Enhancing the Teaching of Statistics Using SPSS Statistics

1
Enhancing the Teaching of Statistics Using SPSS
Statistics

• Prof. Sharon L. Weinberg
• New York University
• sharon.weinberg_at_nyu.edu
• Prof. Sarah K. Abramowitz
• Drew University
• sabramow_at_drew.edu

2
Commonly Asked Questions

• 1. Will I be able to get copies of the slides
  after the event?
• 2. Is this web seminar being taped so I or others
  can view it after the fact?

Yes
Yes
3
The Technology Revolution

• Has changed the way statisticians work and
  should change what and how we teach (GAISE
  (2005) report)
• A caution In choosing among technologies, the
  focus cannot be on the technology itself, but on
  how that technology improves the teaching of our
  subject (Moore, 1997, p. 135).

4
Enhancing Student Learning of Statistics The
GAISE (2005) Report

• Use Real Data (Many others also have made this
  recommendation (e.g., Chance, Ben-Zvi, Garfield,
  and Medina, 2008)
• Use Technology for Developing Conceptual
  Understanding Analyzing Such Data
• Emphasize Statistical Literacy Develop
  Statistical Thinking
• Stress Conceptual Understanding Rather than Mere
  Knowledge of Procedures
• Foster Active Learning in (and Outside) the
  Classroom
• Use Assessments to Improve and Evaluate Student
  Learning

5
Recommendation 1 Use Real Data

• Gives students a better idea of what
  statisticians do by having them analyze real and
  often messy data.
• Facilitates the discussion of more interesting
  problems that often are captured by large and
  more complicated data sets.
• Motivates students to take ownership of the
  process of analyzing and drawing conclusions
  about data so as to uncover answers to timely and
  relevant questions.
• Creates an empowering experience students learn
  skills that may be used in other settings and
  arenas unrelated to the class in question.

6
Sources for Real Data Classroom Activities

• The Data and Story Library (DASL,
  http//lib.stat.cmu.edu/DASL)
• The Journal of Statistics Education (JSE) Dataset
  and Stories feature (see http//www.amstat.org/pub
  lications/jse/jse_data_archive.html)
• CAUSE (http//www.causeweb.org)

7
Additional Real Data Sources

• http//www.statsci.org/datasets.html
• http//www.stat.ucla.edu/data/
• http//www.cdc.gov/datastatistics/
• http//www.sci.usq.edu.au/staff/dunn/Datasets/
• http//www.umass.edu/statdata/statdata/non-local-d
  ata.html
• http//www.amstat.org/publications/jse/jse_data_ar
  chive.html
• http//lib.stat.cmu.edu/
• http//espn.go.com/
• https//www.icpsr.umich.edu/
• http//www.du.edu/idea/data.htm
• http//mathforum.org/workshops/sum96/data.collecti
  ons/datalibrary/other.resources.html
• http//www.google.com/search?qdatasets

8
Another Source of Data NELS

• The NELS data set collected by the U.S.
  Department of Educations National Center of
  Education Statistics (NCES).
• Nationally Representative Longitudinal Data Set
  to measure achievement outcomes in four core
  subject areas (English, history, mathematics, and
  science), in addition to personal, familial,
  social, institutional, and cultural factors that
  might relate to these outcomes.

9
Students May Find Answers to Such Interesting and
Relevant Questions As

• Do boys perform better on math achievement tests
  than girls?
• Does socioeconomic status relate to educational
  and/or income aspirations?
• To what extent does enrollment in advanced math
  in eighth grade predict twelfth-grade math
  achievement scores?
• Can we distinguish between students who use
  marijuana and those who dont in terms of
  self-concept?
• Does owning a computer vary as a function of
  geographical region of residence (Northeast,
  North Central, South, and West)?
• Note The text Statistics Using SPSS An
  Integrative Approach (2nd ed.) by Weinberg
  Abramowitz (2008), contains a subsample of these
  data, with 500 cases and 48 variables on an
  accompanying CD.

10
And Yet Another Source of Data Framingham Heart
Study

• First prospective study of risk factors and their
  joint effects related to coronary heart disease
  (CHD).
• Longitudinal data collection began in 1956 on
  5,209 subjects.
• Risk factors and disease markers of CHD include
  blood pressure, blood chemistry, lung function,
  smoking history, health behaviors, and medication
  use.
• Note Data on a random subsample of 400 cases at
  first examination in 1956, and at third
  examination in 1968, blocking on smoking and
  gender, is included on a CD accompanying
  Statistics Using SPSS.

11
Students May Find Answers to Such Interesting and
Relevant Questions As

• Is the mean body mass index of smokers lower than
  that for non-smokers among the population of
  non-institutionalized adults?
• What evidence is there to suggest that HDL is
  good cholesterol and LDL is bad cholesterol?
• Does total serum cholesterol predict the
  incidence of coronary heart disease?
• Is there a difference in diastolic blood pressure
  levels, on average, between those who do and
  those who do not take anti-hypertensive
  medication?

12
Recommendation 2 Use Technology

• Advantages
• Reduces focus on time-consuming computation
• Frees student to focus on conceptual
  understanding
• Enhances the teaching of our subject
• Models statistical practice
• Pay Attention to Such Features As
• Availability and Cost with student network
  versions available
• Ease of use for particular audiences
• Ease of data entry, ability to import data in
  multiple formats
• Dynamic linking between data, graphical, and
  numerical analyses
• Interactive and High Speed Capabilities
• Versatility all purpose tool for use throughout
  the course beyond, in academic settings and
  industry
• Portability for classroom and home
• Our Software Choice SPSS, which has all of the
  above features.

13
Recommendation 3 Emphasize Statistical Literacy
Thinking

• Modeling statistical thinking from conception to
  conclusion Example 11.8 from Statistics Using
  SPSS.
• Exploring a large data set checking underlying
  inferential assumptions Exercise 6.9 from
  Statistics Using SPSS.
• The importance of open-ended problems Exercise
  3.15 from Statistics Using SPSS.

14
Modeling statistical thinking from conception to
conclusion

• Example 11.8, Statistics Using SPSS, using the
  NELS data set. Does the population of
  college-bound males from the southern United
  States who have always been at grade level differ
  from the corresponding population of females in
  terms of the number of years of math in high
  school? Conduct the significance test at alpha
  .05.

15
Modeling statistical thinking from conception to
conclusion

• Use boxplots of the variable number of years in
  math in high school to investigate visually the
  tenability of the underlying assumptions of the
  t-test
• Boxplots suggest that homogeneity of variance
  assumption is met.
• Boxplots suggest also that median number of years
  taken in math by males and females is quite
  similar.

16
Modeling statistical thinking from conception to
conclusion

• The output of the t-test on means

17
Modeling statistical thinking from conception to
conclusion

• Levenes test -- suggests that homogeneity of
  variance assumption of t-test is met (p .294 gt
  .05).
• Note that t(148) 2.107, p .04.
• Reject null hypothesis in favor of alternative.
• Conclude that for those from the South who have
  always stayed on track, mean number of years of
  math taken in high school by college-bound males
  is statistically significantly different than
  that taken by females.
• Effect size of result, according to Cohens d, is
  small to moderate.
• Mean number of years of math taken by males is
  .35 standard deviations greater than mean number
  taken by females.
• Results appear to contradict visual impressions
  based on the boxplots.

18
Modeling statistical thinking from conception to
conclusion

• Explore apparent contradiction of results with a
  population pyramid provides a more detailed view
  of the separate male and female distributions.
• Even with similarly-shaped distributions, medians
  can provide a different result from means and
  that multiple representations of data can be
  useful.

19
Modeling statistical thinking from conception to
conclusion
20
Exploring a large data set checking underlying
inferential assumptions

• Exercise 6.9, Statistics Using SPSS
• Use the Framingham data set to regress initial
  total cholesterol (TOTCHOL1) on initial body mass
  index (BMI1).
• Create the scatterplot for these two variables.
  Label the scatterplot by ID number and
  superimpose the regression line. Would you say
  that linear regression is appropriate in this
  case? Explain.
• According to the scatterplot, which person is
  most unusual in terms of the linear trend between
  serum cholesterol and BMI? What is his or her ID
  number? Looking at the data set, is this person
  male or female? How old was this person when the
  study began?
• With all people included in the data set, what is
  the equation of the regression line? With the
  bivariate outlier omitted, what is the equation
  of the regression line? Do the coefficients
  change as a result of omitting this person from
  the data set?

21
Exploring a large data set checking underlying
inferential assumptions

• Scatterplot suggests a linear, rather than a
  non-linear, relationship between these variables.
  
• A bivariate outlier (case 205) may be identified
  as 55 years old and female. She has an unusual
  combination of total cholesterol and BMI values
  relative to the other cases.

22
Exploring a large data set checking underlying
inferential assumptions

• To what extent does this individual influence the
  regression coefficients?
• With all people included, the equation is
  predicted TOTCHOL1 1.82(BMI1)189.98
• When omitting ID 205, the equation is predicted
  TOTCHOL1 1.93(BMI1)186.52
• Using technology we are able to demonstrate
  simply that even one case in a data set of 400
  cases can influence the results of a regression
  analysis.

23
The importance of open-ended problems

• Open-ended problems -- the student is required to
  develop an analytic strategy on his/her own
  he/she is not asked to carry out a series of
  directed analyses (e.g., compute the mean,
  compute the SD, etc.)
• As an example, see Exercise 3.15, Statistics
  Using SPSS. This question asks students to
  provide a demographic assessment by sex of total
  serum cholesterol (TOTCHOL1) measured at baseline
  in the Framingham data set.
• The student needs to construct an appropriate
  strategy for arriving at this assessment.

24
The importance of open-ended problems

• One Approach. According to the boxplot, the
  cholesterol distribution is fairly symmetric for
  men, but positively skewed for women. The IQR for
  females is larger, so their cholesterol values
  are more heterogeneous. The median cholesterol
  for women is slightly higher than it is for men.
  Descriptive statistics quantify these
  impressions. According to the skewness ratio, the
  distribution is fairly symmetric for men (1.17)
  and severely positively skewed for women (4.34).
  The median cholesterol for men in the study at
  initial examination (median 231.50) was
  slightly lower than for women (median 239.00).
  The distribution of cholesterol for men was
  slightly more homogeneous (IQR 54) than it was
  for women (IQR 60). For men, the cholesterol
  levels ranged from 133 to 333, whereas for women
  they ranged from 152 to 464.

25
Additional Ways to Emphasize Statistical Literacy
Thinking

• Choosing an appropriate method of analysis
  Leaving it up to the student Exercise 11.29,
  Statistics Using SPSS.
• Visualizing data Table 6.4, Anscombe data sets
  -- Statistics Using SPSS.
• Using simulations Example 9.5, Statistics Using
  SPSS.

26
Choosing an appropriate method of analysis
leaving it up to the student

• Exercise 11.29, Statistics Using SPSS. For each
  of the following questions based on the NELS data
  set, select an appropriate statistical procedure
  to use to answer it from the list that follows.
  Then use SPSS to conduct the appropriate
  hypothesis test in cases where the underlying
  assumptions are tenable. If the result of a
  hypothesis test is statistically significant,
  report and interpret an appropriate measure of
  effect size.
• Among college-bound students who are always at
  grade level, do those who attended nursery school
  (NURSERY) tend to have higher SES than those who
  did not?
• Among college-bound students who are always at
  grade level, does self-concept differ in eighth
  (SLFCNC08) and tenth (SLFCNC10) grades?
• Among college-bound students who are always at
  grade level, do those who attend public school
  (SCHTYP8) perform differently in twelfth-grade
  math achievement (ACHMATH12) from those who
  attend private school? (Note that to answer this
  question the variable SCHTYP8 has to be recoded
  to be dichotomous as described in Chapter 4.)
• Among college-bound students who are always at
  grade level, do families typically have four
  members (FAMSIZE)?
• Among college-bound students who are always at
  grade level, do students tend to take more years
  of English (UNITENGL) than math (UNITMATH)?

27
Visualizing data Anscombes (1973) data sets
from Statistics Using SPSS.
28
Visualizing data Anscombes (1973) data sets
from Statistics Using SPSS.

• While visually quite different, for all four
  panels of data
• Mx 9.0, My 7.5, Sx 3.17, Sy 1.94, rxy
  .82,
• the standard error of the estimate is 1.12, and
• predicted Y 0.5X 3.
• Underscores the importance of having the ability
  to visualize ones data.

29
The Utility of Simulations

• See Example 9.5, Statistics Using SPSS, which
  uses simulation to appreciate the power of the
  Central Limit Theorem.
• Based on the following syntax file, students may
  view first hand how the sampling distribution of
  means varies as a function of sample size.

30
The Utility of Simulations

• The syntax file SAMPDISVER2.SPS appears below
• DEFINE bootmn (nsamp !tokens(1) / nsize
  !tokens(1) /samsize !tokens(1)
• / bootvar !tokens(1) / outfile !tokens(1)).
• Sort cases by !bootvar.
• vector data (!nsize).
• compute data (casenum) !bootvar.
• compute nobreak 1.
• Aggregate outfile
• /break nobreak
• /data1 to !concat(data,!nsize) max(data1 to
  !concat(data,!nsize)).
• Vector data data1 to !concat(data,!nsize).
• vector tmp(!nsize).
• loop p 1 to !nsamp.
• loop q 1 to !nsize.
• compute tmp(q) 0.
• End loop.
• Loop I 1 to !samsize.
• compute id runk(uniform(!nsize) 1).
• Compute tmp(id) tmp(id) 1.

31
The Utility of Simulations

• Figure 9.5. Positively skewed population of 1,000
  scores ? 8, ? 4.

32
The Utility of Simulations

• Figure 9.6. Sampling distribution of 10,000
  means, each of size 100 ? 8, ? 0.4.

33
Recommendation 4 Stress Conceptual Understanding
Over Procedural Knowledge

• Avoid time-consuming mechanical hand computation
  through the use of technology.
• Focus on data exploration of a single data set to
  show that only from multiple analyses can one
  achieve a thorough understanding of the
  information contained in that data set.
• Present formulas in a form that enables greater
  conceptual understanding, not computational ease
  See Equation 3.4 in Statistics Using SPSS.

34
Recommendation 5 Foster active learning in (and
outside) the classroom

• Bring an applied perspective to an otherwise
  theoretical or conceptual presentation by
  demonstrating how one may apply the method(s)
  discussed. We have found that by using SPSS one
  can accomplish this well.
• Demonstrate with the help of real data that
  students can relate to (e.g., the NELS).
• Present the theoretical or conceptual
  underpinnings of a method before demonstrating on
  SPSS, for example.
• Have instructor demonstrate on his/her own
  computer with class following along.
• Provide good notes of how to replicate what has
  been demonstrated in class. Our text has the
  SPSS commands explicitly stated in boxed-in
  areas.
• Assign data-driven problems for homework that
  continue to reinforce statistical literacy and
  thinking.

35
Recommendation 6 Assessments

• Align with Learning Goals.
• Focus on Understanding Key Ideas and Not Just on
  Skills, Procedures, and Computed Answers.
• Include the Communication of Statistical Concepts
  and Analytic Results.
• Use Multiple Formats Quizzes, Exams, Homework
  Problem Sets, Article Critiques, Individual and
  Group Term Projects.

36
Poised for the Future

• With a good conceptual understanding of
  statistics and a good hands-on working knowledge
  of a versatile and accessible software package
  like SPSS, students will be well-poised for
  future study in statistics and for conducting
  their own research at the undergraduate or
  graduate level that relies on a fundamental
  quantitative analysis of data.
• Statistics Using SPSS An Integrative Approach
  has been written to allow students to achieve
  both goals under one cover.

37
Where to Find Materials Discussed Today

• Statistics using SPSS An Integrative Approach
• http//www.cambridge.org
• ISBN 9780521676373
• Download a free, 30-day trial of SPSS Statistics
  17.0 at
• http//www.spss.com/statistics
• Click on the Downloads tab

38
References

• Anscombe, F.J.. (1973). Graphs in Statistical
  Analysis, American Statistician, 27, 17-21.
• Chance, B., Ben-Zvi, D., Garfield, J., Medina,
  E. (2007). The role of technology in improving
  student learning of statistics. Technology
  Innovations in Statistics Education Vol. 1 No.
  1, Article 2. http//repositories.cdlib.org/uclas
  tat/cts/tise/vol1/iss1/art2
• Friel, S. (2007). The research frontier Where
  technology interacts with the teaching and
  learning of data analysis and statistics. In G.W.
  Blume M.K. Heid (Eds.), Research on technology
  and the teaching and learning of mathematics
  Cases and Perspectives (Vol. 2, pp. 279-331).
  Greenwich, CT Information Age Publishing, Inc.
• GAISE (2005). Guidelines for assessment and
  instruction in statistics education (GAISE)
  college report. The American Statistical
  Association (ASA). Retrieved August 25, 2008.
  http//www.amstat.org/education/gaise/GAISEColleg
  e.htm
• Moore, D.S. (1997). New pedagogy and new
  content the case of statistics. International
  Statistics Review, 635, 123-165.
• Weinberg, S.L. Abramowitz, S.K. (2008).
  Statistics Using SPSS An Integrative Approach
  (2nd ed.). New York Cambridge University Press.

39
Contact Information
Prof. Sharon L. Weinberg New York
University sharon.weinberg_at_nyu.edu Prof. Sarah
K. Abramowitz Drew University sabramow_at_drew.edu