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Evaluating Noise Infusion for Disclosure Protection for Two Time 

Periods 

Jared Martin

U.S. Census Bureau

4600 Silver Hill Road

Washington, DC 20233

Proceedings of the 2013 Federal Committee on Statistical Methodology (FCSM) Research Conference

Note: This article reports the results of research and analysis undertaken by U.S. Census Bureau staff. It has

undergone a more limited review than official U.S. Census Bureau publications. It is released to inform interested 

parties of research and to encourage discussion. The views expressed are those of the author and not necessarily 

those of the U.S. Census Bureau. 

Abstract

The U.S. Census Bureau conducts the Economic Census of Island Areas quinquennially. For the 2007 Economic 

Census of Island Areas, the U.S. Census Bureau provided disclosure protection, a protection detailed in Titles 13 of 

the U.S. Code, using a noise infusion technique. Noise infusion consists of perturbing values for each contributing 

establishment prior to table creation by applying a random noise multiplier to the magnitude data (i.e., 

characteristics such as receipts, payroll, and number of employees). The use of noise factors introduces uncertainty 

into the published cell values that protects the confidentiality of the contributors to the cell estimates. In prior 

economic censuses of Island Areas, disclosure protection was accomplished using cell suppression, which reduces 

the number of published values significantly. Census Bureau staff considered the impact of noise infusion on 

estimates of change in published cell values from one census cycle to the next when planning for disclosure 

protection for the 2012 Economic Census of Island Areas. They considered several options for applying noise in the 

2012 economic census in an attempt to minimize distortion in cycle-to-cycle changes while providing sufficient 

uncertainty to protect the confidentiality of the respondents. This paper presents the results of a simulation study 

used to compare and evaluate the options considered, for estimates of varying size and composition. The paper 

illustrates each method and shows the tradeoff between bias and low variability in an estimate due to noise. 

1. Introduction

Statistical disclosure avoidance methods are procedures designed to protect the confidentiality of individuals, 

businesses or other entities that report data used to create data products for public use. Protecting confidentiality 

involves withholding enough information to protect the privacy of individual respondents (Cox and Zayatz, 1995). 

Disclosure avoidance methods restrict the amount of useable data presented to the public. The goal of any

disclosure avoidance method is to maximize the amount of useable information published while ensuring sufficient 

protection and privacy of individual contributors represented in the data. 

The U.S. Census Bureau provided disclosure protection for the 2007 Economic Census of Island Areas using noise 

infusion. In an effort to publish more data while protecting confidentiality of the respondents in the Economic 

Census of Island Areas in 2007, the Census Bureau implemented a method that assigns and multiplies micro level 

data by a multiplicative factor called a noise factor. The use of noise factors introduced uncertainty into an estimate 

that was sufficient to protect the confidentiality of the respondents and their data. This uncertainty decreased the 

usability of the estimates, and introduced variability or uncertainty in changes in estimates from cycle to cycle. This 

paper begins with a brief explanation of the Economic Census of Island Areas (IA), followed by a description of 

noise infusion and an explanation of how the U.S. Census Bureau applied it to IA in 2007. Then it describes some 

concerns with the continued use of the current noise methodology, and some suggestions. Finally, we explain the 

results of a Monte Carlo simulation study replicating each proposed method and find the method that minimizes the 

uncertainty of estimates between census cycles to the next while providing sufficient protection of the 

confidentiality of the respondents. 
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2. The Economic Census of Island Areas

The Economic Census of Island Areas (IA) provides economic data for American Samoa, the Commonwealth of the 

Northern Mariana Islands (CNMI), Guam, Puerto Rico and the U.S. Virgin Islands. It is a quinquennial census 

conducted in years ending in 2 and 7, providing information about the structure and functioning of the economy for 

these islands (U.S. Census Bureau 2013). For purposes of this paper, we focus on the variable sales defined as “total 

monetary collected for goods and services provided by a business” (U.S. Census Bureau 2013). U.S. Census Bureau 

staff collects and publishes sales at the four-digit North American Industry Classification System (NAICS) level for 

each of the islands. 

3. Noise Infusion for Disclosure Avoidance

Noise is one method of protecting respondents’ data from being disclosed. This method perturbs all the micro data 

by a small percentage. Each contributor is protected by the amount the perturbation distorts its contribution. A 

multiplicative noise factor distorts the input data by multiplying each contribution by a factor drawn from a 

symmetric distribution centered on one. This distortion will guarantee minimum required protection by choosing a 

factor distribution with no probability within the desired minimum required protection surrounding one (Evans, 

Zayatz, Slanta 1998). In aggregate, the estimate should have minimal distortion since the factor distribution is 

symmetric about one. If an estimate is sensitive, with a large dominant contributor, the distortion will be larger to 

guarantee minimum required protection. 

3.1 Balanced Noise as Applied to Economic Census of Island Areas 2007

In 2007, the Economic Census of Island Areas (IA) assigned noise factors generated from a split triangular 

distribution symmetric about one and that meets the qualifications discussed above (See Figure 1). The expected 

value of a factor drawn from this distribution is intuitively one, and the expected value of the total noise distortion of 

each contributor is zero. Since overall distortion is the sum of the distortion of each contributor, and the expected 

value of the distortion of each contributor is zero, the expected value of overall distortion is zero. 

Distortion in either direction is between two values (a-1)% and (b-1)%, while the expected value of the factor is one

and expected distortion is zero (See Figure 1). The expected value of noise for any cell is not necessarily zero. If a 

company reports with more than one establishment, we assign each establishment’s noise factor in the same half of 

the distribution, giving them all the same direction as the company’s noise factor, i.e. generated from the same side 

of the distribution. Each establishment also maintains the same factor throughout all cells in a publication. 

Noise factors are ‘balanced’ using sales at the industry level. Balancing lessens the overall distortion a table cell or

estimate receives. The variable and level chosen to balance the noise will have the lowest variance in the 

distribution of distortion due to noise of all estimates in a table. For IA, we chose reported sales at the industry 

category level as the most important estimates to have the least distortion. 

To ‘balance’ the noise factors, we sorted all establishments contributing to an industry estimate in descending order 

of sales and assigned the largest contributor a noise factor. After each assignment, we measured overall distortion, 

for sales at the industry level. If the overall noise was one direction for the cell, we assigned the opposite direction 

to the next company. For example, if noise for sales in an industry was positive, then we assigned a negative 

direction to the noise factor for the next added contributor. A negative direction for noise meant the factor was 

selected from the part of the distribution below one and a positive direction for noise meant the factor was selected 

from the part of the distribution above one. We repeated this process until all establishments were assigned a factor 

corresponding to the appropriate direction. 

After we had applied balanced noise, the confidentiality of respondents is sufficiently protected. The estimates may 

be distorted by noise to varying extents or have data quality issues. To alert the consumer to poor data reliability, 

we suppress from publication cells with fewer than three contributors, and assign noise flags alerting data consumers 

to whether the cell had low, medium, or high noise. For IA, cell values changing less than 2 percent due to noise 

have a low noise flag. Cell values changing by 2 percent or more, but less than 8 percent have a medium noise flag, 

and cell values changing by more than 8 percent have a high noise flag and are suppressed from publication. 
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3.2 Concerns About Noise in Future Publications

A concern arises when implementing noise in consecutive subsequent cycles. If variation in cell noise is large, an 

estimate may swing from large positive noise to large negative noise in the next census cycle. Such a large swing in 

the value of an estimate may mislead the data consumer into thinking something noticeable is happening in the 

economy when in fact, the noise factors changed from one cycle to the next. For example, suppose a cell has three 

contributors, companies A, B, and C. Their noise factors are drawn independently from a split triangular 

distribution with a=1.1 and b=1.15 each cycle (See Figure 1). The first census would report sales of $12.3 million. 

Next census cycle would report $9.6 million (See Table 1). Since census numbers can be directly compared, it 

appears there is a 22% drop in sales even though the values were identical. 

Each contributing establishment may help balance out each other’s noise contribution. A problem arises when a cell 

has relatively few contributing companies or a cell has a large company driving the estimate. These scenarios may 

cause the cell estimate to have relatively large distortion because there are fewer opportunities (establishments) to 

balance out the distortions caused by the largest contributors to the cell. This is what the noise infusion is designed 

to do. It provides protection by creating a less precise estimate so an estimate can be released instead of suppressed

(Evans, Zayatz, Slanta 1998). When a table cell has many contributing companies, the overall noise will be small 

with small variation for overall noise. 

Table 1

Year 1 Year 2

Company Actual Sales

(millions of dollars)

Noise 

Factor

Noisy Data

(millions of dollars)

Actual Sales

(millions of dollars)

Noise 

Factor

Noisy Data

(millions of dollars)

A 10.0 1.14 11.4 10.0 0.85 8.5

B 0.5 0.90 0.45 0.5 1.10 0.55

C 0.5 0.90 0.45 0.5 1.10 0.55

Total 11.0 12.3 11.0 9.6

3.3 New Methods Suggested

Preserving as much of the change between cells from one period to the next is the objective. This means reducing 

the variability of overall effective noise a cell receives from period to period. We proposed to modify the current 

noise application method. One way is to fix the noise factor direction and magnitude each time. Each cell still has 

noise applied, but only once and held constant over time, better preserving differences between censuses. However,

completely removing variability of effective noise a cell receives by fixing the noise factor for every company from 

period to period is data disclosure when the actual change from year to year of a dominant company in a cell can be 

identified with a certain precision (Evans, Zayatz, Slanta 1996). Some form of noise factor change needs to happen 

from one period to the next in order to protect these trend statistics. In practice, even if direction and magnitude are 

Figure 1
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fixed, there are companies entering and leaving the census from cycle to cycle which necessitates assigning new 

factors, adding some change in the amount of effective noise in a cell. We elected to do a simulation study 

replicating choosing noise factor direction and magnitude many times under differing scenarios of fixing some noise 

factor directions and magnitudes and not others from period to period. 

4. Evaluation Study and Results

To conduct our simulation study, we used data from the 2002 and 2007 IA. For the 2002 Economic Census of the 

Island Areas, we achieved disclosure avoidance through cell suppression methodology. We changed to using the 

‘balanced’ noise application method mentioned in section 3.1 for the 2007 IA. Since we are concerned with cells 

that have relatively few contributing companies or cells with a large case that drives the estimate, we decided to 

begin simulations with sales data from American Samoa, the island with the least number of companies. In total, 

we simulated 10 different noise application methods on sales data from American Samoa and the Virgin Islands, 

also an island area that has industries composed of only a few contributors. 

Method 1 - Reassigned Noise Direction and Magnitude

First, we simulated applying noise 1500 times to American Samoan companies reporting 2007 data, using the 

current balanced noise methodology explained in section 3.1, randomly selecting noise factors each time. This 

created a baseline of current methodology for comparison. The current methodology for the Economic Census of 

Island Areas applied balanced noise for cells containing sales data at the industry category level. We recorded the 

overall percent distortion or noise of sales estimates at three digit NAICS industry categories after each replication. 

Method 2 - Fixed Noise Direction and Magnitude

Second, we simulated using current methodology on 2007 American Samoa sales data but this time keeping 

direction and magnitude fixed from replication to replication for companies appearing in both 2002 and 2007 to 

simulate companies that may be retained from period to period of the census. Fixing the factor for each 

establishment appearing from cycle to cycle is the most restrictive method, allowing the least amount of variation in 

overall effective noise. In fact, if every establishment remained in business and reported every cycle there would be 

no variation in noise factors. We recorded the overall percent distortion of sales estimates at three digit NAICS 

industry categories each time, repeating the process 1500 times. 

Method 3 – Fixed Noise Direction

Fixing both direction and magnitude is quite restrictive, especially for estimates that only have a few large 

contributing establishments. The next simulation involved fixing only the noise factor direction for establishments 

appearing from cycle to cycle. We simulated using current methodology on 2007 American Samoa sales data, 

keeping only the direction fixed from replication to replication for companies appearing in both 2002 and 2007. We 

repeated assigning noise in this way 1500 times, recording the overall percent distortion of sales estimates at three 

digit NAICS industry categories each time. Fixing the direction of the noise from cycle to cycle reduced variability 

in the noise distortion of an estimate, at the expense of a biased estimate. Estimates tended to either be positively 

distorted with noise or negatively distorted with noise depending on the fixed direction of the cases present from 

cycle to cycle. 

Method 4 - Fixed Noise Direction and Magnitude for Large Cases

Next, we simulated using current methodology on 2007 American Samoa data but keeping direction and magnitude

fixed for large cases appearing in both 2002 and 2007. We defined large cases as those cases that contributed more 

than 50% of an estimate or were in the top two contributors that together contributed more than 75% of an estimate. 

Cases contributing more than 50% to an estimate greatly influence overall noise distortion in an estimate. Even the 

balancing method we use will rarely counteract and mitigate the distortion or noise in the cell estimate contributed 

by such a large case. We also chose to fix noise factor magnitude and direction for cases in the top two contributors 

that together contributed more than 75% of an estimate to control for cases that may together contribute a large 

amount to an estimate and hence the amount of noise in an estimate. These top two contributors may balance each 
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other’s contribution of noise, but by fixing the noise direction and magnitude, we were able to control one of the 

largest sources of noise variation in an estimate from cycle to cycle. We repeated the simulation 1500 times and 

recorded the overall percent distortion of sales estimates at three digit NAICS industry categories each time. 

 

After analyzing plots of the simulations, we decided that fixing the noise direction of companies, especially large 

companies, appeared to reduce the overall noise variability in the overall estimate. Fixing the magnitude further 

reduced variation of the distortion, but raised concerns about not providing enough protection (See Appendix A) 

since fixing the factors essentially preserved the difference in estimates from cycle to cycle and the estimates would 

nearly be exact except for a nearly fixed constant added to the overall estimate. We decided to pursue fixing 

direction of “large” companies and allowing the magnitude of their factors to vary slightly from the original. We 

also decided to do simulations on the U.S. Virgin Islands data to see if the Virgin Island estimates that also have few 

contributors behave similarly under different noise conditions as compared to estimates of sales in American Samoa. 

After looking more closely at the data, we chose to define a “large” company as any company that contributed more 

than 50% of an estimate. Companies that contributed more than 50% of an estimate contribute noise that rarely is

balanced out by the rest of the contributing companies. In fact, if a company contributed more than 50 + (b-a)/2 % 

of an estimate, its noise can never be completely balanced and the estimate will always be distorted. Few companies 

contributed slightly less than 50% of an estimate but together with another company made up the top two 

contributors and were more than 75% of an estimate. These cases were easily balanced out and did not appear to 

cause too much variability in the amount of noise an estimate received. We decided to include companies that 

together contributed more than 75% of an estimate in the definition of large for Method 10, as a continuation of 

Method 4. 

We repeated the first four simulations with 3000 repetitions for American Samoa and Virgin Island sales data to get 

a more defined picture of the distribution of distortions to each estimate. Similar scenarios and outcomes for noise 

application appear in the Virgin Island estimates and the American Samoa estimates. The results for select three 

digit NAICS industry categories appear in Appendix A.

Method 5 – Fixed Noise Direction for Large Cases, but Magnitude Constrained Around an Initial Value

Method 5, the next attempt at controlling the possible large swings in effective noise distortion to an estimate, 

involved fixing the noise direction for large establishments, but allowing the factor magnitude to vary from cycle to 

cycle around the initial noise factor assignment. We chose to fix the noise direction for establishments that 

contributed more than 50% of an estimate and appeared from cycle to cycle. If a contributor was larger than 50% of 

an estimate, it drove the estimate, and its noise factor drove the overall direction of noise in the estimate. For this 

method, we simulated using current methodology on 2007 Virgin Island and American Samoan sales data but kept 

direction fixed at initial values for companies (single establishments, or sum of establishments in a multi-unit 

company within an estimate) appearing in both 2002 and 2007 and made up more than 50% of an estimate in 2007. 

We also reassigned the magnitude of the noise factors of companies with fixed direction from a triangular 

distribution centered on the old previously assigned noise factor. The triangular distribution we first tried had 

parameters c= old noise factor and b= c + 0.0125 (see Figure 2). We did not allow new factors to exceed the bounds 

a standard noise factor may take. If a factor chosen from the special distribution exceeded the bounds a standard 

noise factor may take, we re-selected a new factor until the new factor fell within the bounds of a standard noise 

factor. We repeated the simulation 3000 times and recorded the overall percent distortion of sales estimates at three 

digit NAICS industry categories each time. See the results for select three digit NAICS industry categories in 

Appendix A. 

Method 6 – Fixed Noise Direction for Large Cases, but Magnitude Constrained Around an Initial Value

Method 6 was similar to method 5. As in method 5, we simulated using current methodology on 2007 Virgin Island 

and American Samoan sales data. We kept direction fixed at assigned 2002 values for companies (single 

establishments, or sum of establishments in a multi-unit company within an estimate) that appeared in both 2002 and 

2007 and made up more than 50% of an estimate. For these companies with fixed noise direction, we allowed the 

magnitude of the factors to be reassigned from a triangular distribution centered on the old previously assigned noise 

factor. For method 6, when reassigning a noise factor, we chose a narrower distribution with parameters c= old 

noise factor and b= c + 0.005 (see Figure 2). This method provided more restriction than method 5 in the amount a 
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noise factor with fixed direction could change. We did not allow new factors to exceed the bounds a standard noise 

factor may have taken. If a factor chosen from the special distribution exceeded the bounds a standard noise factor 

may have taken, we re-selected a new factor until the new factor fell within the bounds of a standard noise factor. 

We repeated the simulation 3000 times and recorded the overall percent distortion of sales estimates at three digit 

NAICS industry categories each time. See the results for select three digit NAICS industry categories in Appendix 

A. 

Method 7 – Fixed Noise Direction for Large Cases

Method 7 used current methodology on 2007 American Samoa and Virgin Island sales data but kept direction fixed 

for companies (single establishments, or sum of establishments in a multi-unit company within an estimate) that 

appeared in both 2002 and 2007 and that made up more than 50% of an estimate in method 7. Cases contributing 

more than 50% to an estimate greatly influence overall noise distortion in an estimate. Even the balancing method 

we use will rarely counteract and mitigate the distortion or noise in the cell estimate contributed by such a large 

case. We also chose to fix the direction for companies with several establishments contributing to an estimate that 

together contributed more than 50% of an estimate to control for cases that have the same direction such as 

establishments in a company and may have together contributed a large amount to an estimate and hence the amount 

of noise an estimate had. We repeated the simulation 3000 times and recorded the overall percent distortion of sales 

estimates at three digit NAICS industry categories each time. Results for select three digit NAICS industry 

categories appear in Appendix A. 

Method 8 – Fixed Noise Direction for Very Large Cases

Method 8 fixed the noise direction for establishments appearing in both 2002 and 2007 and that made up more than 

75% of an estimate and randomly assigned all other cases. We simulated using current methodology on 2007 

American Samoa data but kept the noise direction fixed for establishments that appeared in both 2002 and 2007 and 

made up more than 75% of an estimate and used current methodology to assign direction and magnitude for all other 

cases. We chose to fix the direction of establishments that contributed more than 75% of an estimate because 

establishments this large contribute so much noise that the rest of the contributors cannot balance by assigning a 

noise factor in the opposite direction. Even if we assigned the large establishment the smallest amount of noise, and 

all the other establishments the largest amount of noise in the other direction, the overall estimate would always be 

biased. The change in an estimate from cycle to cycle may be overshadowed by whatever noise factor and direction 

the large establishment may have unless we at least fix its noise direction. See Appendix A for results for select 

three digit NAIS industry categories. 

Method 9 - Fixed Noise Direction for Large Cases or Companies with Multiple Establishments, but 

 Magnitude Constrained Around an Initial Value

For method 9, we simulated using current methodology on 2007 Virgin Island and American Samoan sales data but 

kept noise direction fixed at assigned 2002 values for establishments that appeared in both 2002 and 2007 and made 

up more than 50% of an estimate or were a company with more than one establishment. Since each company within 

a multi-unit establishment had the same direction, they could potentially severely bias the noise in the overall 

estimate if there were many companies from a multi-unit establishment in any one estimate. We allowed the factors 

of companies with their direction fixed to be reassigned from a triangular distribution centered on the old previously 

assigned noise factor, with parameters c = old noise factor and b= c + 0.0125 (see Figure 2). We did not allow new 

factors to exceed the bounds a standard noise factor may take. If a factor chosen from the special distribution 

exceeded the bounds a standard noise factor may take, we chose a new factor until the chosen factor fell within the 

bounds of a standard noise factor. We repeated the simulation 3000 times and recorded the overall percent 

distortion of sales estimates at three digit NAICS industry categories each time. See Appendix A for histograms of 

the results for select three digit industry categories. 

Method 10 – Fixed Noise Direction for Large Cases

In method 10, we simulated using current methodology on 2007 American Samoa and Virgin Island sales data but 

kept noise direction fixed for companies that appeared in both 2002 and 2007 and were single establishments or 

multiple establishments in a company contributing to an estimate that together made up more than 50% of an 
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estimate or were in the top two contributors that together made up 75% of an estimate. Cases that contributed more 

than 50% to an estimate greatly influenced overall noise distortion in an estimate. Even the balancing method we 

used will rarely counteract and mitigate the distortion or noise in the cell estimate contributed by such a large case. 

We also chose to fix the noise factor direction for cases in the top two contributors that together made up more than

75% of an estimate to control for cases that may have together contributed a large amount to an estimate and hence 

the amount of noise an estimate had. These top two contributors may have balanced each other’s contribution of 

noise, but by fixing the noise direction for them, we were able to control the largest sources of noise variation in an 

estimate from cycle to cycle. We repeated the simulation 3000 times and recorded the overall percent distortion of 

sales estimates at three digit NAICS industry categories each time. Appendix A contains histograms of the results 

for select three digit industry categories. 

 

 

5. Discussion

After reviewing methods 5, 6, and 7 we noticed that, for companies with fixed direction, the amount of constraints 

placed on the factor size seemed to matter little. The histograms showing the distribution of potential noise in an 

estimate for American Samoa and the Virgin Islands appeared almost identical in methods 5, 6, and 7. All of these

methods, for the most part, reduced variability due to noise, and produced distributions only slightly biased or 

centered on zero distortion, which is a desirable attribute. 

Method 8 produced distributions of overall percent noise very similar to method 1. This result is understandable 

because very few establishments contributed more than 75% of an estimate, and hence, we fixed the noise direction 

of very few establishments. This meant that most estimates would not have any establishments fixed, which was

method one. One notable exception was industry section 443 Electronics and Appliance Stores in American Samoa. 

In this instance, the distribution of overall percent noise resembled a split triangular distribution in method 1, but in 

method 8, the distribution was only the lower side of what appeared to be the same split triangular distribution. 

Methods 5 and 9 were nearly identical except in method 9 the direction of the noise factor in all multi-unit 

establishments was fixed instead of only the establishments that contributed more than 50% of an estimate. Thus, 

method 9 produced similar results as method 5, with a few exceptions. For example, industry section 339 

Miscellaneous Manufacturing in the Virgin Islands displayed slight negative bias in method 9 compared to method 

5. See Appendix A. 

Methods 3 and 10 produced distributions of overall percent noise that were similar. Neither method stood out as 

superior. Sometimes the variance was larger for percent noise under method 3 (such as in industry section 524 

Insurance Carriers and Related Activities in American Samoa) than under method 10, and sometimes the variance 

was smaller under method 3 (such as in industry section 551 Management of Companies and Enterprises in 

American Samoa) than under method 10. 

Reducing variability in an estimate due to noise was one goal. To assess this goal, we calculated the inner quartile 

range (IQR) of each estimate for each method simulated in section 4. We calculated the IQR by subtracting the 25th

percentile from the 75th percentile of the distribution created from the noise simulations explained in section 4, at the 

Figure 2
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three-digit industry category. There are a total of 42 estimates for American Samoa, and 61 estimates for the Virgin 

Islands for each method. Table 2 summarizes the number and percentage of estimates that had a reduced IQR 

compared to method 1, the base line method. For American Samoa, method 3 had the largest number of estimates 

with a reduced IQR, except for method 2, where direction and magnitude are fixed. Method 2 is not advisable since 

it could potentially lead to a data disclosure as mentioned earlier. Methods 3 and 9 reduced the IQR almost as much 

as Method 2 for the Virgin Islands. Based on the reduced IQR criterion, Method 3 is the most desirable after 

method 2. 

 

Table 2

American Samoa The Virgin Islands

Method Number of 

estimates with IQR 

< IQR Method 1

Number 

of 

estimates

Percent of cells 

with reduced 

IQR

Number of 

estimates with IQR 

< IQR Method 1

Number 

of 

estimates

Percent of cells 

with reduced 

IQR

2 18 42 42.9 13 61 21.3

3 15 42 35.7 11 61 18.0

4 13 42 31.0 10 61 16.4

5 12 42 28.6 9 61 14.8

6 12 42 28.6 9 61 14.8

7 12 42 28.6 9 61 14.8

8 11 42 26.2 8 61 13.1

9 14 42 33.3 12 61 19.7

10 14 42 33.3 8 61 13.1

Another goal was to preserve as much of the change between estimates from one period to the next without creating 

a data disclosure. Therefore, we needed to reduce the variability of overall effective noise a cell received from 

period to period. In an ideal world, we also wanted the estimator (noisy estimate) to be unbiased with respect to the 

actual estimate before we added noise. Based on these criteria, we rejected methods 5 through 7 because of the 

exceptions where the distribution of overall distortion was biased or had too much variation. These three methods 

had relatively less bias overall, but had relatively large variance in overall noise distortion and were similar to the 

method we currently use. We also rejected method 8 because too few establishments had fixed noise factors and the 

result was nearly identical to the current method. Methods 3, 9, and 10 produced similar results. We recommend 

method 3, which fixes the direction of cases appearing from last cycle to the current cycle because it most 

consistently reduced variance and bias in the distribution of overall percent noise of an estimate and is the simplest 

of methods 3, 9, and 10. 
Page 9 of 13

References

Cox, L. H., and Zayatz, L. (1995), “An agenda for Research in Statistical Disclosure Limitation,” Journal of Official 

Statistics, Vol. 11, No. 2, pp.205-220. 

Evans, Timothy, Laura, Zayatz, and John Slanta (1998), “Using Noise for Disclosure Limitation of Establishment 

Tabular Data,” Journal of Official Statistics, Vol.14, No.4, pp.537-551 

URL http://www.jos.nu/Articles/abstract.asp?article=144537

Evans, B.T., Zayatz, L., and Slanta, J. (1996). “Using Noise for Disclosure Limitation of

Establishment Tabular Data,” Proceedings of the Annual Research Conference, U.S.

Bureau of the Census, Washington, DC 20233, pp.65-86.

U.S. Census Bureau, “Economic Census of Island Areas. U.S. Census Bureau”, Web. 7 Aug. 2013. URL 

http://www.census.gov/econ/islandareas
Page 10 of 13

A

Distribution of Distortion as a Percent of Non-Noisy Total Sales for American Samoa

311

1

0

20

40

60

80

100

Percent

443 484 524 551 721

2

0

20

40

60

80

100

Percent

3

0

20

40

60

80

100

Percent

4

0

20

40

60

80

100

Percent

5

-9.6 -5.6 -1.6 2.4 6.4

0

20

40

60

80

100

Percent

-9.6 -5.6 -1.6 2.4 6.4 -9.6 -5.6 -1.6 2.4 6.4 -9.6 -5.6 -1.6 2.4 6.4 -9.6 -5.6 -1.6 2.4 6.4 -9.6 -5.6 -1.6 2.4 6.4

pct_noise

Method

Three Digit Industry Category

ppendix A

Method 1 – Reassigned noise direction and magnitude

Method 2 – Fixed noise direction and magnitude

Method 3 – Fixed noise direction 

Method 4- Fixed noise direction and magnitude for cases that are > 50% of an estimate or in top two contributors that together are > 75% of an estimate

Method 5 – Fixed noise direction and magnitude varies by 0.0125 for cases that are > 50% of an estimate
Page 11 of 13

Appendix A

Distribution of Distortion as a Percent of Non-Noisy Total Sales for American Samoa

311

6

0

20

40

60

80

100

Percent

443 484 524 551 721

7

0

20

40

60

80

100

Percent

8

0

20

40

60

80

100

Percent

9

0

20

40

60

80

100

Percent

10

96 56 16 24 64

0

20

40

60

80

100

Percent

96 56 16 24 64 96 56 16 24 64 96 56 16 24 64 96 56 16 24 64 96 56 16 24 64

Method

Three Digit Industry Category

Method 6 – Fixed noise direction and magnitude varies by 0.005 for cases that are > 50% of an estimate

Method 7 – Fixed noise direction for companies that are > 50% of an estimate

Method 8 – Fixed noise direction for companies that are > 75% of an estimate

Method 9 - Fixed noise direction and magnitude varies by 0.0125 for cases that are > 50% of an estimate or are a company with multiple establishments. 

Method 10 – Fixed noise direction for cases that are > 50% of an estimate or in top two contributors that together are > 75% of an estimate
Page 12 of 13

Appendix A

Distortion as a Percent of Non-Noisy Total Sales for The Virgin Islands

325

1

0

20

40

60

80

100

Percent

339 452 492

2

0

20

40

60

80

100

Percent

3

0

20

40

60

80

100

Percent

4

0

20

40

60

80

100

Percent

5

92 68 44 20 04 28 52 76

0

20

40

60

80

100

Percent

92 68 44 20 04 28 52 76 92 68 44 20 04 28 52 76 92 68 44 20 04 28 52 76

Method

Three Digit Industry Category

Method 1 – Reassigned noise direction and magnitude

Method 2 – Fixed noise direction and magnitude

Method 3 – Fixed noise direction 

Method 4 - Fixed noise direction and magnitude for cases that are > 50% of an estimate or in top two contributors that together are > 75% of an estimate

Method 5 – Fixed noise direction and magnitude varies by 0.0125 for cases that are > 50% of an estimate
Page 13 of 13

Appendix A

Distortion as a Percent of Non-Noisy Total Sales for The Virgin Islands

325

6

0

20

40

60

80

100

Percent

339 452 492

7

0

20

40

60

80

100

Percent

8

0

20

40

60

80

100

Percent

9

0

20

40

60

80

100

Percent

10

-9.2 -6.8 -4.4 -2.0 0.4 2.8 5.2 7.6

0

20

40

60

80

100

Percent

-9.2 -6.8 -4.4 -2.0 0.4 2.8 5.2 7.6 -9.2 -6.8 -4.4 -2.0 0.4 2.8 5.2 7.6 -9.2 -6.8 -4.4 -2.0 0.4 2.8 5.2 7.6

pct_noise

Method

Three Digit Industry Category

Method 6 – Fixed noise direction and magnitude varies by 0.005 for cases that are > 50% of an estimate

Method 7 – Fixed noise direction for companies that are > 50% of an estimate

Method 8 – Fixed noise direction for companies that are > 75% of an estimate

Method 9 - Fixed noise direction and magnitude varies by 0.0125 for cases that are > 50% of an estimate or are a company with multiple establishments. 

Method 10 – Fixed noise direction for cases that are > 50% of an estimate or in top two contributors that together are > 75% of an estimate