Waivers in business surveys: A systematic approach to 

increase the amount of publishable information 

Jean-Sébastien Provençal, Hélène Bérard 

Statistics Canada 

11-L and 11-K, R.H. Coats Building, Ottawa, Canada K1A0T6 / provjea@statcan.ca and berahel@statcan.ca 

1. Introduction 

The suppression in information (cells) of published tabulated survey data is a technique commonly 

used to preserve the confidentiality of a respondent’s data. In business surveys, the suppression 

patterns are usually driven by two criteria: a minimum number of respondents and dominance rules 

where, for example, a cell could be suppressed if a business accounts for more than 80% of the cell 

total. 

Due to the highly skewed business populations with few large businesses and many small ones, the 

suppression of cells frequently stems from the presence of one or several businesses that dominate a 

sector (dominance rule). The suppression of one cell will likely trigger the suppression of other cells in 

order to reduce the risk of residual disclosure. In an effort to publish more cells, waivers are 

sometimes obtained from large contributors that allow the publication of the cell’s data despite the risk 

of disclosure. These businesses are often selected in an ad hoc manner. The decision to obtain a waiver 

from a respondent for a given cell and not another may lead to different suppression patterns, some of 

them can be more optimal than others according to survey and user requirements. 

In this paper, we present a method that attempts to identify the eligible potential waivers that will lead 

to an optimal suppression pattern. First, we describe some of the notions related to confidentiality and 

disclosure. Second, we give some details regarding CONFID, a software used in Statistics Canada to 

identify the information that should be suppressed. We summarize the methodology used in this 

software. Third, we discuss how waivers could be used to minimize the amount of suppressed 

information and we explain the method developed to identify who should be targeted for a waiver in 

order to be more optimal in terms of survey and user requirements. Finally, we discuss results obtained 

with practical example using the Canadian Annual Survey of Manufacturing. 

2. Concepts related to confidentiality 

2.1 Waiver 

A waiver is a written agreement between a statistical agency, in this case Statistics Canada, and a 

respondent. Under this agreement, the respondent releases the statistical agency from any liability 

regarding its obligation to preserve the confidentiality of the respondent. 

2.2 Sensitive Cell 

In the area of confidentiality we use the concept of sensitivity to describe and quantify the risks of 

potential disclosure within a cell. A cell is deemed sensitive if it is felt that there is a probable risk of 

disclosure. The line of demarcation is established according to confidentiality rules that reflect how 

secure we want to be. 

Sensitive cell Not Sensitive cell 

Very high risk Probable risk Low risk of No risk 

of disclosure of disclosure disclosure of disclosure 

Line of demarcation 

for sensitivity 

We use confidentiality rules to quantify this risk,. One type of rule we use is the (n,k) rule. With this 

rule, the sensitivity of a cell is established according to the main contributors of the cell. If the n top 

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contributors represent more than k percents of the cell's total, then the cell is sensitive. We can define 

this rule as a function. 

For example, with a (n,k) rule where n = 3 and k = yy, we can say there is a risk of disclosure if the 

three most dominant contributors: X( 1 ) , X( 2 ) and X( 3 ) , account for more than yy% of the cell's 

total. 

The sensitivity function, s( x ), could be formulated as follows: 

100 s( x ) =

yy 

[X + X + X ]− t( x ) where t( x ) is the cell's total. ( 1 ) ( 2 ) ( 3 ) 

A cell would be qualified as sensitive if s( x )<0 . The value taken by s( x ) allows for quantifying 

a cell’s degree of sensitivity. 

In determining if a cell is sensitive or not, we can also add other criteria related to the number of units. 

For example, if a cell contains fewer than three units, we can say this cell is sensitive. 

2.3 Complementary cell 

If a cell has been identified as sensitive, it is not published because there is a risk of disclosure and it is 

masked. In a published table containing several totals and subtotals, masking a cell may require 

blocking one or more other cells in order to protect the sensitive cell. Concealing these make it 

impossible to deduce the masked value from the other table entries. These complementary cells are 

hidden for reasons of residual confidentiality. For example, consider the following table: 

1 2 3 TOT 

A 12 8 9 29 

B 4 4 6 14 

C 5 3 3 11 

TOT 21 15 18 54 

Suppose that we need to mask cell C2 because it is a sensitive cell. We must also select 

complementary cells to protect C2, therefore we obtain: 

1 2 3 TOT 

A 12 8 9 29 

B C C1 6 14 

C C S2 3 11 

TOT 21 15 18 54 

In protecting cell C2, we need to mask B1, B2 and C1. If any one of these three cells is not masked, the 

value of C2 can be deducted. For example, if B1 is not blocked, we can calculated C1=21-12-B1=5 and 

C2=11-3-C1=3, rendering C2 not confidential. 

We could have blocked another set of cells to ensure confidentiality, such as B2-B3-C3. The choice of 

the complementary cells depends on various parameters and considerations. For example, one 

consideration is the size of the sensitive cell in terms of the variable of interest. We need 

complementary cells large enough to protect the confidentiality of cell C2. The size of the 

complementary cells required depends on the confidentiality rules described earlier. 

3. Methodology with CONFID 

CONFID is a software that identifies sensitive cells according to your confidentiality rules and 

identifies all the complementary cells that should be masked in order to produce tabulations where the 

confidentiality of each contributing unit is preserved. For a given problem, i.e. a set of tabulations to 

produce, there are many possible solutions. Those solutions are called confidentiality patterns. 

CONFID finds an optimal solution according to some pre-specified criteria. 

1Complementary Cell. 

2

Sensitive Cell. 

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The goal is to mask as few cells as possible and withhold as little information as possible. Sometimes, 

you must have to choose between publishing two small cells or one large cell. The strategy will 

depend on your objectives for the survey and the publications. CONFID allows you to prioritize the 

amount of information in dollars value or the number of cells. It is also possible to set up CONFID to 

find an optimal confidentiality pattern that is a trade-off between the two criteria. CONFID will find 

an optimal solution by resolving a system of numerical equations that take into account the tabulations 

to be published, the data set itself, your confidentiality rules and the criteria you want to prioritize. 

4. Use of Waivers 

With the confidentiality pattern obtained using CONFID, you can suppress a considerable amount of 

information. This happens when you have a survey for which you produce very detailed tabulations 

composed of small cells with few units. The use of waivers can help to reduce the amount of 

suppressed information. There are two ways waivers can lead to an increase of publishable 

information: 

1) the sensivity of a cell may be caused by one or a few large contributors. Obtaining waivers 

for these companies will allow you to publish the whole cell. 

2) when you eliminate the sensitivity of a cell, the complementary cells, that were chosen 

initially, may no longer be required to be masked to protect the sensitive cell. Publishing 

these cells may lead to substantial gains in terms of dollars and cells. 

5. New approach : Score function 

Because of cost and operational constraints, it is not always possible or feasible to obtain waivers for 

each sensitive units. You may need to be selective and choose only a subset of units for which you will 

try to obtain waivers. Our approach attempts to identify systematically which units should be 

prioritized. Our goal is to find which waiver provides the best return in terms of the amount of 

publishable information. In other words, we identify which sensitive units are responsible for the 

largest amount of suppressed information originating from sensitive and complementary cells. 

In order to be able to rank potential waiver requests, we sought to establish some criteria. We based 

these criteria on the characteristics of the cell and of the block containing the sensitive unit. 

The cell and the block are the two first levels of a tabulation. A cell corresponds to the most detailed 

element that is being published. In business survey, a cell is usually made of two dimensions. 

Typically, it will include a detailed industrial dimension like a subset of four-digit Standard Industrial 

Classification (SIC) codes and a geographical dimension e.g. a province. A block is an aggregation of 

cells (e.g. four-digits SIC by province) that includes the totals for the first dimension categories, the 

totals for the second dimension categories and the grand total. 

Fig1. Block 

GEO A GEO B GEO A+B 

Industry1 CELL1A CELL1B TOT1,A+B 

Industry2 CELL2A CELL2B TOT2,A+B 

Ind. 1+2 TOT1+2,A TOT1+2,B TOT1+2,A+B 

5.1 Criteria for a cell 

We identified two characteristics that could be used to score a cell. Each criterion is represented as a 

ratio and is read as a percentage. 

4.1.1) Number of waivers required before a cell becomes fully publishable 

4.1.2) Size of the cell based on the main variable of interest 

The percentages are combined to get a unique score. Both criteria are weighted according to their 

deemed importance. Here are a few details on each criterion. 

5.1.1 Number of waivers required. We are better off working on a cell if it requires a smaller number 

of waivers. Our criterion is based the ratio of the number of waivers required to make a cell 

publishable over the maximum number of potential waivers required among all the sensitive cells. This 

criterion scores best if the cell presents a smaller number of waivers. It is defined by: 

(max(x) − x)

ce1 = ×100 

max(x) 

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where x is the number of waivers that have to be requested to remove the cell’s sensitivity and 

max( x ) is the largest possible value of x across all the sensitive cells. ce1 will be a high percentage 

if the number of required waivers is small. 

5.1.2 Size of cell in terms of the variable of interest. We consider here the relative size of the cell in 

terms of the main variable of interest. The reason we use the relative size is to grant more priority to the 

largest cells. The formula for this criterion, in terms of the variable of interest, is: 

y

ce2 = ×100 . 

max(y) 

where y is the cell’s total for the variable of interest and max(y) is the largest possible value of y 

across all the sensitive cells. ce2 will be a higher percentage if y value is larger. 

5.1.3 Function for scoring cells. Using the two criteria for the cells, we can create a function to score 

and rank each cell. This function is formulated as follows: 

f (ce) = w ce + w ce 1 1 2 2 

where the cei variables represent each criterion’s value. The wi variables are the weights applied in 

light of the criterion’s deemed importance. The sum of the wi variables is 1. The f (ce) score for a 

cell is a percentage. 

5.2 Criteria for a block 

We came up with four criteria for the block containing sensitive units. Each criterion is represented as 

a ratio and is read as a percentage. 

5.2.1 Number of waivers required before a cell becomes fully publishable 

5.2.2 Size of the block based on the main variable of interest 

5.2.3 Quantity of masked confidential and residual information 

5.2.4 Number of cells in the block containing a sensitive unit. The form of these criteria 

resembles that used for cells, as follows. 

The percentages are combined to get a unique score. Both criteria are weighted according to their 

deemed importance. Here are a few details on each criterion. 

5.2.1 Number of waivers required. We are better off working on a block if it requires a smaller 

number of waivers. We calculate the ratio of the number of waivers required to make the block 

completely publishable over the maximum number of potential waivers required among all the blocks 

where we observe sensitivity. This criterion therefore scores best if the cell presents a smaller number 

of waivers. It is defined by: 

(max(x) − x)

bl1 = ×100 

max(x) 

where x is the number of waivers that have to be requested to remove the sensitivity observed in the 

block and max( x ) is the largest possible value of x across all the blocks. bl will be a high 1 

percentage if the number of required waivers is small. 

5.2.2 Size of block. We want to grant more priority to the largest blocks. Hence, we defined this 

criterion considering the relative size of the block in terms of the main variable of interest. The formula 

for this criterion is: 

y

bl2 = ×100 

max(y) 

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where y is the block’s total for the variable of interest and max(y) is the largest possible value of 

y across all the blocks presenting sensitivity. bl will be a high percentage if the number of 2 

deliveries is large. 

5.2.3 Masked Information. We also want account for the quantity of concealed confidential and 

residual information in a block where we observe sensitivity in some of its cells. To consider this we 

defined: 

y1 + y2

bl3 = ×100 

max(y1 + y2

) 

where, within the block, y1 is the variable of interest total concealed because of sensitivity, and y2 is 

the amount of the variable of interest masked for complementary purposes (residual disclosure). The 

variable max(y + y ) is the largest possible value of these two variables across all the blocks 1 2 

where information is hidden for confidentiality purposes. bl will have a high value if a large quantity 3 

of information is blocked. 

5.2.4 Number of blocked cells. We want to prioritize the block where a large number of cells is 

suppressed. The goal is to rank blocks according to the number of cells masked. The formula for this 

criterion is: 

bl4 =

x 

×100 

max(x) 

where x is the number of sensitive cells and max( x ) is the largest possible value of x across all the 

blocks presenting sensitivity. bl will be a high percentage if many cells are masked. 4 

5.2.5 Function for scoring blocks. Using the four criteria for the blocks, we can create a function to 

score and rank each block. This function is formulated as follows: 

f (bl) = w bl + w bl + w bl + w bl 1 1 2 2 3 3 4 4 

where the bli variables represent each criterion’s value. The wi variables are the weights applied 

according to the criterion’s deemed importance. The sum of the wi variables is 1. The f (bl) score 

for a block is therefore a percentage. 

By taking the two score functions for the cell ( f (ce) ) and the block ( f (bl) ), we can establish the 

relative priority of each cell. In the following section, we analyze the impact of this kind of 

classification method using a practical example. 

6. Practical example 

In this section, we quantified the gain obtained by using waivers. We used the food industries data 

from 1997 Annual Survey of Mining (ASM). That year, ASM was census of units above a certain 

threshold. In this sector, roughly 3100 units contribute to a total manufacturing shipments of 

50,468,609K $. Data are tabulated to cover a total of 319 cells at various industry by geographical area 

levels (including totals and subtotals). Without using waivers we would publish roughly 55% of these 

cells. 

We compared our score function method to identify waivers versus other type of ranking. All options 

in table 5.1 are expressed in terms number of cells and percentage of manufacturing shipments 

published. In this table, we are comparing 4 options : (i) without using waivers, (ii) using top-10 

waivers according to our score-function, (iii) using top-10 waivers according to manufacturing 

shipments by unit and (iv) using top-10 waivers according to total cell manufacturing shipments. We 

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gave results for each level of industry i.e. SIC2 (10 : Food industries), SIC3 (ex.: 101 : Meat and 

poultry products industry) and SIC4 (Ex.: 1012 Poultry products industry). 

Table 6.1 Efficiency of each option in terms of number of cells published (N) and percentage of 

manufacturing shipments (% of Ship.) 

Industry 

Level 

N 

Total 

Option (i) 

N % of Ship. 

Option (ii) 

N % of Ship. 

Option (iii) 

N % of Ship. 

Option (iv) 

N % of Ship. 

SIC2 

SIC3 

SIC4 

13 

88 

218 

13 

61 

100 

100 

97.1 

87.6 

13 

65 

116 

100 

97.5 

91.4 

13 

61 

105 

100 

97.4 

90.2 

13 

62 

103 

100 

97.1 

89.5 

As we can see, by comparing option (i) with (ii), (iii) and (iv), using waivers will increase the amount 

of published information. The gains are greater at the most detailed level (SIC4). Also, if you compare 

the three options used to prioritized waivers, you can notice that our score function (option (i)) allows 

us to publish a non-negligible extra amount of information, especially again for the most detailed 

levels. At the most detailed level (SIC4), we can see that using 10 waivers with our score function 

allow us to publish an extra 5% of manufacturing shipments and, roughly, an extra 15% of cells. 

7. Conclusion

To summarize, we can say that using waivers and prioritizing them can really lead to a significant 

increase of published information when you have to deal with tabulated survey data. Our score 

function based on cell and block characteristics of a sensitive cell help to optimise gains obtained by 

using waivers. 

Further work related to this score function could be to define a more optimal way to combine cell and 

block characteristics. It would be also possible to look at the weighting used to quantify each criteria in 

each function (cell and block). Certain aspects of the weighting could be optimised, but there will be 

always a part of the decision that will depend on users priorities. 

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