Surfing the education wave with official statistics

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Surfing the education wave with official
statistics

• Sharleen Forbes
• Statistics New Zealand
• School of Government, Victoria University

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To cover

• The role of a National Statistics Office in
  education - why surf at all?
• Prioritising - what can we afford and where
  should we invest?
• Current initiatives
• - Community groups
• Schools
• - Tertiary education
• Playing with official statistics
• Examples for classroom use
• Where to in the future?
• Providing more sets of real data
• New ways of visualising data

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Role of Statistics New Zealand

• Lead the state sector in production of official
  statistics (official statistics system
  responsibility)
• Employ large number of statisticians
• Not funded specifically for education (promote,
  partner or facilitate rather than provide)
• Need to provide easily understood statistics
  (Public Good requirement)
• Should target informal / second chance education
  (NSO Workshop ICOTS 6, Singapore)
• Focus on official statistics

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• Differences between official and other statistics

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Prioritising - what can we afford
- where should we invest?

• Need to balance external demands with internal
  training needs
• Limited funds (need to pick the wave - where
  can we make a difference?)

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Current initiatives -
community groups

• State sector (Official Statistics System)
• Certificate of Official Statistics (Level 4)
• School of Government and ANZSOG courses
• Workshops and seminars
• Journalists
• JTO compulsory statistics unit(s)
• Statistics prize
• Small businesses
• GoStats!
• Maori communities
• Pilot projects

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Current initiatives -
schools

• Resources to support the new curriculum
• Schools Corner on Statistics New Zealand website
  (http//www.stats.govt.nz/schools-corner)
• CensusAtSchools
• Joint funder (http//www.censusatschool.org.nz)
• Dataset provision
• Census
• Official Statistics Surveys
• Synthetic Unit Record Files (SURFs)

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Current initiatives -
tertiary education

• Network of Academics in Official Statistics
• To provide training and research
• Undergraduate student prizes (1000)
• Official Statistics Research Fund
• Partnerships with researchers
• Vice-Chancellors agreement
• Confidentialised Unit Record Files (CURFs)
• Half-time Professor of Official Statistics
• School of Government, Victoria University

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Playing with official statistics - Examples

• Census data
• Official Statistics Survey data
• Specially constructed data sets
• Confidentialised Unit Record Files (CURFS)
• Synthesised Unit Record Files (SURFS)

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The statistical investigation (PPDAC)
cycle(Creators Wild and Pfannkuch, Auckland
University,1999)

• Problem statement of the research
  questions
• Plan procedures used to carry out the study
• Data data collection process
• Analysis summaries and analyses of the data to
  answer the questions posed
• Conclusion about what has been learned.

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1. Census data example

• Problem (Question)Is Hamilton greener than
  Wellington?
• Plan / DataUse 2006 Census data on the way
  people travel to work to indicate how green a
  city is. (www.stats.govt.nz/census/)

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• Analysis

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Definitions (Re)classifications

• How many and what classes of green shall we
  have?
• Have defined green-ness by mode of travel to
  work
• Lets have only 3 classes of green-ness
• Not green Driving private or company vehicles
• Green Passenger in private vehicle or using
  public transport
• Very green Walking, biking or working at home
• Omit other categories

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More analysis
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Conclusion (and classroom questions)

• Conclusion
• Wellington is greener than Hamilton
• Questions
• Is mode of travel to work a good indicator of
  green-ness?
• What other variables might affect mode of
  travel?
• Should we use more than one indicator?

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Official Statistics Survey data

• Problem (questions)
• Are fewer people unemployed now than in previous
  years?
• Are you less likely to be unemployed if you have
  a high level of education ?
• Plan / Data
• Analyse time series data on national
  unemployment rates
• Statistics New Zealands Household Labour Force
  Survey (www.stats.govt.nz)

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Analysis - Question a).
Time series plots
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Conclusions (and classroom questions)

• Conclusions
• Unemployment has been lower since 2004 than in
  previous years
• Since 2004 unemployment has stayed at roughly the
  same level (about 4)
• Seasonality is not marked
• Questions
• What was the cause of the peaks (1991-3 and 1999)
  in unemployment?
• What do the small peaks in 2004 - 2007 reflect?
• Should we answer a count question (number
  unemployed) with a rate (percent unemployed in
  the labour force)?

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Analysis - Question b).
Time series plots
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Conclusions (and classroom questions)

• Conclusions
• Pattern over time is similar for all
  qualification groups.
• Unemployment rate always highest for workers with
  no educational qualifications.
• Questions
• Which group appears to be the most disadvantaged
  when unemployment is high?
• What appears to be different in recent (compared
  to past) years between the qualification groups?

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Another sample survey example - a
simple look at seasonality

• Problem (question)
• Is there an annual pattern in retail sales?
• Plan / data
• Check for seasonality in quarterly summary time
  series data for monthly retail trade sales (in
  dollars)
• Statistics New Zealands Retail Trade Survey
• (www.stats.govt.nz)

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Analysis Time series
plot
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Conclusions (and classroom questions)

• Conclusions
• Annual seasonality - peak every December /
  January
• Rising trend over time - plateau in last 3
  quarters
• Questions
• What components of retail trade would contribute
  most to the December peaks?
• What does it mean when the seasonally adjusted
  and trend lines lie virtually on top of each
  other?
• Easter fell in the March rather than June quarter
  in 2008. Is there any evidence that this affected
  the pattern of retail sales?

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3. Specially constructed data sets -
Confidentialised datasets
(e.g. 2004 Income Survey)
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SURFING Classroom Examples (SURF creator
Pauline Stuart, Statistics NZ)

• Using 2004 Income Survey SURF data.
• Data available on CD or downloaded from Schools
  Corner on the Statistics New Zealand website
  (www.stats.govt.nz/schoolscorner/).
• Dataset has 200 records and seven variables
• gender (male, female)
• highest education qualification (none, school,
  vocational, degree)
• marital status (married, never, previously,
  other)
• ethnic group (European, Maori, Other)
• age (15-45)
• hours worked weekly (0-79)
• weekly income (0-2000).

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Example

• Background
• In this example we let the SURF dataset represent
  a companys employees.
• Every employee creates the same administration
  costs regardless of how many hours are worked.
• The company is concerned that its staff
  administration costs are too high.
• Problem (questions)
• Do most employees work a normal (40 hour) week?
• What variables are related to the number of hours
  worked?

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Specific questions for secondary school classrooms

• What proportion of employees work at least 40
  hours per week? (Summary)
• 2. Are these proportions different for males
  and females? (Comparison)
• 3. Do males tend to work more hours per week
  than females? (Comparison)
• 4. What is the relationship between hours
  worked and income? (Relationship between two
  measurement variables)

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Plan / Data (a).Take a random sample of 35 from
the SURF

• Analysis

Table Sample Summary Statistics
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Conclusions (and classroom questions)

• Conclusions
• Only half of all employees work 40 hours or more.
  
• On average (mean) males work longer hours than
  femalesHours females work vary (standard
  deviation, inter-quartile range) more than hours
  males work.
• Questions
• Are samples of size 17 and 18 large enough?
  (beware of categorical data)
• What does it indicate when the mean and the
  median are different?

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Plan / Data (b). - Resample

• Compare between students samples (summary
  statistics)
• Combine students samples and create new summary
  statistics
• Sample (another 35 say) and compare (or combine)
  summary statistics

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Plan / Data (c). - Use all the
SURF data

• Analysis

• How do sample statistics compare with total SURF?
• Would a graph be easier to interpret than the
  table?

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• Analysis
• Graphs of SURF data

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Conclusions (and classroom questions)

• Conclusions
• Use tables for reference, graphs to tell a story.
• Females bimodal? at 5-25 hours (part-time) and
  35-50 hours (full-time)?
• Males tri-modal? small at 10-15 hours
  (part-time), large at 35-55 hours (full-time),
  small at 60-75 hours (maybe managers)?
• Proportions of males and females working 40 hours
  or more are different. About half of the males do
  but only about a quarter of the females do.
• Questions
• What is the clumping at 40 hours?
• Given the size of the SURF do you think the above
  patterns will be similar if other SURFs are
  taken?

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Analysis - Question 4. Relationship between
hours worked and income?
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Conclusion (and classroom questions)

• Conclusion
• Income increases as work more hours.
• Questions
• What is the estimated income for someone who
  doesnt work?
• What extra income (on average) is expected if
  work an extra hour per week?
• Is the (regression) line a good fit to the data?

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Other factors related to hours worked?(Sex /
Highest qualification / Ethnicity, etc.)Example
from a first-year university course Creator
John Harraway, Otago University

• Plan / Data
• Recategorise highest qualification
• Secondary None OR Secondary (105) S
• Tertiary Vocational OR Tertiary (95) T
• Do a linear regression in SPSS(equivalent to
  t-test for difference in means)

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AnalysisSPSS regression output

• Weekly Income (414 344Tertiary)
• 95 confidence interval for increase in income if
  have a tertiary qualification is257 - 431
• T 7.8, p 0.000..
• R2 0.24 (only about quarter of the variation in
  the points explained by the best-fitting line)

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Conclusion (and classroom question)

• Conclusion
• Income is higher on average (by 344) if have a
  tertiary qualification.
• Question
• Is qualification a good explanator of income
  earned?

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Are there multiple factors related to income?

• Problem (Question)Are both qualification and
  hours worked related to income?
• Plan / DataDo a multiple regression (main
  effects model - no interaction terms) in SPSS
  using SURF data

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AnalysisScatterplot Income by hours worked
and qualification
(S secondary, T tertiary)
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SPSS regression output (values extracted
rounded for all 3 models)
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Conclusions

• Weekly Income (-19 15xHours Worked
  183xTertiary)
• Conclusions
• Both hours worked and highest qualification are
  related to weekly income earned
• Mean increase in income per hour worked is
  reduced (from 17 to 15) if tertiary also
  considered
• Mean increase in income if have a tertiary
  qualification is also reduced (from 344 to 183)
  when adjusted for number of hours worked
• 95 confidence interval for the intercept (income
  when no hours are worked) still contains zero

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Classroom questions

• Questions
• Is there any interaction between hours worked
  and qualification?
• Which of the above models fits the data best?
• Are there any outliers?
• What does a scatterplot of the residuals
  (distances from the line) indicate?

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More resampling

• Use SURF as sample from CURF population
• Bootstrapping
• Take repeated samples with replacement (of same
  size as original, n200).
• Jack-knifing
• Take repeated samples dropping one value from
  original sample each time (n199).
• Calculate mean and standard deviation of sample
  means
• Compare summary statistics with CURF (or full
  2004 Income Survey).

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Where to from here?

• Continue and develop partnerships (academics,
  teachers, community groups)
• More CURFs and SURFs(official launch 1 September
  2008 - 2001 Savings Survey SURF
  www.stats.govt.nz/schools-corner)
• Increased free access to data for post-graduate
  students
• Data visualisation (dynamic graphs)
• More across-discipline outputs

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Animated population pyramids(Creator Martin
Ralphs, Statistics NZ)
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Economic structure population pyramid(Office of
National Statistics UK)
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Gapminder www.gapminder.orgGeography, history,
demography, econometrics(Creator Hans Rosling)
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Questions and comments

• What are your ideas for the future?
• Contact sharleen.forbes_at_stats.govt.nz
• Thank you.