1. Surfing the education wave with official statistics
Sharleen Forbes
Statistics New Zealand
School of Government, Victoria University

2. 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

3. 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

4. Differences between official and other statistics
OFFICIAL 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

5. 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?)

6. 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

7. Current initiatives - schools
Resources to support the new curriculum
Schools Corner on Statistics New Zealand website (
CensusAtSchools
Joint funder (
Dataset provision
Census
Official Statistics Surveys
Synthetic Unit Record Files (SURFs)

8. 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

9. 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)

10. 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.

11. 1. Census data example
Problem (Question) Is Hamilton ‘greener’ than Wellington?
Plan / Data Use 2006 Census data on ‘the way people travel to work’ to indicate how ‘green’ a city is. (

12. Analysis

13. 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

14. More analysis

15. Conclusion (and classroom questions)
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?

16. 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 Zealand’s Household Labour Force Survey (

17. Analysis - Question a). Time series plots

18. Conclusions (and classroom questions)
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 ( and 1999) in unemployment?
What do the small peaks in reflect?
Should we answer a count question (number unemployed) with a rate (percent unemployed in the labour force)?

19. Analysis - Question b). Time series plots

20. Conclusions (and classroom questions)
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?

21. 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 Zealand’s Retail Trade Survey (

22. Analysis Time series plot

23. Conclusions (and classroom questions)
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 Is there any evidence that this affected the pattern of retail sales?

24. 3. Specially constructed data sets - Confidentialised datasets (e. g
3. Specially constructed data sets Confidentialised datasets (e.g Income Survey)

25. 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 (
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).

26. Example Background Problem (questions)
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?

27. 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)

28. Plan / Data (a). Take a random sample of 35 from the SURF
Analysis
Table: Sample Summary Statistics
Total
By gender
(Records)
(35)
Male(17) Female(18)
Mean
40.0
Standard deviation
11.9
Minimum 6
Lower quartile 38
Median 40
Upper Quartile 45
Maximum 65

29. Conclusions (and classroom questions)
Only half of all employees work 40 hours or more.
On average (mean) males work longer hours than females Hours 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?

30. 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

31. Plan / Data (c). - Use all the SURF data
Analysis
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
Lower quartile 20 39 14
Median 40 25
Upper Quartile 45 50
Maximum 70 60
How do sample statistics compare with total SURF?
Would a graph be easier to interpret than the table?

32. Analysis
Graphs of SURF data

33. Conclusions (and classroom questions)
Use tables for reference, graphs to tell a story.
Females bimodal?: at 5-25 hours (part-time) and hours (full-time)?
Males tri-modal?: small at hours (part-time), large at hours (full-time), small at 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?

34. Analysis - Question 4. Relationship between hours worked and income?

35. Conclusion (and classroom questions)
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?

36. Other factors related to hours worked
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)

37. Analysis SPSS regression output
Weekly Income = $( Tertiary)
95% confidence interval for increase in income if have a tertiary qualification is $257 - $431
T = 7.8, p =
R2 = 0.24 (only about quarter of the variation in the points explained by the best-fitting line)

38. Conclusion (and classroom question)
Income is higher on average (by $344) if have a tertiary qualification.
Question
Is ‘qualification’ a good explanator of income earned?

39. Are there multiple factors related to income?
Problem (Question) Are both ‘qualification’ and ‘hours worked’ related to income?
Plan / Data Do a multiple regression (main effects model - no interaction terms) in SPSS using SURF data

40. Analysis Scatterplot: Income by hours worked and qualification
(S = secondary, T = tertiary)

41. SPSS regression output (values extracted & rounded for all 3 models)
Unstandardised
Coefficients
95% Confidence Interval t
Sig. R2 ß
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
.24
Tertiary
344 44
(257, 431)
7.8
3. (Constant)
-19 32
(-83, 45)
-0.59
.553
.69 15
(14,16)
16.4
& Tertiary
183
(125, 242)
6.1

42. Conclusions Conclusions
Weekly Income = $ ( xHours + 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

43. 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?

44. 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).

45. Where to from here?
Continue and develop partnerships (academics, teachers, community groups)
More CURFs and SURFs (official launch 1 September Savings Survey SURF
Increased free access to data for post-graduate students
Data visualisation (dynamic graphs)
More across-discipline outputs

46. Animated population pyramids (Creator: Martin Ralphs, Statistics NZ)

47. Economic structure population pyramid (Office of National Statistics: UK)

48. Gapminder: www. gapminder
Gapminder: Geography, history, demography, econometrics (Creator: Hans Rosling)

49. Questions and comments
What are your ideas for the future?
Contact
Thank you.