An Integrated Approach to Teaching with Real Data

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An Integrated Approach to Teaching with Real Data

• Joint Mathematics Meetings, January 2005
• MAA Contributed Paper Session
• Using Real-World Data to Illustrate Statistical
  Concepts
• Sarah Knapp Abramowitz, Drew University
• Sharon Lawner Weinberg, New York University

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The National Education Longitudinal Study of 1988

• based on a survey conducted by the National
  Center of Education Statistics (NCES) of a
  nationally representative sample of eighth
  graders
• Initiated in 1988, additional waves in 1990,
  1992, and 1994
• The goal of the study was to measure achievement
  outcomes in four core subject areas (English,
  history, mathematics, and science), and personal,
  familial, social, institutional, and cultural
  factors that might relate to these outcomes

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Our NELS

• Sub-sample of 500 cases and 48 variables
• Sampled randomly from the approximately 5,000
  students who responded to all four
  administrations of the survey and who pursued
  some form of post-secondary education

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Beneficial Properties of NELS

• Contains a variety of variables
• Can be used throughout the course because it can
  be analyzed by multiple methods
• Is appropriately analyzed using a computer
  statistics package, modeling practical data
  analytic skills.
• Demonstrates some of the subtleties in selecting
  the appropriate statistical technique for a given
  research question
• Contains real values, many which are intuitive,
  so that interpretation is emphasized and students
  gain number sense

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Selected Variables in the NELS

• Naturally numeric FAMSIZE, the number of
  members in the students household
• Instrument based composites SLFCNC08, eighth
  grade self-concept, and SES, socio-economic
  status
• Coded categories GENDER, HOMELANG, the home
  language background of the student with 1
  representing non-English only, 2 representing
  non-English dominant, 3 representing English
  dominant, and 4 representing English only, and
  CUTS12 that represents the number of times the
  student skipped or cut classes in twelfth grade
  on an ordinal scale with 0 representing never, 1
  representing one to two times, 2 representing
  three to six times, etc
• Likert-type variables TCHERINT, which measures
  the level of agreement with the statement my
  teachers are interested in students on a
  four-point scale.

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Variety of DistributionsScale Variables

• Approximately symmetric SES and achievement
  variables like ACHMAT12
• Negatively skewed SLFCNC08 and SCHATTRT
• Positively skewed EXPINC30, the estimate the
  student makes in eighth grade for his or her
  income at age 30 and APOFFER, the number of
  advanced placement courses offered by the school
  the student attends

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Variety of DistributionsCategorical Variables

• Fairly evenly distributed between categories
  GENDER
• Unevenly distributed HOMELANG (81 speak only
  English at home) and CIGARETT, whether or not the
  student had ever smoked a cigarette by eighth
  grade (85 indicated that they had not).

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Examples Using NELS in Paper

• Graphical displays of a single variable
• Measures of central tendency
• Describing relationships between variables
• Independent samples t-test

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Describing relationships between variables

• Exemplify a variety of magnitudes for the Pearson
  correlation
• Exemplify relationships between variables with a
  variety of levels of measurement

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Pearson Correlations of different directions and
magnitudes

• Between ACHMAT12 and TCHERINT,
• r -.18. For TCHERINT, a low score indicates
  greater perceived teacher interest.
• Between ACHMAT12 and ACHRDG12,
• r .64.
• Between ACHMAT12 and FAMSIZE,
• r .02.

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Other cases of Pearson

• Point-biserial Between ACHMAT12 and NURSERY, r
  .13
• Phi-coefficient Between NURSERY and COMPUTER, r
  .20

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Other types of relationships

• Dichotomous variables and those that are nominal
  or ordinal with fewer than five categories.
  Method contingency table
• Ordinal variables and those that are dichotomous,
  ordinal, interval, or ratio. Method Spearman
  correlation
• Nominal or ordinal with fewer than five
  categories variables and those that are interval
  or ratio. Method Measures of central tendency

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Examples of other types of relationships

• Between REGION and NURSERY
• Method Contingency table
• Conclusion Approximately 34 percent of the
  children who had not attended nursery school
  owned a computer in eighth grade, whereas
  approximately 56 percent of those who had
  attended nursery school owned a computer in
  eighth grade

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Examples of other types of relationships

• Between HWKIN12 and HWKOUT12
• Method Spearman correlation, rho .38
• Conclusion Students who spend more time in
  school on homework tend to do so outside of
  school too.

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Examples of other types of relationships

• Between ACHMAT12 and REGION
• Method Measures of central tendency. Because the
  distribution of twelfth grade math achievement is
  skewed for the Northeast and the North Central,
  we compare medians.
• Conclusion We see that among students in the
  NELS data set, the highest typical achievement is
  found in the West (median 59.03), followed by
  the Northeast (median 58.74), the North Central
  (median 56.50), and then the South (median
  55.29).

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Benefits of the Approach

• Correlation magnitudes are typical
• Can easily study the effects of transformations
  such as translation and reflection
• Emphasizes choosing an appropriate statistical
  technique and the importance of the level of
  measurement and the shape of the distribution of
  the variable
• Demonstrates that several analytical approaches
  may be possible

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Obtaining the NELS data set

• The following website contains a copy of the
  paper, this Powerpoint presentation, and the NELS
  data set formatted for SPSS. http//www.users.dre
  w.edu/sabramow/
• Send an e-mail request to sabramow_at_drew.edu
• Make your own version of the NELS through the
  NELS88 page of the National Center for Education
  Statistics website, http//nces.ed.gov/surveys/nel
  s88/