1. SUGGESTIONS FOR BEST PRACTICES
FOR STATISTICS EDUCATION AND USING
STATISTICAL SOFTWARE AS AN
EDUCATIONAL TOOL IN THE
CLASSROOM
1 Simon KING
High School Statistics Teacher – Cary Academy, Cary, NC
Texas A & M Department of Statistics
STAT685

2. BACKGROUND
o Most of high school statistics classes incorporate the graphing
calculator with occasional use of statistical software (school
resources permitting) to give students experience of seeing
statistical output.
o High school statistics curriculum follow the College Board AP
Statistics Curriculum (College Board, 2001)
o “Students are expected to bring a graphing calculator with
statistical capabilities to the exam, and to be familiar with this
use.” (College Board, 2005).
o Designed Advanced Statistics and Analytics course that did not
follow the College Board AP Statistics curriculum and used
JMP® as the main statistical and educational tool. No graphing
calculator.
College Board. (2001). www.collegeboard.com. Retrieved from www.collegeboard.com: www.collegeboard.com 2
College Board. (2005). Calculators on the AP Statistics Exam. Retrieved from apcentral.collegeboard.com:
http://apcentral.collegeboard.com/apc/members/exam/exam_information/23032.html

3. SECTION 1 - SUGGESTIONS FOR BEST
PRACTICES IN THE CLASSROOM
1.1 Most of the students taught in statistics
class will not be statisticians.
 Use the course to explore student concerns and interests
1.2 Give students experience of research and
reading of journal papers and articles.
 Explore “statistical thinking”
3
Discussed in STAT641

4. SECTION 1 - SUGGESTIONS FOR BEST
PRACTICES IN THE CLASSROOM
1.3 Teacher as the statistical consultant
o As an end-point for the course, for final student experiment/paper the teacher is
used as a statistical consultant and the student applies what they learned
throughout the year
1.4 Use psychology to teach statistics
o Psychology is an example, but rather teaching statistics as an applied
subject, present context first
1.5 Promote „statistical literacy‟
o Beyond course content, it is crucial students develop and retain this skill.
1.6 The statistics teacher „living and breathing‟ statistics
o If we want our students to enjoy and be curious about the discipline, then we
need to role model the behavior we want to see in them
1.7 Statistics should not be taught like a mathematics
course
o “In mathematics, context obscures structure. In data analysis, context provides
meaning” (Cobb & Moore, November 1997)
4
Cobb, G. W., & Moore, D. S. (2000). Statistics and mathematics: Tension and cooperation. American Mathematical Monthly, August-
September, 615-630.

5. SECTION 1 - SUGGESTIONS FOR BEST PRACTICES IN THE
CLASSROOM
1.8 Teach without the textbook
o General overreliance on textbooks in US education
o facilitates creativity by the teacher
o Teacher is in full control of learning
o Not recommended for new to statistics education teachers
1.9 Student feedback
o Role-model being a reflective learner
o Collect anonymous feedback on the course from the students
o Share the feedback and make reasonable changes to the course
1.10 Incorporate a multicultural curriculum
o Through context and interpretation
1.11 Collect datasets
o Plan curriculum first then consider which datasets will best support the learning
objectives
1.12 Use of statistical applets
o Must be purposeful application with reflection on learning
o Better applets generally use real data or actual context
1.13 Play games to collect student data in-class 5
o Fun, but must be linked to learning objectives

6. SECTION 2 – USING ANALYTICAL SOFTWARE AS
AN EDUCATIONAL LEARNING TOOL
This section presents examples of how statistical
software (in this case, JMP®) can be used as an
educational tool.
This section also discusses the challenges of
adopting such software that the teacher has to
consider including how to assess students and the
„the black box‟ issue of statistical software.
6

7. 2.1 SUPPORTING THE USE OF STATISTICAL
SOFTWARE
7
Example of video tutorial for use of JMP®

8. 2.2 VISUALS
Explore history of visuals
Charles Joseph Minard, 1869
8
Discussed in STAT604 Florence Nightingale, 1857

9. Explore poor visuals
o Poor media use of visuals
o poor visual created in JMP®
o Students spend time learning best
practices
9
Discussed in STAT604 and STAT641

10. Kinesthetic learning – manipulating visuals
o Students explore good and bad influential
points by excluding points and refitting a
regression line 10
o While the data is not „real‟, it is a context that
Discussed in students can relate to.
STAT608

11. 2.3 EXPLORE TEST ASSUMPTIONS
o JMP® script confidence intervals (sample size of two) from a normal
„population‟ 11
Discussed in STAT641 and STAT642

12. 2.4 CREATE AND EXPLORE VISUALS NOT IN A TRADITIONAL
HIGH SCHOOL CURRICULUM
o bubble plot of year, median house price and median house income
(data: U.S. Census Bureau, 2009) 12
U.S. Census Bureau. (2009). Income. Retrieved 10 15, 2011, from www.census.gov:
http://www.census.gov/hhes/www/income/income.html

13. 2.5 TEACHING CONTENT BEYOND THE HIGH SCHOOL CURRICULUM
o Exploring normality with histogram, qq plot and Shapiro-Wilk test
13

14. 2.6 Exploring large datasets with multiple variables
Bivariate Plot of TOTAL SAT score versus Percent Taking by STATE with added
indicator of US region (Data: College Board, 2001) 14
College Board. (2001). www.collegeboard.com. Retrieved 10 15, 2011, from www.collegeboard.com:
www.collegeboard.com

15. 15
o Correlation matrix of body measurements (Data: SAS)
SAS . (n.d.). JMP-SE 8.01 - Body Measurements.jmp.

16. 2.7 NATURAL VARIABILITY
o Twice done exercise. First time when students are exploring
„Natural Variation‟. Second time with chi-square goodness-of-fit
test
16
o This supports student understanding of natural variation and
that it is measurable.

17. Typical JMP® output from „dodgy dice‟ exercise
o When exploring natural variability, they compare the distributions to
the expected distributions and „draw a line in the sand‟; if the
expected and observed distributions are too far apart, they will
reject the dice/coins as „dodgy‟.
o When applying chi-square goodness-of-fit, they enter into JMP®
17
what the expected values should be in order to measure natural
variability.

18. 2.8 EXPLORE DISTRIBUTIONS
o Rather than explore individual binomial
probabilities, explore and visualize entire distributions to
examine concepts in more depth.
18

19. Typical student JMP® output for Zener Cards exercise
This question provokes student reflection and class discussion
on the following conceptual topics either already covered or to
be covered in class:
• Probability density functions
• Cumulative probability
• Sum of expected outcomes
• Null Hypothesis setting on a value for alpha
• Natural variability 19

20. 2.10 “ASSOCIATION IS NOT CAUSATION” (ALIAGA, ET AL., 2010)
Bubble plot of „Storks Deliver Babies‟ by country
The data set “Storks deliver babies” ” (Matthews, 2000), will show an
association between Storks (pairs) and Birth Rate (1000‟s/yr). By adding the
variable (country) Area (km2) and visualizing the data through a bubble plot
where the country area is the size of the bubble, the presence of a covariate
is evident.
20
• Matthews, R. (2000). Storks Deliver Babies. Teaching Statistics, Vo. 22, No. 2, pages 36 - 38.
• Aliaga, M., Cobb, G., Cuff, C., Garfield, J., Gould, R., Lock, R., et al. (2010). GAISE: Guidelines for Assessment and Instruction in
Statistics Education: College Report. American Statistical Association.

21. 3D Scatter plot “Storks Deliver Babies” with a fourth variable (Humans
(millions)) added.
o In JMP® a 3D scatterplot can be rotated, etc. It is less effective 21
represented as a 2D image.

22. 2.9 „THE BALANCING ACT‟ – USING STATISTICAL SOFTWARE
PURPOSEFULLY AND HOW TO ASSESS STUDENTS
o GAISE report “We caution against using technology merely for the
sake of using technology” (Aliaga, et al., 2010)
o “Rather than let the output be the result, . . . , it is important to discuss
the output and results with students and require them to provide
explanations and justifications for the conclusions they draw from the
output and to be able to communicate their conclusions effectively”
(Chance, Ben-Zvi, Garfield, & Medina, 2007)
o “Conceptual understanding takes precedence over procedural skill”
(Burrill & Elliott, 2000)
o In a traditional statistics course, all too often procedure blurs concept;
some students can use formulae to get correct answers, but cannot
tell you why they are doing what they are doing.
o Align a course and assessment to conceptual understanding and
interpretation, supported through “statistical literacy” and “statistical
thinking”.
• Aliaga, M., Cobb, G., Cuff, C., Garfield, J., Gould, R., Lock, R., et al. (2010). GAISE: Guidelines for Assessment and Instruction in Statistics Education:
College Report. American Statistical Association. 22
• Chance, B., Ben-Zvi, D., Garfield, J., & Medina, E. (2007). The Role of technology in Imporving Student Learning of Statistics. Technology Innovations in
Statistics Education, 1(1).
• Burrill, G. F., & Elliott, P. C. (2000). Thinking and Reasoning with Data and Chance. National Council of teachers of Mathematics.

23. 2.9 „THE BALANCING ACT‟ - ASSESSMENT
23
Exercise – Weight Loss Programs

24. Typical output for Exercise – Weight Loss Programs
The following reflective questions are then asked:
• What type of distribution are the four „bell curves‟ on the right of the output and what is their
relationship with the t-statistic and „degrees of freedom‟?
• Given that the Null Hypothesis for each test is initially true, what does the p-value tell us (hint:
think natural variability)?
• As the mean weight loss increases over the four weight loss programs, how and why does this
effect: 24
• The t-test statistic?
• The p-value?
• The Null Hypothesis?

25. Assessment examples: z-score
• What does a z-score measure? Include a sketch to help explain.
• For the z-score formula, what is the purpose of the numerator and denominator?
• If a z-score of 1 equals a p-value of 0.84 and a z-score of 2 equals a p-value of
0.975, then does a z-score of 1.5 equal (0.84+0.975)/2? Give your answer and
explain your reasoning (a sketch would be useful)
• A student calculates a p-value for a corresponding z-score of 2.8 for a normal
distribution to be 0.997. Does this result seem reasonable? Justify your reason.
• It was found that the mean IQ of the population is 100 with a standard deviation of
15 (Neisser, 1997). Discuss how you would calculate the percentage of the
population with an IQ between 69 and 130. The visual below is to help you if
required.
25
Neisser, U. (1997). Rising Scores on Intelligence Tests. American Scientist, 85 (440-7).

26. Assessment examples: binomial distribution
A study conducted in in Europe and North America indicated that the ratio of births of male to female is
1.06 males/female. (Grech, Savona-Ventura, & Vassallo-Agius, 2002). This results in the probability of
a giving birth to a boy as approximately 51.5%. Presuming this article is accurate, if we distribute the
expected probability of number of boys born out of 10 births, we get the following bar graph:
Figure 1 – distribution of expected probabilities of number of boys out of 10 births
a. What type of probability is being used to model this distribution and why?
b. What assumption do we have to make to be able to use this type of probability and why is this
assumption important?
c. Do you expect this distribution to be symmetric? Justify your decision.
d. Show how you would calculate one expected probability outcome from the example
(but do not actually calculate it).
26
Grech, V., Savona-Ventura, C., & Vassallo-Agius, P. (2002). Unexplained differences in sex ratios at birth in Europe and North America. BMJ
(Clinical research ed.), 324 (7344): 1010–1.

27. FUTURE WORK
Write a paper to address the following:
“Students are expected to bring a graphing calculator with statistical capabilities
to the exam, and to be familiar with this use.” (College Board, 2005).
While high school statistics education will be permanently indebted to the College
Board for the introduction of the AP Statistics curriculum and examination, I
believe the above policy regarding graphing calculators slows the development of
K-12 statistics education as teachers and school systems have no pressing need
to explore adoption of statistical software.
While the use of the most generic graphing calculators has not really changed
that much in statistics class since 1993, statistical software has evolved and
continues to evolve at a fast pace.
By removing the above policy, it could be argued that teachers and school
systems would be more motivated to seek out statistical software and thus
facilitate more innovation in statistics education.
College Board. (2005). Calculators on the AP Statistics Exam. Retrieved 10 15, 2011, from apcentral.collegeboard.com: 27
http://apcentral.collegeboard.com/apc/members/exam/exam_information/23032.html