Data
 Summarize Data
 Make Conclusions
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Discuss Basic Definitions:
Sample vs. Population, Statistic vs. Parameter, Categorical vs. Numerical
Sampling
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Weighing a "Random" Sample Activity (Gelman & Nolan, 2002)
If conclusions are to be valid, data must be collected according to a well-developed plan.
How can we choose elements for a sample?
o Simple Random Sampling
o Stratified Sampling
o Cluster Sampling
o Systematic Sampling
o Convenience Sampling
Random Rectangles Activity (Scheaffer, Watkins, Witmer, & Gnanadesikan, 2004)
Experimental Design
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Jumping Frogs Activity (Scheaffer et al., 2004)
Principles of Experimental Design (Connect to Jumping Frogs Activity)
o Randomization
o Replication
o Control
o Other Important Concepts: Confounding, Experimental Unit
Observational vs. Experimental Studies
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Discuss differences between each type of study. Why don't we always use randomized
experiments?
Graphical Displays (Connect to Jumping Frogs Activity)
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Dot Plots
Stem and Leaf Plots
Histograms - Histogram Bin Width Applet (Garcia, Lima, Chance, Holmes, & Gill, n.d.)
Examples of Bad/Misleading Graphs
Describing Numerical Data Distributions:
o Shape of the Distribution
o Center of the Distribution
o Spread of the Distribution
Measures of Center
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Mean vs. Median
o Demo 2: Mean and Median (Erickson, 2008)
o When is one more appropriate to use than the other?
Other Numerical Summaries (Connect to Jumping Frogs Activity)
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Five Number Summary: Min, Q1, Median, Q3, Max
Boxplots
Measures of Spread
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Variance
Compare data sets with different variances. For example,
Data Set 1: 20, 20, 20, 20, 20
Data Set 2: 18, 19, 20, 21, 22
Data Set 3: 1, 5, 7, 8, 79
Use a sample data set (e.g., Data Set 2) to derive its standard deviation by discussing how
you could measure the “average” distance between each point and the mean.
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Calculate sample variance/standard deviation with a graphing calculator.
What Makes the Standard Deviation Larger or Smaller? Activity (delMas, 2001)
Demo 4: Transforming the Mean and Standard Deviation (Erickson, 2008)
Day 2
Random Variables
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Definition, Examples
Discrete vs. Continuous Random Variables
Probability
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Basic Probability Rules & Definitions (De Veaux, Velleman, & Bock, 2006, pp. 325327)
o Any probability cannot be less than zero or greater than one.
o Something Has to Happen Rule
o Complement Rule
o Addition Rule
o Equally Likely Rule
o Conditional probability is the probability of an event A occurring, given that
event B has already occurred. If two events are independent, then knowing that
event B has already occurred does not change the probability that event A occurs.
o Multiplication Rule
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Examples (De Veaux et al., 2006)
o Problem 10, p. 334
o Problems 12 & 14, p. 334
o Problem 2, p. 398
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Simulation to Estimate Probability
o Birthday Paradox Activity (National Council of Teachers of Mathematics, 2008)
Normal Distribution
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Properties: Shape, Center, Spread
68-95-99.7 Rule: Problem 17, p. 123 (De Veaux et al., 2006)
Z-scores
Find probabilities and percentiles with a graphing calculator.
Standardized Test Reports: Discuss reported percentiles and percents.
Dear Abby Example (Larsen & Marx, 1990, pp. 333-334)
The following letter appeared in the "Dear Abby" column in the Tennessean (Nashville)
on January 20, 1973:
Dear Abby,
You wrote in your column that a woman is pregnant for 266 days. Who said so? I carried
my baby for ten months and five days, and there is no doubt about it because I know the
exact date my baby was conceived. My husband is in the Navy and it couldn't possibly
have been conceived any other time because I saw him only once for an hour, and I didn't
see him again until the day before the baby was born.
I don't drink or run around, and there is no way this baby isn't his, so please print a
retraction about the 266-day carrying time because otherwise I am in a lot of trouble.
San Diego Reader
Assume that the standard deviation of pregnancy length is 16 days. The San Diego
Reader’s 10 month, 5 day pregnancy is about the same as 310 days. How likely is it that a
pregnancy would last at least 310 days?
Sampling Distributions
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Sampling Distributions of Sample Means and Variances: Dear Abby Activity
o Create a stem-and-leaf plot of 100 pregnancy lengths simulated from a Normal
model with a mean of 266 days and a standard deviation of 16 days. Students
select multiple random samples of pregnancy lengths (three of each size: n = 4
and n = 9) from this simulated population distribution. Students add their sample
averages and variances to classroom plots for each statistic and sample size
combination.
o Discuss the shape, center, and spread of each plot. How do these characteristics
vary with the sample size? statistic?
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Sampling Distributions of Sample Proportions: Coins and Dice Activity
o Create a dot plot of student observations for each of the following random
variables:
 Number of heads observed in 20 flips of a coin.
 Number of {0, 1, 2}s observed in 20 rolls of a 10-sided die.
 Number of {0}s observed in 20 rolls of a 10-sided die.
o Discuss the shape, center, and spread of each plot. How do these characteristics
vary with the true probability of success? What happens when converted to
sample proportions?
Central Limit Theorem (CLT)
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Cents and the Central Limit Theorem Activity (Scheaffer et al., 2004)
Summary of Sampling Distributions and the CLT
Day 3
Introduction to Confidence Intervals (CIs)
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Spinning Pennies Activity (Scheaffer et al., 2004) adapted to use 68-95-99.7 Rule for
introducing confidence intervals
Confidence Intervals for Proportions
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Land or Water? Activity (Gelman & Nolan, 2002)
Find confidence intervals for proportions with a graphing calculator.
Examples (De Veaux et al., 2006)
o Problem 13, p. 444
o Problem 24, p. 515
Margin of Error
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In general, confidence intervals look like: Estimate ± Margin of Error.
Use Simulating Confidence Intervals for Population Parameter - Newer Version Applet
(Garcia et al., n.d.) to explore the following questions:
o What does 95% confidence really mean?
o What happens to the confidence interval when we change the confidence level?
o What happens to the confidence interval when the sample size changes?
Example: Problem 6, p. 443 (De Veaux et al., 2006)
Confidence Intervals for Means
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Use recently discussed concepts of sampling distributions of sample means and
confidence intervals to brainstorm the general formula for confidence intervals for means.
Briefly explain why using t-distribution.
Find confidence intervals for means with a graphing calculator.
Examples (De Veaux et al., 2006)
o Problem 15, p. 541
o Problem 17, p. 541
o Problem 34 (a-c), p. 543
Hypothesis Tests (HTs) for Proportions
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Ducks and Green - An Introduction to the Ideas of Hypothesis Testing Activity (Seier &
Robe, 2002)
Do hypothesis tests for proportions with a graphing calculator.
Examples (De Veaux et al., 2006)
o Problem 27, p. 469
o Problem 30, p. 470
o Problem 2, p. 467
Day 4
Hypothesis Tests for Means
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Do hypothesis tests for means with a graphing calculator.
Examples (De Veaux et al., 2006)
o Problem 26, p. 542
o Problem 35 (a-d), pp. 543-544
More Practice with HTs and CIs for Proportions & Means (De Veaux et al., 2006)
o Problem 32, p. 543
o Problem 3, p. 596
o Problem 4, p. 596
o Problem 20, p. 599
o Problem 30, p. 601
Hypothesis Tests and Confidence Intervals: Relationship between the Two Methods
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Discuss relationship between confidence intervals and hypothesis tests
Inference for Two Means, Independent Samples
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Example: Problem 4, p. 565 (De Veaux et al., 2006)
Do hypothesis test and confidence interval for a difference between two independent
means with a graphing calculator.
Discuss difference between equal variance and unequal variance tests.
Example: Problem 7, p. 566 (De Veaux et al., 2006)
Inference for Two Means, Dependent Samples
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Matched Pairs Activity
o Carry out an activity to compare two dependent samples. For example, average
number of snaps on dominant vs. non-dominant hand, average heart rate before
and after exercise, etc.
o Discuss appropriateness of previously discussed methods.
Dependent vs. Independent Samples
Do hypothesis test and confidence interval for mean difference with a graphing
calculator.
Examples (De Veaux et al., 2006)
o Problem 26, pp. 591-592
o Problem 15, p. 589
o Problem 19, pp. 598-599
Lab Time
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Provide students with a data set for them to explore. Each group should create and answer
their own research questions.
Day 5
Group Presentations
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Each group presents research questions and conclusions from previous day's explorations.
Inference for Two Proportions, Independent Samples
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Hershey Kisses Activity
o Carry out a study to answer the research question:
Is the probability a Hershey's Special Dark Kiss lands on its base when spilled
from a cup different than the probability a Hershey's Milk Chocolate with
Almonds Kiss does?
Do hypothesis test and confidence interval for difference between proportions with a
graphing calculator.
Examples (De Veaux et al., 2006)
o Problem 30, page 510
o Problem 36, p. 516
Relationships between Two Categorical Variables
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Contingency Tables
Use data from Problem 26, p. 630 (De Veaux et al., 2006) to discuss:
o Row and Column Percents
o Risks and Relative Risks
o Odds and Odds Ratios
Example: Problem 25, p. 630 (De Veaux et al., 2006)
Relationships between Two Numerical Variables
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Scatterplots
o Explanatory and Response Variables; Independent and Dependent Variables
o Direction/Association (Positive vs. Negative), Pattern (Linear, etc.), Outliers,
Strength of Pattern
o Examples (De Veaux et al., 2006)
 Problem 2, p. 158
 Problem 6, p. 159
Correlation Coefficient, r
o Facts about r
o Correlation ⇏ Causation
o Examples (De Veaux et al., 2006)
 Problem 11, pg. 160
 Problem 25, p. 163
Least-Squares Regression Equation
o Simple Examples of Least Squares Activity (Gelman & Nolan, 2002)
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Find regression statistics and least squares regression lines with a graphing
calculator.
Interpret the slope and intercept.
Lurking Variables (Levitt & Dubner, 2005, pp. 161-176)
Coefficient of Determination
 Class Examples, 4 - Price vs. Number of Pizza Toppings (De Veaux et al.,
2006, p. IG 8-C)
Barbie Bungee Activity (Zordak, 2008)
Wrap-Up
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Summarize Big Ideas in Statistics
References
De Veaux, R. D., Velleman, P. F., & Bock, D. E. (2006). Introductory statistics: Instructor's
edition (2nd Ed.). Boston, MA: Pearson.
delMas, R. C. (2001). What makes the standard deviation larger or smaller? Statistics Teaching
and Resource Library. Retrieved from http://www.oercommons.org/courses/star-librarystandard-deviation/view
Erickson, T. (2008). Fifty fathoms: Statistics demonstrations for deeper understanding.
Emeryville, CA: Key Curriculum.
Garcia, F., Lima, C., Chance, B., Holmes, E., & Gill, R. (n.d.). Histogram bin width.
Rossman/Chance Applet Collection. Retrieved June 27, 2011, from
http://www.rossmanchance.com/applets/
Gelman, A., & Nolan, D. (2002). Teaching statistics: A bag of tricks. New York: Oxford
University.
Larsen, R. J., & Marx, M. L. (1990). Statistics: Annotated instructor's edition. Englewood Cliffs,
NJ: Prentice Hall.
Levitt, S.D., & Dubner, S. J. (2005). Freakonomics: A rogue economist explores the hidden side
of everything. New York: HarperCollins.
National Council of Teachers of Mathematics. (2008). Birthday paradox: Random integers on
TI83/TI84Plus. Retrieved from
http://illuminations.nctm.org/lessons/CommonSheets/RandInts-OV-UsingCalc.pdf
Scheaffer, R. L., Watkins, A., Witmer, J., & Gnanadesikan, M. (2004). Activity-based statistics:
Student guide (2nd ed., revised by Tim Erickson). Emeryville, CA: Key College
Publishing.
Seier, E., & Robe, C. (2002). Ducks and green - An introduction to the ideas of hypothesis
testing. Teaching Statistics, 24(3), 82-86.
Zordak, S. E. (2008). Barbie bungee. Retrieved from National Council of Teachers of
Mathematics Illuminations website:
http://illuminations.nctm.org/LessonDetail.aspx?id=L646