Magnitude table suppression

Introduction

The GaussSuppression package contains several easy-to-use wrapper functions and in this vignette we will look at the SuppressFewContributors and SuppressDominantCells functions. In these functions, primary suppression is based on the number of contributors or by dominance rules. Then, as always in this package, secondary suppression is performed using the Gauss method.

We begin by loading a dataset to be used below.

 library(GaussSuppression)
dataset <- SSBtoolsData("magnitude1")
dataset
 #> sector4 sector2 geo eu company value
 #> 1 Agriculture private Portugal EU A 75.9
 #> 2 Agriculture private Portugal EU B 24.5
 #> 3 Agriculture private Spain EU A 96.6
 #> 4 Agriculture private Spain EU B 43.2
 #> 5 Entertainment private Iceland nonEU B 16.8
 #> 6 Entertainment private Portugal EU B 7.1
 #> 7 Entertainment private Portugal EU D 2.3
 #> 8 Entertainment private Spain EU A 77.4
 #> 9 Entertainment private Spain EU B 11.5
 #> 10 Entertainment private Spain EU C 16.4
 #> 11 Governmental public Portugal EU B 21.6
 #> 12 Governmental public Portugal EU D 2.0
 #> 13 Governmental public Spain EU C 6.5
 #> 14 Governmental public Spain EU D 2.7
 #> 15 Industry private Iceland nonEU B 9.6
 #> 16 Industry private Iceland nonEU C 8.8
 #> 17 Industry private Iceland nonEU D 1.9
 #> 18 Industry private Portugal EU B 25.7
 #> 19 Industry private Portugal EU D 3.4
 #> 20 Industry private Spain EU C 8.4

We can imagine the figures in the variable "value" represent sales value to different sectors from different companies. In the first examples, we will not use the "company" variable, but instead assume that each row represents the contribution of a unique company. Our input data can then be reformatted and illustrated like this:

**Table 1**: Input data with the 20 contributions.
sector4	Iceland	Portugal	Spain
Agriculture		75.9, 24.5	96.6, 43.2
Entertainment	16.8	7.1, 2.3	77.4, 11.5, 16.4
Governmental		21.6, 2.0	6.5, 2.7
Industry	9.6, 8.8, 1.9	25.7, 3.4	8.4

Initial basic examples

Using few contributors primary suppression

In the first example, we use SuppressFewContributors with maxN = 1. This means that cells based on a single contributor are primary suppressed.

 SuppressFewContributors(data=dataset, 
 numVar = "value", 
 dimVar= c("sector4", "geo"), 
 maxN=1)
 #> [extraAggregate 20*3->10*4] Checking ....
 #> GaussSuppression_numttHTT: ..............::::
 #> sector4 geo value nRule nAll primary suppressed
 #> 1 Total Total 462.3 20 20 FALSE FALSE
 #> 2 Total Iceland 37.1 4 4 FALSE FALSE
 #> 3 Total Portugal 162.5 8 8 FALSE FALSE
 #> 4 Total Spain 262.7 8 8 FALSE FALSE
 #> 5 Agriculture Total 240.2 4 4 FALSE FALSE
 #> 6 Agriculture Iceland 0.0 0 0 FALSE FALSE
 #> 7 Agriculture Portugal 100.4 2 2 FALSE FALSE
 #> 8 Agriculture Spain 139.8 2 2 FALSE FALSE
 #> 9 Entertainment Total 131.5 6 6 FALSE FALSE
 #> 10 Entertainment Iceland 16.8 1 1 TRUE TRUE
 #> 11 Entertainment Portugal 9.4 2 2 FALSE TRUE
 #> 12 Entertainment Spain 105.3 3 3 FALSE FALSE
 #> 13 Governmental Total 32.8 4 4 FALSE FALSE
 #> 14 Governmental Iceland 0.0 0 0 FALSE FALSE
 #> 15 Governmental Portugal 23.6 2 2 FALSE TRUE
 #> 16 Governmental Spain 9.2 2 2 FALSE TRUE
 #> 17 Industry Total 57.8 6 6 FALSE FALSE
 #> 18 Industry Iceland 20.3 3 3 FALSE TRUE
 #> 19 Industry Portugal 29.1 2 2 FALSE TRUE
 #> 20 Industry Spain 8.4 1 1 TRUE TRUE

In the output, the number of contributors is in columns nRule and nAll. The two columns are equal under normal usage.

A formatted version of this output is given in Table 2 below. Primary suppressed cells are underlined and labeled in red, while the secondary suppressed cells are labeled in purple.

**Table 2**: Output from `SuppressFewContributors` with `maxN = 1` (number of contributors in parenthesis)
sector4	Iceland	Portugal	Spain	Total
Agriculture	0 (0)	100.4 (2)	139.8 (2)	240.2 (4)
Entertainment	16.8 (1)	9.4 (2)	105.3 (3)	131.5 (6)
Governmental	0 (0)	23.6 (2)	9.2 (2)	32.8 (4)
Industry	20.3 (3)	29.1 (2)	8.4 (1)	57.8 (6)
Total	37.1 (4)	162.5 (8)	262.7 (8)	462.3 (20)

Using dominant cell primary suppression

In the second example, we use SuppressDominantCells with n = 1 and k = 80. This means that aggregates are primary suppressed whenever the largest contribution exceeds 80% of the cell total.

 SuppressDominantCells(data=dataset, 
 numVar = "value", 
 dimVar= c("sector4", "geo"), 
 n = 1, k = 80, allDominance = TRUE)
 #> [extraAggregate 20*3->10*4] Checking ....
 #> GaussSuppression_numttHTT: ..............::
 #> sector4 geo value dominant1 max1contributor n_contr n_non0_contr
 #> 1 Total Total 462.3 0.2089552 3 20 20
 #> 2 Total Iceland 37.1 0.4528302 5 4 4
 #> 3 Total Portugal 162.5 0.4670769 1 8 8
 #> 4 Total Spain 262.7 0.3677198 3 8 8
 #> 5 Agriculture Total 240.2 0.4021649 3 4 4
 #> 6 Agriculture Iceland 0.0 0.0000000 NA 0 0
 #> 7 Agriculture Portugal 100.4 0.7559761 1 2 2
 #> 8 Agriculture Spain 139.8 0.6909871 3 2 2
 #> 9 Entertainment Total 131.5 0.5885932 8 6 6
 #> 10 Entertainment Iceland 16.8 1.0000000 5 1 1
 #> 11 Entertainment Portugal 9.4 0.7553191 6 2 2
 #> 12 Entertainment Spain 105.3 0.7350427 8 3 3
 #> 13 Governmental Total 32.8 0.6585366 11 4 4
 #> 14 Governmental Iceland 0.0 0.0000000 NA 0 0
 #> 15 Governmental Portugal 23.6 0.9152542 11 2 2
 #> 16 Governmental Spain 9.2 0.7065217 13 2 2
 #> 17 Industry Total 57.8 0.4446367 18 6 6
 #> 18 Industry Iceland 20.3 0.4729064 15 3 3
 #> 19 Industry Portugal 29.1 0.8831615 18 2 2
 #> 20 Industry Spain 8.4 1.0000000 20 1 1
 #> primary suppressed
 #> 1 FALSE FALSE
 #> 2 FALSE FALSE
 #> 3 FALSE FALSE
 #> 4 FALSE FALSE
 #> 5 FALSE FALSE
 #> 6 FALSE FALSE
 #> 7 FALSE FALSE
 #> 8 FALSE FALSE
 #> 9 FALSE FALSE
 #> 10 TRUE TRUE
 #> 11 FALSE TRUE
 #> 12 FALSE FALSE
 #> 13 FALSE TRUE
 #> 14 FALSE FALSE
 #> 15 TRUE TRUE
 #> 16 FALSE TRUE
 #> 17 FALSE TRUE
 #> 18 FALSE TRUE
 #> 19 TRUE TRUE
 #> 20 TRUE TRUE

To incorporate the percentage of the two largest contributions in the output, the parameter allDominance = TRUE was utilized. A formatted version of this output is given in Table 3 below.

**Table 3**: Output from `SuppressDominantCells`
with `n = 1` and `k = 80`
(percentage from largest contribution in parenthesis)
sector4	Iceland	Portugal	Spain	Total
Agriculture	0 (0%)	100.4 (76%)	139.8 (69%)	240.2 (40%)
Entertainment	16.8 (100%)	9.4 (76%)	105.3 (74%)	131.5 (59%)
Governmental	0 (0%)	23.6 (92%)	9.2 (71%)	32.8 (66%)
Industry	20.3 (47%)	29.1 (88%)	8.4 (100%)	57.8 (44%)
Total	37.1 (45%)	162.5 (47%)	262.7 (37%)	462.3 (21%)

Note that this table, as well as Table 2, is discussed below in the section on the singleton problem.

An hierarchical table and two dominance rules

Here we use SuppressDominantCells with n = 1:2 and k = c(80, 99). This means that aggregates are primary suppressed whenever the largest contribution exceeds 80% of the cell total or when the two largest contributions exceed 99% of the cell total.

In addition, the example below is made even more advanced by including the variables "sector2" and "eu".

output <- SuppressDominantCells(data=dataset, 
 numVar = "value", 
 dimVar= c("sector4", "sector2", "geo", "eu"), 
 n = 1:2, k = c(80, 99))
 #> [extraAggregate 20*5->10*6] Checking ....
 #> GaussSuppression_numttHTT: .............::::::
 head(output)
 #> sector4 geo value primary suppressed
 #> 1 Total Total 462.3 FALSE FALSE
 #> 2 Total EU 425.2 FALSE FALSE
 #> 3 Total nonEU 37.1 FALSE FALSE
 #> 4 Total Iceland 37.1 FALSE FALSE
 #> 5 Total Portugal 162.5 FALSE FALSE
 #> 6 Total Spain 262.7 FALSE FALSE

**Table 4**: Output from `SuppressDominantCells`
with `n = 1:2` and `k = c(80, 99)`
sector4	Iceland	Portugal	Spain	nonEU	EU	Total
Agriculture	0	100.4	139.8	0	240.2	240.2
Entertainment	16.8	9.4	105.3	16.8	114.7	131.5
Governmental	0	23.6	9.2	0	32.8	32.8
Industry	20.3	29.1	8.4	20.3	37.5	57.8
private	37.1	138.9	253.5	37.1	392.4	429.5
public	0	23.6	9.2	0	32.8	32.8
Total	37.1	162.5	262.7	37.1	425.2	462.3

As described in the define-tables vignette hierarchies are here detected automatically. The same output is obtained if we first generate hierarchies by:

dimlists <- SSBtools::FindDimLists(dataset[c("sector4", "sector2", "geo", "eu")])
dimlists
 #> $sector4
 #> levels codes
 #> 1 @ Total
 #> 2 @@ private
 #> 3 @@@ Agriculture
 #> 4 @@@ Entertainment
 #> 5 @@@ Industry
 #> 6 @@ public
 #> 7 @@@ Governmental
 #> 
 #> $geo
 #> levels codes
 #> 1 @ Total
 #> 2 @@ EU
 #> 3 @@@ Portugal
 #> 4 @@@ Spain
 #> 5 @@ nonEU
 #> 6 @@@ Iceland

And thereafter run SuppressDominantCells with these hierarchies as input:

output <- SuppressDominantCells(data=dataset, 
 numVar = "value", 
 hierarchies = dimlists, 
 n = 1:2, k = c(80, 99))
 #> [extraAggregate 20*3->10*4] Checking ....
 #> GaussSuppression_numttHTT: .............::::::

Using the formula interface

Using the formula interface is one way to achieve fewer cells in the output. Below we use SuppressFewContributors with maxN = 2. This means that table cells based on one or two contributors are primary suppressed.

output <- SuppressFewContributors(data=dataset, 
 numVar = "value", 
 formula = ~sector2*geo + sector4*eu, 
 maxN=2,
 removeEmpty = FALSE)
 #> [extraAggregate 20*5->10*6] Checking ....
 #> GaussSuppression_numttHTT: ............:::::
 head(output)
 #> geo sector4 value nRule nAll primary suppressed
 #> 1 Total Total 462.3 20 20 FALSE FALSE
 #> 2 Total private 429.5 16 16 FALSE FALSE
 #> 3 Total public 32.8 4 4 FALSE FALSE
 #> 4 Iceland Total 37.1 4 4 FALSE FALSE
 #> 5 Portugal Total 162.5 8 8 FALSE FALSE
 #> 6 Spain Total 262.7 8 8 FALSE FALSE
 tail(output)
 #> geo sector4 value nRule nAll primary suppressed
 #> 21 EU Entertainment 114.7 5 5 FALSE TRUE
 #> 22 nonEU Entertainment 16.8 1 1 TRUE TRUE
 #> 23 EU Governmental 32.8 4 4 FALSE FALSE
 #> 24 nonEU Governmental 0.0 0 0 FALSE FALSE
 #> 25 EU Industry 37.5 3 3 FALSE TRUE
 #> 26 nonEU Industry 20.3 3 3 FALSE TRUE

In the formatted version of this output, blank cells indicate that they are not included in the output.

**Table 5**: Output from `SuppressFewContributors` with `maxN = 2`
(number of contributors in parenthesis)
sector4	Iceland	Portugal	Spain	nonEU	EU	Total
Agriculture				0 (0)	240.2 (4)	240.2 (4)
Entertainment				16.8 (1)	114.7 (5)	131.5 (6)
Governmental				0 (0)	32.8 (4)	32.8 (4)
Industry				20.3 (3)	37.5 (3)	57.8 (6)
private	37.1 (4)	138.9 (6)	253.5 (6)			429.5 (16)
public	0 (0)	23.6 (2)	9.2 (2)			32.8 (4)
Total	37.1 (4)	162.5 (8)	262.7 (8)	37.1 (4)	425.2 (16)	462.3 (20)

Please note that in order to include the three empty cells with no contributors, the removeEmpty parameter was set to FALSE. By default, this parameter is set to TRUE when using the formula interface.

Using the contributorVar parameter (`contributorVar = "company"`)

According to the "company" variable in the data set, there are only four contribution companies (A, B, C and D). We specify this using the contributorVar parameter, which corresponds to a variable within the dataset, in this case, "company". In general, this variable refers to the holding information to be used by the suppression method. When this is taken into account, the primary suppression rules will be applied to data that, within each cell, is aggregated within each contributor. Our example data aggregated in this way is shown below.

**Table 6**: The "value" data aggregated according to hierarchy and contributor
sector4	Iceland	Portugal	Spain	nonEU	EU	Total
Agriculture		A=75.9, B=24.5	A=96.6, B=43.2		A=172.5, B=67.7	A=172.5, B=67.7
Entertainment	B=16.8	B=7.1, D=2.3	A=77.4, B=11.5, C=16.4	B=16.8	A=77.4, B=18.6, C=16.4, D=2.3	A=77.4, B=35.4, C=16.4, D=2.3
Governmental		B=21.6, D=2.0	C=6.5, D=2.7		B=21.6, C=6.5, D=4.7	B=21.6, C=6.5, D=4.7
Industry	B=9.6, C=8.8, D=1.9	B=25.7, D=3.4	C=8.4	B=9.6, C=8.8, D=1.9	B=25.7, C=8.4, D=3.4	B=35.3, C=17.2, D=5.3
private	B=26.4, C=8.8, D=1.9	A=75.9, B=57.3, D=5.7	A=174.0, B=54.7, C=24.8	B=26.4, C=8.8, D=1.9	A=249.9, B=112.0, C=24.8, D=5.7	A=249.9, B=138.4, C=33.6, D=7.6
public		B=21.6, D=2.0	C=6.5, D=2.7		B=21.6, C=6.5, D=4.7	B=21.6, C=6.5, D=4.7
Total	B=26.4, C=8.8, D=1.9	A=75.9, B=78.9, D=7.7	A=174.0, B=54.7, C=31.3, D=2.7	B=26.4, C=8.8, D=1.9	A=249.9, B=133.6, C=31.3, D=10.4	A=249.9, B=160.0, C=40.1, D=12.3

Below we take into account contributor IDs when using few contributors primary suppression.

output <- SuppressFewContributors(data=dataset, 
 numVar = "value", 
 dimVar = c("sector4", "sector2", "geo", "eu"),
 maxN=2,
 contributorVar = "company")
 #> [preAggregate 20*6->20*7]
 #> [extraAggregate 20*7->10*7] Checking .....
 #> GaussSuppression_numttHTT: ............::::::
 head(output)
 #> sector4 geo freq value nRule nAll primary suppressed
 #> 1 Total Total 20 462.3 4 4 FALSE FALSE
 #> 2 Total EU 16 425.2 4 4 FALSE FALSE
 #> 3 Total nonEU 4 37.1 3 3 FALSE FALSE
 #> 4 Total Iceland 4 37.1 3 3 FALSE FALSE
 #> 5 Total Portugal 8 162.5 3 3 FALSE FALSE
 #> 6 Total Spain 8 262.7 4 4 FALSE FALSE

**Table 7**: Output from `SuppressFewContributors` with `maxN = 2` and with `contributorVar = "company"` (number contributors in parenthesis)
sector4	Iceland	Portugal	Spain	nonEU	EU	Total
Agriculture	0 (0)	100.4 (2)	139.8 (2)	0 (0)	240.2 (2)	240.2 (2)
Entertainment	16.8 (1)	9.4 (2)	105.3 (3)	16.8 (1)	114.7 (4)	131.5 (4)
Governmental	0 (0)	23.6 (2)	9.2 (2)	0 (0)	32.8 (3)	32.8 (3)
Industry	20.3 (3)	29.1 (2)	8.4 (1)	20.3 (3)	37.5 (3)	57.8 (3)
private	37.1 (3)	138.9 (3)	253.5 (3)	37.1 (3)	392.4 (4)	429.5 (4)
public	0 (0)	23.6 (2)	9.2 (2)	0 (0)	32.8 (3)	32.8 (3)
Total	37.1 (3)	162.5 (3)	262.7 (4)	37.1 (3)	425.2 (4)	462.3 (4)

Below we take into account contributor IDs when using dominant cell primary suppression.

output <- SuppressDominantCells(data=dataset, 
 numVar = "value", 
 formula = ~sector2*geo + sector4*eu,
 contributorVar = "company",
 n = 1:2, k = c(80, 99))
 #> [preAggregate 20*6->20*7]
 #> [extraAggregate 20*7->10*7] Checking .....
 #> GaussSuppression_numttHTT: .........:::::
 head(output)
 #> geo sector4 freq value primary suppressed
 #> 1 Total Total 20 462.3 FALSE FALSE
 #> 2 Total private 16 429.5 FALSE FALSE
 #> 3 Total public 4 32.8 FALSE FALSE
 #> 4 Iceland Total 4 37.1 FALSE FALSE
 #> 5 Portugal Total 8 162.5 FALSE FALSE
 #> 6 Spain Total 8 262.7 FALSE FALSE

Here we have also made use of the formula interface.

**Table 8**: Output from `SuppressDominantCells` with `n = 1:2` and
`k = c(80, 99)` and with `contributorVar = "company"`
sector4	Iceland	Portugal	Spain	nonEU	EU	Total
Agriculture					240.2	240.2
Entertainment				16.8	114.7	131.5
Governmental					32.8	32.8
Industry				20.3	37.5	57.8
private	37.1	138.9	253.5			429.5
public		23.6	9.2			32.8
Total	37.1	162.5	262.7	37.1	425.2	462.3

The singleton problem

Below, the data is suppressed in the same way as in Table 7, but with a different formula.

output <- SuppressDominantCells(data=dataset,
 numVar = "value", 
 formula = ~sector4*geo + sector2*eu,
 contributorVar = "company",
 n = 1:2, k = c(80, 99))
 #> [preAggregate 20*6->20*7]
 #> [extraAggregate 20*7->10*7] Checking .....
 #> GaussSuppression_numttHTT: ............
 head(output)
 #> sector4 geo freq value primary suppressed
 #> 1 Total Total 20 462.3 FALSE FALSE
 #> 2 Agriculture Total 4 240.2 TRUE TRUE
 #> 3 Entertainment Total 6 131.5 FALSE FALSE
 #> 4 Governmental Total 4 32.8 FALSE FALSE
 #> 5 Industry Total 6 57.8 FALSE TRUE
 #> 6 Total Iceland 4 37.1 FALSE FALSE

**Table 9**: Output from `SuppressDominantCells` with `n = 1:2` and `k = c(80, 99)` and with `contributorVar = "company"`
sector4	Iceland	Portugal	Spain	nonEU	EU	Total
Agriculture		100.4	139.8			240.2
Entertainment	16.8	9.4	105.3			131.5
Governmental		23.6	9.2			32.8
Industry	20.3	29.1	8.4			57.8
private				37.1	392.4	429.5
public					32.8	32.8
Total	37.1	162.5	262.7	37.1	425.2	462.3

By using singletonMethod = "none" in this case, Entertainment:Spain will not be suppressed. This cell is suppressed due to the default handling of the singleton problem. The reason is that Entertainment:Iceland has a single contributor. This contributor can reveal Entertainment:Portugal if Entertainment:Spain is not suppressed.

Here it might appear that the table contains another issue, Entertainment:Iceland can reveal Industry:Iceland. However, this can be considered ok in this case. Industry:Iceland is secondary suppressed and the only reason for this is to protect Entertainment:Iceland.

Nevertheless, in most cases, secondary suppressed cells introduce further complexity to the handling of singletons. A part of the singleton handling of magnitude tables is to add virtual primary suppressed cells prior to the secondary suppression algorithm. Secondary suppressed cells cannot, therefore, be treated in this way. However, another part of the singleton handling solves many of the remaining problems. This is done within the suppression algorithm.

Here we can observe the effect of this in Tables 2 and 3. By using singletonMethod = "none" in Table 2, Industry:Portugal will not be suppressed. In that case, Industry:Spain can reveal Industry:Iceland and consequently Entertainment:Iceland. In Table 3, Governmental:Total and Industry:Total are suppressed due to advanced singleton handling. In fact, by using singletonMethod = "none", all tables above will be suppressed differently.

Intervals

Intervals for the primarily suppressed cells are computed whenever the lpPackage parameter is specified. Additionally, if rangePercent and/or rangeMin are provided, further suppression is performed to ensure that the interval width requirements are met. See the documentation for the lpPackage parameter in ?GaussSuppressionFromData for more details.

In the example below, the interval widths for output lines 12, 14, 17, and 20 are 60.7, which is too narrow since a minimum width of 80 is required. Therefore, the cell on line 16 is additionally suppressed

output <- SuppressDominantCells(data = dataset, 
 numVar = "value", 
 dimVar = c("geo", "sector2", "sector4"), 
 pPercent = 30, 
 rangePercent = 70, rangeMin = 80, 
 lpPackage = "Rglpk")
 #> [extraAggregate 20*4->10*5] Checking ....
 #> GaussSuppression_numttHTT: ............
 #> (10*8-DDcol->10*6-0exact->10*5-GaussI->10*5)
 #> 
 #> Using Rglpk for intervals...
 #> -----------
 #> (10*8-DDcol->10*6-DDrow->9*6->)
 #> ......
 #> 4+1-3+2-
 #> 2: 1 new, (138.9) 1+
 #> GaussSuppression_none: ......
 #> (10*7-DDcol->10*5-0exact->10*4-GaussI->10*4)
 #> 
 #> Using Rglpk for intervals...
 #> -----------
output[c(12, 14, 16, 17, 20, 25), ] # some output lines 
 #> geo sector4 value rlim_value lo_1 up_1 lo up
 #> 12 Iceland Entertainment 16.8 80.00 0.0 60.7 0.0 131.5
 #> 14 Iceland Industry 20.3 80.00 0.0 60.7 0.0 90.6
 #> 16 Portugal private 138.9 NA NA NA NA NA
 #> 17 Portugal public 23.6 80.00 0.0 60.7 0.0 90.6
 #> 20 Portugal Governmental 23.6 80.00 0.0 60.7 0.0 90.6
 #> 25 Spain Agriculture 139.8 97.86 101.3 240.2 40.6 240.2
 #> suppressed_integer primary suppressed
 #> 12 1 TRUE TRUE
 #> 14 1 TRUE TRUE
 #> 16 3 FALSE TRUE
 #> 17 1 TRUE TRUE
 #> 20 1 TRUE TRUE
 #> 25 1 TRUE TRUE

In the formatted output shown in Table 10 below, the final intervals are given in parentheses.

**Table 10**: Output from `SuppressDominantCells` with `pPercent = 30`, `rangePercent = 70`, `rangeMin = 80`, `lpPackage = "Rglpk"`
sector4	Iceland	Portugal	Spain	Total
Agriculture	0	100.4 [0, 199.6]	139.8 [40.6, 240.2]	240.2
Entertainment	16.8 [0, 131.5]	9.4 [0, 131.5]	105.3 [0, 131.5]	131.5
Governmental	0	23.6 [0, 90.6]	9.2 [0, 90.6]	32.8 [0, 90.6]
Industry	20.3 [0, 90.6]	29.1 [0, 90.6]	8.4 [0, 90.6]	57.8
private	37.1	138.9	253.5	429.5
public	0	23.6 [0, 90.6]	9.2 [0, 90.6]	32.8 [0, 90.6]
Total	37.1	162.5	262.7	462.3