1. New Zealand Business Demography Statistics: Noise for Counts and Magnitudes (NCM) confidentiality method
Mathew Page
September 2018

2. This Presentation History of business demography statistics
Customer needs
Overview of NCM method
NCM method – business counts
NCM method – employee counts
NCM method in practice

3. History of business demography statistics - until 2014
Enterprise (legal business) and geographic unit (business location) not suppressed or rounded
Employee count not suppressed, but was subject to graduated random rounding (GRR)

4. History of business demography statistics - compliance
Not fully aligned with section 37 of Statistics Act
Statistics Act currently being reviewed

5. History of business demography statistics – 2015 release
Enterprise/geographic unit counts:
Enterprise/geographic unit counts of 1 or 2 suppressed
Geographic unit counts suppressed where the number of enterprises owning those geographic units is 1 or 2
Remaining enterprise/geographic unit counts random rounded to base 3 (RR3)
Employee counts:
Employee counts relating to a suppressed enterprise or geographic unit suppressed
Remaining employee counts subject to graduated random rounding (GRR)

6. History of business demography statistics – 2015 example
ANZSIC06
A019 Other Livestock Farming
Area
Total NZ by Regional Council/Area Unit
Houhora
Measure
Geographic Units
Employee Count
Year
Employment Size Group
2015
3168 C
1 to 5
426
970 ..
6 to 9 84
600
10 to 19 42
580
20 to 49 21
620
50 to 99
100+
Total
3747
3040

7. Customer needs Make more data available – Stats NZ’s vision
Avoid suppressions – more meaningful data
Look for a standard confidentiality method for all data outputs

8. Overview of noise for counts and magnitudes (NCM) method
No suppressed cells in BD data tables
Greater utility for customers – every cell has a value
Consistency of cell values across different tables

9. Overview of NCM method - seed
Seed – each business is assigned a random number
Seed – determines the degree of perturbation applied to the statistics
Same seed applied to each business each year
For single geo enterprises, enterprise seed is same as geo seed
For multi geo enterprise, enterprise seed is the seed of the earlier geo
Members of a group of enterprises all have the same seed

10. NCM method – business counts
Business counts are rounded to base 3 as part of the perturbation process
The combined value of the businesses’ seeds determines the count perturbation (rounding up or down)
Eg 4 geos form a data cell
geo1 has a seed of 0.118
geo
geo
geo
Total of the seeds = =1.698
Cell-level seed = (non integer part)
This is greater than 0.667
So the FRR3 business count = 6

11. NCM method – business counts
Adding extra uncertainty to protect rounded counts of zero (particularly those with employee counts)
Under normal random rounding to base 3 the value of 3 would be unchanged
This means that a random rounded cell of 0 corresponds to an actual count of 0,1 or 2
New rule adds more uncertainty with an actual value of 3 with a probability of one third to 0, one third of remaining unchanged at 3 and one third to 6
This means that the random rounded cells with a count of 0 could have an actual count of 1, 2 or 3.

12. NCM method – employee counts
Employee counts of 10 or greater
The seed is used to generate a ‘noise multiplier’
Individual values are protected by at least +/- 10% (with equal probabilities of 50%)
We then apply a further rounding step:
For noised employee counts under 22 we round to 3
For counts from from 22 to under 100 we round to 5
For counts from 100 to under 1000 we round to 10
For counts from 1000 to under 5000 we round to 50
For counts 5000 and over we round to 100

13. NCM method – employee counts
Employee counts of less than 10
Small employee counts (e.g. 1,2) won’t be sufficiently protected by 10% noise after rounding back to integer values
For non-zero employee counts < 10 we add 1 (p=1/3) subtract 1 (p=1/3) or leave as is (p=1/3)

14. NCM method in practice 2015 rule NCM rule 2000 2001 2002
2000
2001
2002
Auckland Region
No of Geographic Units
Employee count
Central Bank C
Banking
426
22,380
420
22,190
417
22,270
Building Society 3 60 65
Credit Union 21 18
NCM rule
2000
2001
2002
Auckland Region
No of Geographic Units
Employee count
Central Bank 30 --
Banking
426
22,300
420
22,100
417
22,200
Building Society 3 50 55
Credit Union 21 65

15. NCM method in practice By regional council Regional Council No of Geos
Geographic Employee Count Change
Percent
Difference
Northland
20048
-0.44
-240
Auckland
172795
0.30
2020
Waikato
52692
0.32
560
Bay of Plenty
33928
-0.50
-570
Gisborne
4974
0.12 30
Hawke’s Bay
18211
-0.48
-350
Taranaki
15030
-0.39
-200
Manawatu-Wanganui
25511
-0.60
-580
Wellington
53700
0.50
1190
West Coast
3890
-0.29
-50
Canterbury
68298
0.52
1440
Otago
27265
0.46
460
Southland
13802
-0.68
-330
Tasman
6628
0.58
120
Nelson
5897
-0.38
-100
Marlborough
6970
-0.17
-40
Area Outside
190
1.79 10

16. NCM method in practice By ANZSIC (industry) ANZSIC Division No of Geos
Geographic Employee Count Change
Percent
Difference
Agriculture, forestry & fishing
71648
0.14
170
Mining
906
0.19 10
Manufacturing
22267
0.42
910
Electricity, gas, water & waste services
1526
0.78
110
Construction
53269
-0.21
-280
Wholesale Trade
20450
-0.29
-310
Retail Trade
34294
-0.11
-220
Accommodation and Food Services
20659
-0.27
-380
Transport, Postal and Warehousing
16324
0.74
620
Information Media and Telecommunications
5699
0.68
260
Financial and Insurance Services
35233
0.08 40
Rental, Hiring and Real Estate services
107087
0.28 80
Professional, Scientific and Technical services
55062
-0.06
-90
Administrative and Support services
17255
-0.39
-390
Public Administration and Safety
3843
-70
Education and Training
10300
0.58
1000
Health Care and Social Services
20591
0.88
1900
Arts and Recreation Services
10193
-0.01
Other Services
23223
0.02

17. Questions? Mathew Page (mathew.page@stats.govt.nz)
Venu Nair
Table 2 – Units directly collected versus modelled units – Business data collection (March 2018 quarter)