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Surfing the education wave with official statistics
Sharleen Forbes
Statistics New Zealand
School of Government, Victoria University
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
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
Differences between official and other statisticsOFFICIAL STATISTICS ”OTHER” STATISTICS / RESEARCH
Often based on complex sample designs
Often simple surveys or designed experiments
Broad coverage (many variables – often high-level measures)
In-depth studies
Large-scale (provide comparisons between groups)
Usually relatively small scale
(experiments or surveys)
Usually repeated regularly
(provide long time series)
Mainly cross-sectional
(single point of time)
Internationally comparable
(agreed standards, classifications, indexes)
Relevant to population studied
(focused on research/policy question)
Simple analysis provided by collectors (Univariate or bivariate)
Sophisticated analysis (Multivariate)
Provide primary data source Can involve secondary analysis (of other data sources)
High cost Generally lower cost
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?)
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
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)
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-Chancellor’s agreement – Confidentialised Unit Record Files (CURFs)
• Half-time Professor of Official Statistics– School of Government, Victoria University
Playing with official statistics - Examples
1. Census data
2. Official Statistics Survey data
3. Specially constructed data sets– Confidentialised Unit Record Files (CURFS)
– Synthesised Unit Record Files (SURFS)
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.
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/)
M o d e o f t r a v e l t o w o r k
0 %
1 0 %
2 0 %
3 0 %
4 0 %
5 0 %
6 0 %
W o r k e d a t
H o m e
D i d N o t G o
T o W o r k
T o d a y
D r o v e a
P r i v a t e C a r ,
T r u c k o r
V a n
D r o v e a
C o m p a n y
C a r , T r u c k
o r V a n
P a s s e n g e r
i n a C a r ,
T r u c k , V a n
o r
C o m p a n y
B u s
P u b l i c B u s T r a i n M o t o r C y c l e
o r P o w e r
C y c l e
B i c y c l e W a l k e d o r
J o g g e d
O t h e r N o t
E l s e w h e r e
I n c l u d e d
M o d e o f t r a v e l
Percenatge of population
H a m i l t o n C i t y
W e l l i n g t o n C i t y
• Analysis
Definitions & (Re)classifications
• How many and what classes of ‘green’ shall we have?- Have defined ‘green-ness’ by mode of travel to work
- Let’s 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
• More analysis
G r e e n - n e s s o f t r a v e l t o w o r k
0 %
1 0 %
2 0 %
3 0 %
4 0 %
5 0 %
6 0 %
7 0 %
V e r y g r e e n G r e e n N o t g r e e n
G r e e n s t a t u s o f m o d e o f t r a v e l t o w o r k
Percentage of
popualtion
H a m i l t o n C i t y
W e l l i n g t o n C i t y
• 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?
2. Official Statistics Survey data
• Problem (questions)a) Are fewer people unemployed now than in
previous years?b) Are you less likely to be unemployed if you
have a high level of education ?
• Plan / DataAnalyse time series data on national unemployment rates – Statistics New Zealand’s Household Labour Force Survey
(www.stats.govt.nz)
• Analysis - Question a).
Time series plotsQ u a r t e r l y N e w Z e a l a n d u n e m p l o y m e n t r a t e s
0
4
8
1 2
M a r
8 6
M a r
8 7
M a r
8 8
M a r
8 9
M a r
9 0
M a r
9 1
M a r
9 2
M a r
9 3
M a r
9 4
M a r
9 5
M a r
9 6
M a r
9 7
M a r
9 8
M a r
9 9
M a r
0 0
M a r
0 1
M a r
0 2
M a r
0 3
M a r
0 4
M a r
0 5
M a r
0 6
M a r
0 7
Q u a r t e r
P e r c e n t
3 p o i n t m o v i n g
a v e r a g e
7 p o i n t m o v i n g
a v e r a g e
U n a d j u s t e d D a t a
• 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)?
• Analysis - Question b).
Time series plotsQuarterly NZ Unemployment Rates by Highest Education
Qualification
0.0
5.0
10.0
15.0
20.0
Mar 86 Mar 87 Mar 88 Mar 89 Mar 90 Mar 91 Mar 92 Mar 93 Mar 94 Mar 95 Mar 96 Mar 97 Mar 98 Mar 99 Mar 00 Mar 01 Mar 02 Mar 03 Mar 04 Mar 05 Mar 06 Mar 07
Quarter
Percent
No SchoolPost SchoolSchool
• 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?
Another sample survey example - a simple look at seasonality
• Problem (question)Is there an annual pattern in retail sales?
• Plan / dataCheck for seasonality in quarterly summary time series data for monthly retail trade sales (in dollars)
– Statistics New Zealand’s Retail Trade Survey (www.stats.govt.nz)
• Analysis Time series plot
Quarterly Retail Trade Sales
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
20,000
2001Jun
Dec Jun Dec Jun Dec Jun Dec Jun Dec Jun Dec Jun Dec Jun
Quarter
Value ($Million)
Actual Seasonally adjusted Trend
• 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?
3. Specially constructed data sets - Confidentialised datasets (e.g. 2004 Income Survey)
HouseholdLabour Force Survey June 2004
New Zealand Income Survey 2004
130 variables
29 000 records
HLFS/NZIS CURF 2004
7 variables
200 records
Our SURF
130 variables
Teachers and students
Researchers (Government, Academic)
29 000 records
29 000 records
130 variables
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).
Example• Background
– In this example we let the SURF dataset represent a company’s 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?
Specific questions for secondary school classrooms
1. 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)
• Plan / Data (a).Take a random sample of 35 from the SURF
Total By gender
(Records) (35) Male(17) Female(18)
Mean 40.0 45.5 34.7
Standard deviation 11.9 8.4 12.6
Minimum 6 38 6
Lower quartile 38 40 27
Median 40 40 38.5
Upper Quartile 45 45 42
Maximum 65 65 50
• AnalysisTable: Sample Summary Statistics
• Conclusions (and classroom questions)
• Conclusions1. Only half of all employees work 40 hours or more.
3. 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?
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
• Plan / Data (c). - Use all the SURF data
• How do sample statistics compare with total SURF?• Would a graph be easier to interpret than the table?
Summary Statistics (Total SURF): Hours worked
Total SURF
By gender
(Records) (200) Male(93) Female(107)
Mean 33.7 42.1 26.4
Standard deviation 16.2 13.2 14.9
Minimum 2 5 2
Lower quartile 20 39 14
Median 40 40 25
Upper Quartile 45 50 40
Maximum 70 70 60
• Analysis
0
5
10
15
20
25
30
female
5
10
15
20
25
30
male
Hours_Worked
0 10 20 30 40 50 60 70 80
Collection 1Histogram
Hours_Worked
0 10 20 30 40 50 60 70
Collection 1Dot Plot
Hours_Worked
0 10 20 30 40 50 60 70
Collection 1Box Plot
• Analysis Graphs of SURF data
• 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?
• Analysis - Question 4. Relationship between hours worked and income?
Weekly_Income = 17.1Hours_Worked + 0.35 ; r2
= 0.63
200
400
600
800
1000
1200
1400
1600
1800
Hours_Worked
0 10 20 30 40 50 60 70 80
Collection 1Scatter Plot
• Conclusion (and classroom questions)
• Conclusion– Income increases as work more hours.
• Questions– What is the estimated income for someone who
doesn’t 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?
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)
• AnalysisSPSS regression output
• Weekly Income = $(414 + 344Tertiary)
• 95% confidence interval for increase in income if have a tertiary qualification is$257 - $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)
• 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?
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
• Analysis
Scatterplot: Income by hours worked and qualification
(S = secondary, T = tertiary)
SPSS regression output (values extracted & rounded for all 3 models)
Model
UnstandardisedCoefficients
95% Confidence
Interval t Sig. R2ß Std error
1. (Constant) .3 34 (-68,68) 0.01 .992 .63
Hours 17 1 (15,19) 18.5 .000
2. (Constant) 414 30 (356, 472) 14.0 .000 .24
Tertiary 344 44 (257, 431) 7.8 .000
3. (Constant) -19 32 (-83, 45) -0.59 .553 .69
Hours 15 1 (14,16) 16.4 .000
& Tertiary 183 30 (125, 242) 6.1 .000
• 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
• 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?
More resampling
Use SURF as sample from CURF population
• Bootstrapping – Take repeated samples with replacement (of same size as
original, n=200).
• Jack-knifing– Take repeated samples dropping one value from original
sample each time (n=199).
• Calculate mean and standard deviation of sample means
• Compare summary statistics with CURF (or full 2004 Income Survey).
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
Animated population pyramids(Creator: Martin Ralphs, Statistics NZ)
Economic structure population pyramid(Office of National Statistics: UK)
Gapminder: www.gapminder.orgGeography, history, demography, econometrics(Creator: Hans Rosling)
