Transcript An Integrated Approach to Teaching with Real Data

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
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
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
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
Selected Variables in the NELS
• Naturally numeric: FAMSIZE, the number of members in the
student’s household
• Instrument based composites: SLFCNC08, eighth grade selfconcept, 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.
Variety of Distributions
Scale 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
Variety of Distributions
Categorical 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).
Examples Using NELS in Paper
•
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Graphical displays of a single variable
Measures of central tendency
Describing relationships between variables
Independent samples t-test
Describing relationships between
variables
• Exemplify a variety of magnitudes for the
Pearson correlation
• Exemplify relationships between variables
with a variety of levels of measurement
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.
Other cases of Pearson
• Point-biserial: Between ACHMAT12 and
NURSERY, r = .13
• Phi-coefficient: Between NURSERY and
COMPUTER, r = .20
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
Examples of other types of
relationships
• Between REGION and NURSERY
• Method: Contingency table:
Count
NURSERY Nursery
School Attended?
Total
0 No
1 Yes
COMPUTER Computer
Owned by Family in 8th
Grade?
0 No
1 Yes
92
47
125
156
217
203
Total
139
281
420
• 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
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.
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).
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
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.drew.edu/sabramow/
• Send an e-mail request to [email protected]
• Make your own version of the NELS through the
NELS88 page of the National Center for
Education Statistics website,
http://nces.ed.gov/surveys/nels88/