# Meet Maths People Day

Support for School Statistics from Statistics NZ [email protected] Statistics New Zealand Auckland Maths Assoc, University of Auckland Tue 25 Nov 08 1 Achievement objectives for today: Participants will: Use Stats NZ resources to deliver curriculum objectives Feel more confident and have more fun with teaching the stats in Mathematics and Statistics in the NZ Curriculum Find out (if time) what do (some Stats NZ) statisticians

really do! 2 Activities with www.stats.govt.nz: After an introductory ramble: Schools corner StatZing! SURFs 1, 2, 3 CensusAtSchool (a mention) Table Builder (= TB); esp Census data Infoshare: Time series galore Hot Off The Presses (= HOTPs): HOTPs and Statistical Literacy QuickStats: about your place etc Then: what do (some) statisticians really do!

3 Curriculum and Stats NZ Resources 1: The threads in the Stats and Probability strand: Statistical investigation phenomena involving: multivariate (case) datasets time-series datasets Statistical literacy reports with words, numbers, graphs risk Probability distributions dependence etc 4 Curriculum and Stats NZ Resources 2: The threads and resources for them:

Statistical investigation Schools Corner,StatZing! phenomena involving: HOTPs multivariate (case) datasets: SURFs,TB,CaS time-series datasets: Infoshare Statistical literacy NZ in Profile reports with Quickstats words, numbers, graphs: HOTPs risk, relative risk:HOTPs, Tables Probability distributions: Tables dependence etc: Tables; 2 way 5 Curriculum and Stats NZ Resources 3: Some are designed for schools Some are

(a big one) inadvertently useful for schools! EG: The HOTPs (Hot Off The Presses): EG: a rich source of real (we hope) info: New Zealand Income Survey: June 2008 quarter (a big one) Highlights | Commentary | Technical notes | Erratum | Tables | Stat Literacy: Evaluate stat reports (L 6,7,8) Stat investigation: Methodology: defining questions, sampling methods, errors (samp and non) etc etc etc etc Stat investigation:

Story, Data Time series Probability: One-way tables Two-way tables Statistical Enquiry Cycle: PPDAC PPDAC PPDAC PPDAC PPDAC6 Why be nice to schools?? Stats NZ: Dataset Dataset Dataset The World: Respondents: People Businesses

Data Inform ation Users: Public Professional Technical We need our clients to be informed & positive School stats is a vital way to achieve this 7 Two groups with converging interests: The Official Stats sector

The Mathematics and Statistics Education Community Vision: an informed society using statistics. Curriculum: students will be: thinking mathematically and statistically; solving problems, modelling situations. 8 A small problem: Dataset Dataset Dataset

Unit-record multivariate datasets: Teachers need them! Official Stats agencies have lots but cant release them! SURF 1 SURF 2 Some smart solutions: SURF 3 CensusAtSchool (sort-of) SURFs for Schools: 1, 2, 3 Area Unit Tables by Henderson North South

geographical Area Henderson Tangutu Woodglen Glen Eden East New Lynn North New Lynn South Males06 Females06 2,487 2,817 1,956 2,070 1,404 1,554 2,013 2,193 3,237 3,372

1,173 1,233 1,185 1,287 Tot06 5,304 4,023 2,955 4,203 6,609 2,406 9 2,472 Census at school 2009 New dates: 3 March 2009 until 9 April 2009 Register online:

http://www.censusatschool.org.nz/2007/register/ If you have previously registered, OK. Confirmation in November. Funded: X% by Stats NZ (1-X)% by MoE Expertise: Lots of it; from UoA 10 New for 2009 Teachers get their class results back if they choose. Early in year so 2009 data can be used for 2009 teaching. New questions: from consultations: Dept of Stats UoA, MoE, Stats NZ, teachers nationwide

Questionnaire critiqued by StatsNZ Questionnaire design team www.censusatschool.org.nz 11 www.stats.govt.nz se s a e l 4 Re 5Q u ic k by

P HOT : e l tit s 3 Infoshare Build 2 Table Sta ts er

1 Schools Corn er: StatZing!, S URFs 12 nd Fi fo In by r /fo

SU RF s StatZing! Latest Sec (Economics) SURF 2 13 SURFs for Schools Synthetic Unit Record Files: Multivariate datasets from Stats NZ surveys 1. Income supplement from the 2004 Household Labour Force Survey

2. 2001 Household Savings Survey 3. Coming soon 2006 Census 14 15 2001 Household Savings Survey SURF Based on a survey that collected information including income, assests, debt,net worth. 300 synthetic people representing the 5000+ people who responded to the survey. 16 2001 Household Savings Survey SURF Variables include:

Gender Employment Qualification Ethnicity Partnered Age Age of Partner Total income Wages/Salary income Total debt Total networth 17 18

19 Using the SURF 20 Teacher page for each activity Curriculum links Possible answers Available as a PDF document 21 What can we improve? For teachers For students

22 Census: SURF 3 Under development; final checking Based on 2006 Census of Population and Dwellings Contains unit record datasets for each of New Zealands 16 main Regional Authorities 300 synthetic people who represent everyone that responded for each region 23 Census: SURF 3 Variables included Sex Work and Labour force status

Qualification Ethnicity Income Age Group Mode of transport to work Hours worked Cigarette smoking behaviour Access to a cellphone/mobile phone Access to the internet 24 Access to internet Age x Cigarette smoking behaviour Ethnicity

Hours worked in employment per week x x Main means of travel to work Qualification highest Sex Work and labour force status x x x x x

Cigarette smoking behaviour Ethnicity Hours worked in employment per week Main means of travel to work Sex x x

x x x x Qualification highest Work and labour force status Variable Access to a Cellphone/Mobile Phone Personal Income Preserved relationships

x x x x x x 25 Limitations: SURF 3: Census Synthetic data Not all relationships and patterns are preserved Joining tables together does not represent the whole of New Zealand However, you can compare regions!

26 Battle for the greener suburb: an example using case data Compare the traveling to work habits of geographic areas. Which area has the greener workers? Walking / Running / Cycling Public transport Carpooling??? Working at home? (Graphic from CensusAtSchool ) 27

Battle for the greener suburb: where to find the data We want a data source that contains information about modes of travel to work by area units. Luckily, we have the 2006 Census of Population and Dwellings on Table Builder! 28 uilder B e l b a

2T 29 op 2006 P Census 30 dt Selecte ables 31

ve l to W or k s oon Tr a Sex; Age by

32 33 34 35 36 37 38 39 40

41 42 43 Travel to work in the four Auckland cities Counts: People by City of usual residence, Main Means of Travel to Work: 2006 Census

Not Elsew here Included Other Walked or Jogged Bicycle Motor Cycle or Pow er Cycle Train Manukau City Public Bus Auckland City Passenger in a Car, Truck,

Van or Company Bus Waitakere City North Shore City Drove a Company Car, Truck or Van Drove a Private Car, Truck or Van Did Not Go To Work Today Worked at Home 0 50,000 100,000

44 Travel to work in Kapiti and Wellington 50% Kapiti Coast District Wellington City 40% 30% 20% 10% 0% Worked at Home

Did Not Go Drove a Drove a Passenger Public Bus To Work Private Car, Company in a Car, Today Truck or Van Car, Truck Truck, Van or Van or Company Bus Train Motor Cycle or Power Cycle

Bicycle Walked or Jogged Other Not Elsewhere Included 45 Table Builder: Datasets on Area Units: At this point the screen-shots stop. But theres a

2-slide summary 8000 Population: Census 2006 vs Population: Census 2001 for Area Units of Waitakere City 6000 Sturges North 4000 Here's data for 10 Area Units: Area Unit Tot01 Tot06 Sturges North

2283 5772 Kingdale 3480 3537 Fairdene 4410 4554 2000 Whenuapai West 1836 1842 Herald 1656 1698 Hobsonville 3342 3378 Westgate 705 1092 Royal Road West 2424 2664 0 West Harbour 4569 4932 0

Lucken Point 4656 5238 2000 4000 6000 46 8000 www.stats.govt.nz for schools: short guide: p1 Schools Corner SURF (No. 2) About the data source | The dataset | Activities (copy the dataset and paste into your spreadsheet)

StatZing! (the latest Activities) Find by (find old StatZing!s etc) Table Builder 2006 Population Census Selected tables Travel to Work Expand (find the Areas you want) Tick (use the ticks above and to left) Click the Table icon Actions, download to XL format (then copy and paste into your spreadsheet package) Age by Sex for 1996, 2001, 2006 (then as above) 47 www.stats.govt.nz for schools: short guide: p2 Infoshare Browse Work, Income and Spending

Linked Employer-Employee Dataset Age and ANZIC96 (ANZ Industry Classification 1996) Select a few items, and for Time, Select All Go Pivot clockwise, to get data into a column Save as xls (copy the dataset and paste into your spreadsheet) Releases by Title (Takes you to Hot Off The Presses) NZ Income Survey NZ Income Survey; June 2008 (then explore these:) Highlights|Commentary|Technical notes|Erratum|Tables QuickStats about a Place (and also see QuickStats about a Subject, and NZ in Profile) Place List (and find your suburb) (and use the 12 tabs). 48

What Statisticians do all day: an eg: The new Immigration Survey: Pop: 36,620 approved immigrants in 2004 Sample: 7,125 of them We find Estimates (via resampling) with Sample Errors (= half the confidence interval) Immigration survey: Labour Force Activity Labour force status: Employed Looking for work Immigration approval category Number Samp err Number Samp err Skilled Primary Applicant 11,630 220

510 90 Skilled Secondary Applicant 5,130 410 350 130 Business 1,210 40 100 30 Family partner 4,770 240 150 80 Pacific

1,120 70 160 10 Notes: This is an example: values are not necessarily the actual ones. table is incomplete Samp Err is sample error: approximately 2 times the standard error found by jackknife. Number is the estimate, from the sample, o of the total number of people in the cell, for the population studied. The confidence interval for the estimate is: Number Sample error. 49 Sample Error vs Estimate:

300 Sample Error vs Estimate for cells from a LISNZ table jackknife 200 100 0 0 1000 2000 Hmmmmmm: what does that show?

50 Sample Error (up) vs Estimate (across): 300 For cells from the Immigration Survey NZ Sample Error vs Estimate for cells from a LISNZ table jackknife, binomial 1 Sample Error from the data by Jackknife (ie resampling) 200

100 Standard Deviation from binomial model = (p (1-p) N) 0 0 1000 2000 Sample error has lots of variation: Can we explain some of it? How? What function might it fit? For the lower (blue) points, what did we forget?

51 Some consultation: We asked Pat: You need to multiply by the 2 value: Sample Error = z * Standard Error = 1.96 * Standard Error They forgot to multiply by 2 (or 2 ish) Why are they so dumb in Wellington?? 52

Sample Error vs Estimate: 300 Sample Error vs Estimate for cells from a LISNZ table Jackknife, binomial 2 Sample Error from the data by Jackknife (ie resampling) 200 Sample Error from binomial model = z * (p (1-p) N) 100

0 0 1000 2000 Hmmmmmm: how does that look? 53 To confidentialise, we added noise: 4 300 Sample Error vs Estimate for cells from a LISNZ table jackknife

Noise from confidentialising is about this big: 200 100 Noise from sampling varies, but is this big 0 0 1000 2000

Does the noise from confidentialising matter? 54 What do we do all day? In a Stats office Find a problem that matters Find some Data (Evidence) Talk, scratch heads Do some graphs Try models using Maths Make mistakes Consult with wise heads Do more graphs Make decisions Communicate results in: words, numbers, graphs In a Stats classroom

Find a problem that matters Find some Data (Evidence) Talk, scratch heads Do some graphs Try models using Maths Make mistakes Consult with wise heads Do more graphs Make decisions Communicate results in: words, numbers, graphs We hope you enjoy statistical discovery as we do!! 55 Gender Balance in Waitakere: Females vs Males

for Area Units of Waitakere Cit 2006 Census 3000 Y+X line 2000 1000 Herald 0 0 1000 2000

3000 56 The Maths and Stats teachers vital role: If the next cohorts of adults can handle statistical evidence and thinking: Thatll be nice for Statistics NZ! which produces: social, economic and environmental stats Thats utterly essential for solutions to NZs and the Earths challenges. Enjoy!! 57

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