Manual - University of Liverpool
Contents
1. 5 SDC_Direct_Impacts_run_parameters txt Stored in the RunParamters folder pointed to in Jnput_and_output_paths txt The main purpose of SDC_Direct_Impacts is to evaluate the difference between perturbed and unperturbed count and percentage data Users can select from a wide variety of goodness of fit measures at cellular tabular and cross table i e global average measures by modifying the relevant options in the file SDC_Direct_Impacts_run_parameters txt Options should be registered by changing the relevant values to the right of the comma on each line The default settings are shown below Please note that the spacing blank lines between sections is vital to the correct execution of the program and should not be altered in any way Following the example file the remainder of this section explains the meaning of the various parameters and the options available for each file information on input counts Data source Create_Aggregates User Create_Aggregates No of samples Wee vO Sampling strata 1 All 2 P20 P80 3 All P20 P80 2 Sample type a 3 Sample size We 20 Report table mapping on off Me al Use counts percentages 0 count 1 2 count amp 0 Strata source file popdens fmt Report types Table Totals on off WO Table specific Area specific Cell based on off Wwe 0 Table specific Area specific Table based on off 0 Table s2. 2 Tabular measures for count data Definitions Table input tables will typically comprise a set of internal cell counts possible plus a set of table margins It is possible to envisage assessing the impact of disclosure control on all table cells on internal cells only on marginal cells only and so on For analytical purposes therefore a table is taken to represent a set of cells of common cell type e g all marginal cells based on the summation of 4 internal cells In consequence one input table may have generate multiple table outputs Measures frequency n a count of the number of cells within a given table n_changed NC NC where NC 1 if O lt gt E 0 otherwise O observed post disclosure control counts E expected pre disclosure control counts i specific cell within table p_changed PC 2 NC n max_change MNC max O Ei for i 1 ton maxPchange MPC max O E E for i 1 ton TotalError TE O E for i 1 ton TAE TAE O E for i 1 ton RAE RAE 100 TAE TVC see below for definition of TVC SAE SAE TAE x E for i 1 ton Sq_Error E E O E fori 1 ton RMSE RMSE E n SSZ SSZ Z7 fori 1 ton NFC NFC 2 NFC fori 1 ton NFT NFT 1 if SSZ exceeds 7 critical value for table p 0 05 df n else 0 i Degrees of freedom calculation of NFT assumes that all cells internal and marginal
3. bpn 20 0 By a 61 49 Sy 0 0 3 0 0 6 0 0 6 Gee Be ie OR OR Ope HOR OR A Aa tor O 5 3 0 0 0 0 0 OO 2 0 0 0 520 AMG Sie Oe HORS Oe OE COS SIS Ok 2DiS eum AQ S86 Aa 20 OR Be LOR a SPA OM TOR 0 Oi Se Oe 105 Oe dy Orr 90 Be YOA 0 2 As shown above the counts for each area must be preceded by a header This header should be used to identify the area which the set of counts represents in a way which is meaningful to the user and should be in quotes if the identifier includes a space Data for the next area should start on the next empty row Do NOT leave a blank row between areas For example s71_v0_s1 7399 104 7226 69 2991 40 718 9 709 0 298 0 s71_v0_s2 7021 121 6823 77 3057 43 706 12 694 0 307 0 Files created via Create_Aggregates automatically conform to the above requirements 5 3 Post perturbation counts Stored in the JnputCounts folder pointed to in Input_and_output_paths txt One file per table variant containing the perturbed table counts arising from a particular disclosure control method for 1 1000 areas samples A sample 1 or more areas previously selected at random and aggregated if appropriate from a larger set of user supplied areas Files containing perturbed counts for a set of samples may be supplied by the user themselves or produced using Create Aggregates Users lacking perturbed counts may produce perturbed versions of user supplied counts
4. perturbation table counts and or percentages These outputs include a range of cellular and tabular measures as well as an optional assessment of differences in pre and post adjustment area rankings SDC_Direct_Impacts can also summarise the average impact of disclosure control across multiple table layouts e g tables with differing numbers of counts focus on more or less rare population sub groups marginals based on summation across differing numbers of cells SDC_Direct_Impacts if used in conjunction with the outputs from Create Aggregates is also capable of summarising the average impact of disclosure control across multiple versions of the same table generated by alternative sampling strategies e g inputs based upon differing sized aggregates of input areas inputs drawn from different strata such as urban vs rural or rich vs poor SDC_Direct_Impacts optionally allows for assessment of the impact of indirect perturbation Indirect perturbation occurs when a table marginal is derived from summation of perturbed table counts rather than from direct perturbation of the original marginal count even if the original input marginal counts were independently perturbed Program limits Input tables 20 Samples areas per table 1000 Rows columns cells per table 40 20 800 Total cells in all tables 16000 Cell types count marginal s per table 50 Cell types across all input tables 200 Marginal mappi
5. specific table based reports with measures calculated separately for each cell type Hence tabular measures reported for in the column headed 4 represent the cross table average of all marginal cells dependent upon the values of four internal cells The results are reported separately for each user supplied input area sample 14 Cross table Area specific Table based report Cell type no of contributing cells Measure Sample Marginal Internal All 1 2 3 10 20 n_changed 16 000000 25 000000 41 000000 25 000000 11 000000 2 000000 2 000000 1 000000 n_changed 2 15 000000 26 000000 41 000000 26 000000 10 000000 2 000000 2 000000 1 000000 n_changed 3 13 000000 28 000000 41 000000 28 000000 10 000000 2 000000 0 000000 1 000000 n_changed 4 14 000000 28 000000 42 000000 28 000000 9 000000 2 000000 2 000000 1 000000 Cell type no of contributing cells Measure Sample Marginal Internal All 1 2 3 10 20 p_changed 1 100 000000 78 125000 85 416667 78 125000 100 000000 100 000000 100 000000 100 000000 p_changed 2 93 750000 81 250000 85 416667 81 250000 90 909091 100 000000 100 000000 100 000000 p_changed 3 81 250000 87 500000 85 416667 87 500000 90 909091 100 000000 0 000000 100 000000 p_changed 4 87 500000 87 500000 87 500000 87 500000 81 818182 100 000000 100 000000 100 000000 5b vii Cross table Cross area Table based this report summarises user specified measures of tabular fit across all user supplied input areas samples and all
6. 6 SDC_Direct_Impacts_Count_input_tables fmt Stored in the RunParameters folder pointed to in Input_and_output_paths txt A list of files containing lists of pre post perturbation table counts to be used in assessment of disclosure control one pair of comparison tables per row of file The format for each comparison pair row in the file is lt table name gt lt original count variant gt lt perturbed count variant gt E g sd06 O 2 It is important that 1 the table name is in quotes 11 all items in the row are comma separated iii the table name supplied matches the table name used in the naming of input and map files see 1 2 and 3 above if in doubt The file SDC_Disclosure_Impacts_run_parameters txt contains all additional information required to generate full input file names covering both map files and original perturbed count data regardless of data source user supplied or created via Create Aggregates For a user supplied set of tables the example given above is equivalent to requesting that the counts contained in the file S06_vO fmt are compared to their equivalents in 20 S06_v2 fmt If the data source for the tables is Create Aggregates the example above is equivalent to requesting that the counts contained in the file S06a_v0_P20 Popdens _n20 R _s1000 fmt are compared to their equivalents in SO6a_v2_P20 Popdens _n20 R _s1000 fmt 7 SDC_Direct_Impacts_Percentage_input_tab
7. 77 272727 100 000000 100 000000 100 000000 2 n_changed 13 000000 20 000000 33 000000 20 000000 10 000000 2 000000 1 000000 2 p_changed 92 857143 90 909091 91 666667 90 909091 90 909091 100 000000 100 000000 3 n_changed 11 000000 20 000000 31 000000 20 000000 10 000000 0 000000 1 000000 3 p_changed 78 571429 90 909091 86 111111 90 909091 90 909091 0 000000 100 000000 4 n_changed 12 000000 20 000000 32 000000 20 000000 9 000000 2 000000 1 000000 4 p_changed 85 714286 90 909091 88 888889 90 909091 81 818182 100 000000 100 000000 5 n changed 13 000000 19 000000 32 000000 19 000000 10 000000 2 000000 1 000000 5 p_changed 92 857143 86 363636 88 888889 86 363636 90 909091 100 000000 100 000000 and so on 5b iv Table specific Cross area Cell based summarises the distribution of user requested cell based measures across all input areas samples on a table by table basis For example the user might require the mean and maximum percentage change in a cell based value across all user supplied input areas arising from disclosure control Table specific Cross area Cell based report user requested s71 original_cnt Maximum 10426 00000 152 00000 10191 00000 411 00000 3789 00000 224 00000 original_cnt Mean 9746 90000 54 20000 9383 60000 309 10000 3682 40000 147 60000 original_cnt Maximum 997 00000 14 00000 997 00000 0 00000 380 00000 0 00000 original_cnt Mean 931 70000 5 20000 926 50000 0 00000 368 70000 0 00000 cell_changed Maximum 1 00
8. NFCm NFTm V L Therefore even if requested SDC_Direct_Impacts will not report these measures for percentage data 5 Distributional measures Available measures Maximum minimum mean 2 5 and 97 5 percentiles The latter two measures may be used to derive a 95 confidence interval Percentiles calculated by interpolation given Q Q rank of value for given percentile Q 1 p N 1 where p percentile required expressed as a fraction e g 0 975 97 5 percentile and N no of ranked values i e no of input areas 26
9. _in_sample _Correct classes 10 10 100 00 10 10 100 00 Percentile 10 class 1 Lower bound 1 Upper bound I Percentile 20 class 2 Lower bound 2 Upper bound 2 Percentile 30 class 3 Lower bound 3 Upper bound 3 Percentile 40 class 4 Lower bound 4 Upper bound 4 Percentile 50 class 5 Lower bound 5 Upper bound 5 Percentile 60 class 6 Lower bound 6 Upper bound 6 Percentile 70 class 7 Lower bound 7 Upper bound 7 Percentile 80 class 8 Lower bound 8 Upper bound 8 Percentile 90 class 9 Lower bound 9 Upper bound 9 Percentile 100 class 10 Lower bound 10 Upper bound 10 Etc The report Correct Neighbouring Class appears between any table specific and cross table reports requested 5 c Cell based measures For each measure of fit 0 off 1 on 5c i Measures available SDC_Impact_Direct calculates and can report if required 8 cell based measures Note that to report cell based measures a cell based report type must also have been requested cell_exp expected cell value original value cell_obs observed cell value value after application of disclosure control 17 cell_changed A flag indicating whether expected and observed cell values differ 1 differ 0 no difference cell_TE Total Error size of difference between expected and observed values cell_Z Z score depends upon size of difference and table total see p 38 for details cell_ NFC Flag set to 1 if cell Z
10. and post disclosure control quantile class is reported for each of three quantile types 20 10 5 For each quantile type the report commences by identifying the relevant upper and lower class boundaries This is followed by an assessment of classification by individual class which is followed in turn by an overall assessment Example output is given below for only two percentage additional percentages would appear in additional columns Edited here to ensure column alignment this space separated output is best viewed by via a spreadsheet The column headed Near_Class records the number of observed input areas falling within the relevant or an adjacent class Quantile boundaries 5 classes percentages Percentile 20 class Lower bound 1 Upper bound 2 Percentile 40 class 2 Lower bound 3 Upper bound 4 Percentile 60 class 3 Lower bound 5 Upper bound 6 Percentile 80 class 4 Lower bound 7 Upper bound 8 Percentile 100 class 5 Lower bound 9 Upper bound 10 Correct Neighbouring class 5 quantiles percentages Percentage pltill pltill pltill punemp punemp punemp Class Near_Class no _in_class _Correct Near_Class no _in_class _Correct a 2 2 100 00 2 2 100 00 2 2 2 100 00 2 2 100 00 3 2 2 100 00 2 2 100 00 4 2 2 100 00 2 2 100 00 5 2 2 100 00 2 2 100 00 Quantile boundaries 10 classes percentages All Near_Class no _in_sample _Correct Near_Class no
11. are not constrained in their fit to pre disclosure control values Hence degrees of freedom for any table is taken to be n This stance is justified as follows First few if any disclosure control methods currently implemented by statistical agencies involve modifying internal cells in such a way that they are guaranteed to total to original marginals Such a method would in any case probably open up the possibility of reverse engineering the perturbations applied Consequently in assessing degrees of freedom all internal cells may be regarded as unconstrained If post 24 disclosure control marginal values are also not constrained then the assumption that df n remains valid However it is possible that margins are independently supplied and constrained to fit to original margins in which case degrees of freedom for marginal cells 0 If this is the case the values of NFT for all cell types except internal should be disregarded SSZm SSZm Zm fori 1 ton NFCm NFCm NFCm for i 1 ton NETm NFTm 1 if SSZm exceeds 7 critical value for table p 0 05 df n else 0 Gibsons_D D 0 5 E ZE O XO fori 1 ton i If XA 0 set E LE 0 if XO 0 set O LO 0 Cramers_V V 37 n min r 1 c 1 where r no of rows of given cell type in table c no of columns in table in table i If minimum r c 1 V 9 undefined 11 For cell types other than internal the val
12. score is gt 1 96 indicating a non fitting cell i e difference between expected and observed count greater than would be expected by change alone 0 05 significance level else flag set to 0 cell_ Zm Modified Z score Z which takes account of cases when expected and observed table totals are markedly different see appendix p 38 for details cell NFCm Flag set to 1 if cell Zm is gt 1 96 indicating a non fitting cell else flag set to 0 modified Z does not have a known sampling distribution although if expected table total observed table total Zm Z Sc ii Cross area summary values available For each cell based measure five sample summary values are available Cell_ Summary Max Maximum value of cell based measure across all input areas Cell Summary 97 5 tile 97 5 percentile value of cell based measure across all input areas Cell_ Summary mean mean value of cell based measure across all input areas Cell Summary 2 5 tile 2 5 percentile value of cell based measure across all input areas Cell_Summary min Minimum value of cell based measure across all input areas 5 d Table based measures In i and ii below the term table is used in the sense outlined in more detail in section iii Full definitions of all measures are given in pages 38 41 The measures listed below will only be reported if a table based report type has also been requested 5d i Available
13. sum to give column marginal s if any Example 1 Table containing only independently perturbed table counts Sex Ethnic group Persons and Black Black Black Other groups born in Age White C bean African other Indian P stani B deshi Chinese Asian Other Ireland Total Persons 94 4 0 0 3 0 0 12 0 2 7 Given that all of the counts in the above table are independent of each other the full description of this table required by SDC_Direct_Impacts is Ly eT Description Row 1 number of rows in table followed by number of columns above example table with 1 row and 11 columns Example 2 Table containing one dependent table marginal Sex Ethnic group Persons and Total Black Black Black Other groups born in Age Persons White C bean African other Indian P stani B deshi Chinese Asian Other Ireland Total Persons LES 94 4 0 0 3 0 0 12 0 2 7 The original total persons count in the above table is based on the sum of the interior ethnic group counts Additional information is required therefore mapping the contribution of each table count to this table marginal In this case the full table description required by SDC_Direct_Impacts would be BALZ LLZ gA Ee 78 8 10 ETO The description is compiled as follows Description Row 1 number of rows in table followed by
14. the internal cell counts contributing to the overall table total may not equal the actual table total If required both table totals will be reported for both the original and perturbed table variants For example Revised table totals for s06a Table s06a As published Expected total 9834 Observed total 9831 Table s06a Sum of internal counts Expected total 9834 Observed total 9882 11 S5b ii Table specific Area specific Cell based reports all user requested cell based measures for each table cell in each input table for each input area The available cell based measures are listed in the section headed cell based measures below The following example report includes three of the available cell based measures Table specific Area specific Cell based report for s06a Sample 1 cell_exp 9834 7351 371 180 100 687 212 666 50 92 125 328 4807 3547 175 84 45 335 122 360 21 49 69 145 5027 3804 196 96 55 352 90 306 29 43 56 183 cell_changed ls li als ls 1 1 A 1 3 i as 1 1 1 al 1 0 1 d 0 d 1 1 1 di 0 J 0 1 g di 0 di di g 1 cell_diff 3 i 1 3 2 93 2 3 5 5 2 2 4 mail 6 0 4 4 0 6 5 9 4 5 0 4 0 4 5 ma 0 13 8 1 3 Table specific Area specific Cell based report for s06a Sample 2 cell_exp 9780 8011 461 258 137 417 110 60 64 130 132 215 4629 3782 201 125 62 217 52 30 34 59 67 96 5151 4229 260 133 75 200 58 30 30 71 65 119 cell_changed 1 1 1 1 1 0 1 1 1 1 1 1 J 1 J J 1 A J 0 J 1 1
15. using Perturb Input files supplied directly by the user should use the following naming convention lt table name gt _vn fmt where n is any user specified number indicating a particular disclosure control variant E g User_supplied_table_v2 fmt It is recommended but not essential that 0 is reserved to indicate files containing the original unperturbed counts The names of input files created via Create_Aggregates should be left unchanged For example the following three files would contain the perturbed counts arising from three different statistical disclosure control methods SO06_v1 f mt S06_v2 f mt S06_v3 fmt The file layout required is the same as that used for original counts as outline in 2 above 4 Table mappings Stored in the TableMappings folder pointed to in Input_and _output_paths txt For each input table a file is required specifying the table structure rows columns marginals etc For this file the naming convention lt table name gt map should be followed e g User_supplied_table map or s06 map for the examples presented in 2 above Creating an appropriate table mapping is by far the most onerous part of preparing data for input to SDC_Direct_Impacts and to Perturb Full details on how to create such table mappings are set out below but in general the file will include 1 number of rows and columns in table 1i row counts which sum to give row marginal s if any iii column counts which
16. with the other requested measures as illustrated above and once in a stand alone section as illustrated below Table specific Cross area Table based report mean s71 Cell type no of contributing cells Measure Distrib Marginal Internal All r 3 n_changed Mean 1 800000 7 000000 8 800000 7 000000 1 800000 p_changed Mean 90 000000 70 000000 13333333 70 000000 90 000000 Note that distributional information is not available for the optional tabular measure frequency which provides a simple count of the number of cells of each type in a table Consequently if this measure is requested it will effectively be added as an additional header row For example Table specific Cross area Table based report user requested s71 Cell type no of contributing cells Measure Distrib Marginal Internal All i 3 frequency Count 2 10 uy 10 2 n_changed Maximum 2 000000 8 000000 10 000000 8 000000 2 000000 n_changed Mean 1 800000 7 000000 8 800000 7 000000 1 800000 n_changed Minimum 1 000000 6 000000 8 000000 6 000000 1 000000 p_changed Maximum 100 000000 80 000000 832333333 80 000000 100 000000 p_changed Mean 90 000000 70 000000 73 333333 70 000000 90 000000 p_changed Minimum 50 000000 60 000000 66 666667 60 000000 50 000000 5b vi Area specific Cross table Table based a report of user specified table based measures averaged across all user supplied input tables The report layout follows that of area specific table
17. 0 J J J le J J 1 d J dJ 1 i cell_diff 3 7 1 6 2 0 Fa 3 8 a1 3 10 3 2 3 2 ul 4 2 0 4 7 0 6 O 11 4 3 4 2 3 a8 7 2 10 Table specific Area specific Cell based report for s06a Sample 3 etc As may be seen from above all requested cell based measures are reported for each input area sample in turn The layout of the cells directly mirrors the layout of the cells as input to SDC_Direct_Impacts with the number of columns and rows conforming to that recorded in the table mapping The example above presents results for the following input table layout Sex Ethnic group Persons and Total Black Black Black Other groups _ born in Age Persons White C bean African other Indian P stani B deshi Chinese Asian Other Ireland Total Persons TITS 94 4 0 0 3 0 0 12 0 2 7 0 4 6 5 0 0 0 0 0 0 1 0 0 0 5 15 5 3 0 0 0 0 0 0 2 0 0 0 WARNING for large input datasets with many areas and or many tables the potential size of the output file produced by this report option is very large The main purpose of this reporting option is simply to aid quality assurance of outputs from SDC_Direct_Impacts using small pilot datasets 5b iii Table specific Area specific Table based reports all user requested table based measures for each user supplied input table for each input area sample The available table based measures of fit are described belo
18. 000 00000 1 00000 1 00000 1 00000 1 00000 cell_changed Mean 0 80000 0 90000 0 80000 1 00000 0 90000 0 90000 cell_changed Maximum 1 00000 00000 1 00000 0 00000 1 00000 0 00000 cell_changed Mean 1 00000 0 60000 1 00000 0 00000 0 90000 0 00000 As for table specific area specific cell based reports 5b ii the layout of cells conforms to the layout of cells in the user supplied input tables in this case a table comprising one row and six columns The full range of cellular measures and distributional summary statistics available are set out below see section 5 c below headed Cell based measures If multiple distributional measures are requested including the mean the report output will include report the mean twice once in conjunction with the other requested measures as illustrated above and once in a stand alone section as illustrated below Table specific Cross area Cell based report mean s71 original_cnt Mean 9746 90000 54 20000 9383 60000 309 10000 3682 40000 147 60000 cell_changed Mean 0 80000 0 90000 0 80000 1 00000 0 90000 0 90000 original_cnt Mean 931 70000 5 20000 926 50000 0 00000 368 70000 0 00000 cell_changed Mean 1 00000 0 60000 1 00000 0 00000 0 90000 0 00000 If produced the stand alone mean section precedes the section containing all requested distributional measures This feature is designed to aid summary results analysis 13 5b v Table specific Cross area Table based summarises
19. On Ole KON MOS a eos Se as OOo OL One Os OS UO HO Ore Ors BO Or 0 20 2 VOR 0 OS 208 008 CO BO NOs CO HOKE SO SOs 0 OSs Os A 8 BO 208 20 M22 60 Oe 0 g 8Q gt 0 2 0 0 00 00 00 00 00 0 0 0 0 0 0 0 0 0 0 0 1 25 26 27 28 QAR A200 Oe TO 206 205 10 O 10 0 0 SG 20 vo 08 0 0 205 502 20 10m 05 HOP 0 MOa Ox 20 2 CO ORO COE Oe OS BO Oe Oe ORO OE 0 6 oO Oe OE LO Or 0 CON 24 Or Or 0 0 Note the need for one mapping per table marginal being mapped Note also that in this example to save time some table marginals are expressed as the sum of other table marginals Table 08 Economic position residents aged 16 and over Sex by economic position Total aged 16 and over Age 16 20 25 30 35 45 55 60 19 24 29 34 44 54 59 64 65 Students Econ active or inactive Males Economically active Employees full time Employees part time Self emp employees Self emp 0 employees On a govt scheme Unemployed Student incl Above Economically inactive Students Permanently sick Retired Other inactive Females Economically active Employees full time Employees part time Self emp employees Self emp 0 employees On a govt scheme Unemployed Student incl Above Economically inactive Students Permanently sick Retired Other inactive
20. S 1 Cellular measures for count data Definitions Cell type the number of internal cell counts on which a cell s value is based Internal cells have a cell type of 0 marginal cells have a cell type of 2 or more Cells of type 1 are direct copies of internal cells and are treated as internal cells for classification purposes Cell 7 specific cell within table i ranges from 1 to number of cells in table Measures Exp expected pre disclosure control cell value Obs Oj observed post disclosure control cell value value after application of disclosure control Changed Cj 1 if O lt gt E else 0 TE TE O E Z Z O ZO E ZE Q E ZEX 1 E ZE 2O0 where Qi 0 if E 0 else if O xO Ei XE gt 0 Qi 1 ZE 0 else Q 1 ZE XO To avoid Z becoming undefined i if E 0 substitute 1 ii if E XE substitute LE with XE 1 iii if Ei gt ZE substitute LE with E 1 iv if E O and LE xO Zi 0 NFC NFC 1 if Z exceeds critical value of 1 96 p 0 05 else 0 Zm Zm O E E 2 E E 2 EX 1 E ED X E To avoid Zm becoming undefined i if E 0 substitute 1 ii if E XE substitute LE with XE 1 iii if Ei gt ZE substitute LE with E 1 iv if E O and LE xO j Zm 0 NFCm NFCm 1 if Zm gt 1 96 else 0 23
21. Working Paper 2005 3 SDC Direct Impacts SOFTWARE MANUAL V1 0 Software for assessing the impact of statistical disclosure controls on end user analyses Paul Williamson June 2005 Population Microdata Unit Department of Geography University of Liverpool Contents Introduction for first time users Quick Start Guide SDC_Direct_Impacts PROGRAM LIMITS PROGRAM INPUTS Program Pathnames Pre perturbation counts Post perturbation counts Table mappings User definable Parameters Input counts Report types Cell based measures Table based measures Table and cell types Listing input tables counts Listing input tables percentages Percentage mappings Chi square data PROGRAM OUTPUTS FULL DESCRIPTION OF CELLULAR AND TABULAR MEASURES Cellular measures for count data Tabular measures for count data Cross table measures for count data Measures for use with percentages Distributional measures 22 23 23 24 29 26 26 Introduction for first time users SDC 1 is a software suite aimed at helping to assess the impact of statistical disclosure control on end user analyses Figure 1 p 4 illustrates the logic flow of the program suite However each main element can also be run as stand alone module For example users with their own set of pre and post adjustment cell counts can use the SDC_Direct_Impacts module to measure the impacts of adjustment without having to run any of the other modules Quick Start Gu
22. ased measure across all input areas e Tables and cell types Conventionally measures of tabular fit are based on a table s internal cells i e all cells whose value depends on no other cell However in terms of disclosure control the cumulative impact on marginals is of particular interest For this reason SDC_Direct_Impact produces table based measures based on evaluation not only of all internal cells but also separately for all cells of a given type within each table A cell s type is defined by the number of other cells within the table upon which it s value depends Internal cells are type 0 their values depend on no other cells In contrast cells of type 4 represent all marginal cells in a table whose value depends upon the summation of 4 internal cells In addition two other cell types are also recognised all cells whether marginal or internal denoted by cell type 2 and all marginal cells i e all cells depending on the value of 1 other cells denoted by cell type 1 During calculation a table is regarded as comprising all table cells of a given type Please note that for internal programming reasons all cells reported in all SDC_Direct_Impacts output as cells of type 1 are in fact cells of type 0 1 e type 1 internal cells This is because cells of type 1 depending on only 1 cell are in effect simply direct copies of existing internal type 0 cells
23. bove output shows that when ranked by illness pltill 6 out of 10 areas 60 had the same ranking pre and post disclosure control The report Correct Rank appears between any table specific and cross table reports requested N B In the case of areas with identical values all are assigned the rank of the first occurring instance of the value with the next occurring value having a rank to this rank no of duplicate values Ranking is from lowest to highest value with rank 1 equalling lowest value E g Values in ascending order Assigned rank 0 1 0 2 0 4 0 4 0 5 AwWWN e 5b ix Correct Class If this flag is switched on and use counts percentages lt gt 0 the number of areas placed into the same pre and post disclosure control quantiles classes is reported for each of three quantile types 20 10 5 For each quantile type the report commences by identifying the relevant upper and lower class boundaries This is followed by an assessment of classification by individual class which is followed in turn by an overall assessment Example output is given below for only two percentages additional percentages would appear in additional columns Edited here to ensure column alignment this space separated output is best viewed by via a spreadsheet Quantile boundaries 5 classes percentages Percentile 20 class 1 lLower bound 1 Upper bound 2 Percentile 40 class 2 lLower bound 3 Upper bo
24. bular or vector format The first line of the file lt percentage name gt map describes the number of rows and columns per input area For example EEL describes an input file with 17 percentages per input area laid out as a vector 1 row 21 For percentages whose value depends on the summation of other percentages additional mapping information is required just as for count data see section 3 Table Mappings above 9 Chisquare dat Stored in the RunParamters folder pointed to in Input_and_output_paths txt A file supplied with the program that gives chi square critical values at 0 05 significance level for 0 to 5000 degrees of freedom Needed to check whether or not pre and post disclosure counts agree at the tabular level using squared Z score which has unit normal distribution PROGRAM OUTPUTS SDC_Direct_Impacts_results txt Stored in the folder pointed to by ProgramPath All output from SDC_Direct_Impacts is written to this file The precise contents of the output depend upon the reports requested by the user via SDC_Direct_Impacts_run_parameters txt Details of the output produced by each report are given under the relevant report heading in section 5 of Program Inputs above More complex output may best be viewed via a spreadsheet package For the purpose of importing to a spreadsheet package the program output should be regarded as space separated 22 FULL DESCRIPTIONS OF TABULAR AND CELLULAR MEASURE
25. gates sample size should reflect that used in Create Aggregates Report table mapping If set to 1 the output file SDC_Direct_Impacts_results txt located in the ProgramPath folder will contain a table mapping indicating for each table cell the number of other table cells on which its value depends This is useful for checking that table mappings have been properly declared If set to 0 table mappings will not be reported Use counts percentages O count 1 2 count amp A choice of whether assessment of disclosure control impact should be made for counts only 0 percentages only 1 or both counts and percentages 2 Note that options 1 and 2 require the user to supply percentage mappings see 8 below Strata source file If the sampling strata option has been set to 2 or 3 the name of the datafile upon which stratification by Create_Aggregates was based should be specified e g popdens fmt else leave set to the default None 5 b Report types The output from SDC_Direct_Impacts is written to the file SDC_Direct_Impacts_results txt located in the ProgramPath folder In addition to the cell based and table based measures chosen see c and d below the precise contents of this file depends upon the report type selected The basic report types available are outlined below For all report types a parameter value of 0 off 1 on 5b i Table Totals For some input tables the sum of
26. ide To get the most out of SDC_Direct_Impacts it will be necessary to read the full manual However the basic functionality of the program can be mastered will less effort 1 Download zipped executable version 2 Unzip package includes executable code default program parameters example benchmark data and copy of user manual 3 Double click on program to run to check program works on system run time c 2 4 mins 4 Examine files in folder SDCi Input Counts containing example pre and post perturbation counts use as template for formatting own input data Name each file using the convention lt table name gt _vn fmt where n 0 if pre perturbation of counts and n 1 for post perturbation variant e g UserTable_v0 fmt 5 Read pages 6 9 of manual explaining steps necessary for creation of table mappings 6 In the Parameters folder edit the file SDC_Direct_Impacts_Count_input_tables to list instead user supplied table s see pages 20 21 section 6 of user manual for details 7 Run program results of comparison will be placed in file SDC_Direct_Impacts_results txt 8 Change user parameters to request alternative summary measures as required and re run program see pages 9 20 of user manual for details Data Extraction User supplied or Data extraction process will be user specific but Penhmark data an account is provided of how SDC i compatible A set of pre and post benchmark cell counts were extracted fro
27. les fmt Stored in the RunParamters folder pointed to in Jnput_and_output_paths txt If the Use counts percentages option has been set to 1 or 2 in SDC_Direct_Impacts_run_parameters txt then this file is required as input The file should list files containing pre post perturbation table percentages to be used in assessment of disclosure control one pair of comparison tables per row of file For example The format for each comparison pair row in the file is lt table name gt lt original count variant gt lt perturbed count variant gt E g percentages 0 2 It is important that 1 the table name is in quotes 1i all items in the row are comma separated iii the table name supplied matches the table name used in the naming of input and map files see 1 2 and 3 above if in doubt SDC_Direct_Impacts will parse root table name s into full input filename s in precisely the same manner as for files containing count data as outlined for SDC_Direct_Impacts_Count_input_tables fmt above 8 lt percentage name gt map Located in the TableMappings folder If the Use counts percentages option has been set to 1 or 2 in SDC_Direct_Impacts_run_parameters txt then this file is required as input one map file per input file listed in SDC_Direct_Impacts_Percentage_input_tables txt This file describes the format of the associated percentage input file Just as for count data percentage data can be supplied in ta
28. m adjustment cell counts UK Census Perturb_v3 Creates perturbed variants of input cell counts Also offers calculation of user defined pre and post adjustment percentages derived from these counts Create_Aggregates_v2 Aggregates counts from multiple input areas to produce a series of new output zones clusters using one of a variety of sampling strategies SDC_Direct_Impacts_v11 Assesses the difference between two sets of input counts and or percentages using a wide variety of user selected measures SDC_Indirect_Impacts_v10 Measures the impact of disclosure control upon ecological analyses correlation and regression This module is currently unavailable for public use due to software licensing restrictions Figure 1 Linkage between SDC i modules SDC_Direct_Impacts SDC_Direct_Impacts measures the direct impact of disclosure control measures on tabular outputs A typical tabular output comprises both interior and marginal counts In this guide e A marginal is any table cell whose value prior to the application of disclosure control measures equals the sum of two or more counts present elsewhere in the same table e A count is any table cell that is not a marginal The main input to SDC_Direct_Impacts is a set of pre and post perturbation table counts and marginals and or percentages based upon these counts The main output is a set of statistics summarising the difference between the pre and post
29. measures of tabular fit SDC_Direct_Impact produces the following range of measures of tabular fit Table_frequency of cell type No of cells in a table of a given type see iii below Table_n_changed No of cells in table who s expected original and observed post disclosure control values differ Table_p_changed of cells in table who s expected and observed values differ Table_max_change Maximum difference change in pre and post disclosure control cell values 18 Table_maxPchange Maximum difference change in pre and post disclosure control cell values Table_TotalError Total Error difference between expected and observed counts summed across all table cells Table_TAE Total Absolute Error absolute difference between expected and observed counts summed across all table cells Table_RAE Relative Absolute Error TAE as of total value of changed cells Table SAE Standardised Absolute Error TAE sum of table cells table total Table_Sq_Error Total Square Error sum of square of difference between expected and observed cell values Table RMSE Square root of the average square error across all table cells Table_SSZ Sum of the square of the cell Z scores Table NFC No of Non Fitting Cells in table i e no of cells with Z score gt 1 96 i e no of cells for which difference between expected and observed values is greater than can be explained by chance at the 0 05 sig
30. ngs per table 30 A cell s type is defined by the number of counts upon which its original value depends Cell types is the number of unique cell types in an input table dataset including interior cell counts of type 1 Program Run time Increases with both the number of measures of fit requested and the number of pre post adjustment cell counts to be evaluated Using the default settings with the supplied benchmark data 11 410 cell counts program run time is 4 minutes on a Pentium IV 3GHz desktop PC with 0 5Gb RAM Execution speed will slow dramatically if adequate RAM is not provided PROGRAM INPUTS 1 Program pathnames a Program path If running SDC_Direct_Impacts direct from its compiled executable version the root folder Program path is automatically assigned as the folder in which the executable code is located If compiling and running SDC_Direct_Impacts via VisualBasic change the line of code ProgramPath C Temp Test SDCi to point to the folder a root folder of your own choice e g C Program Files SDCi Note that this pathname should NOT end with a slash Alternatively to compile and run the code as an executable comment out the above line of code and comment in the preceding line ProgramPath CurDir b Input_and_output_paths txt SDC_Direct_Impacts requires a number of data inputs To allow maximum flexibility users are able to specify the locations for four types of inpu
31. nificance level Table NFT Non fitting table 1 if table SSZ exceeds critical value at 0 05 significance level else 0 Table_SSZm Sum of the square of the cell modified Z scores see p 38 A for full explanation of Zm Table NFCm No of Non Fitting Cells in table i e no of cells with Z score gt 1 96 N B value of 1 96 is arbitrary as Zm has no known sampling distribution unless expected and observed table totals are the same Table _NFTm Non fitting table 1 if table SSZm exceeds SSZ critical value at 0 05 significance level else 0 SSZ has unknown sampling distribution unless expected and observed table totals are the same Table_Gibsons_D Gibson s D Table_Cramers_V Cramer s V Table_PearsonsR Pearsons Correlation Coefficient Table_ChiSquare Chi square Table_TVCC Total expected value of all cells for whom expected and observed values differ Table_v_expcells Sum of expected cell values Table_v_obscells Sum of observed cell values Sd ii Cross area five sample summary values are available 19 Table_Summary Max Maximum value of table based measure across all input areas Table Summary 97 5 tile 97 5 percentile value of table based measure across all input areas Table_Summary mean mean value of table based measure across all input areas Table Summary 2 5 tile 2 5 percentile value of table based measure across all input areas Table_Summary min Minimum value of table b
32. number of columns above example table with 1 row and 12 columns Description Row 2 first number flag to indicate whether following numbers give a mapping for a row or column marginal 1 row 2 column In this case total persons is a row marginal sum of counts in row so first number in row 2 of the table mapping is 1 Second row remaining numbers A flag is given for each column in the table reading from left to right as follows Flag Meaning 1 Column containing the row marginal being mapped gt 0 Column containing a count that contributes to the row marginal being mapped 0 Column containing a count that does NOT contribute to the row marginal being mapped When appropriate the same flags are used to record the contribution of each row to a column marginal reading from top to bottom In the above example the row marginal recorded in column 1 column 1 flagged with a 1 is the sum of columns 2 through 11 each column flagged by a positive number Column 12 is present only due to table concatenation and does not contribute to the calculation of the table marginal It is therefore flagged with a 0 Example 3 Table with dependent column and row marginals Sex Ethnic group Persons and Total Black Black Black Other groups born in Age Persons White C bean African other Indian P stani B deshi Chinese Asian Other Ireland Total Pe
33. on off Ta Table_v_obscells on off wy Table_Summary Max on off Te Table_Summary 95 tile on off u Table_Summary mean on off ar Table_Summary 5 tile on off Hi Table_Summary min on off W Note 1 For all on off switches 1 on any other number off 10 5 a Information on input counts Data source Create_Aggregates User For user supplied inputs set option to User If the program Create Aggregates has been used to create the input files of perturbed unperturbed counts set to Create_Aggreagtes No of samples No of input areas i e no of areas for which data are supplied via the input files described in 1 and 2 above Sampling strata 1 All 2 P20 P80 3 All P20 P80 If the data source is User then sampling strata may be set to any whole number as the actual value chosen will have no impact on program operation if the source is Create Aggregates strata selection should reflect that previously used in Create_Aggregates Sample type If the data source is User then sample type should be set to any whole number as the actual value chosen will have no impact on program operation if the source is Create Aggregates sample type should reflect that used in Create Aggregates Sample size If the data source is User then sample type should be set to any whole number as the actual value chosen will have no impact on program operation if the source is Create Aggre
34. pecific Cross area Cell based on off Tg Table specific Cross area Table based on off y 0 Cross table Area specific Table based on off 0 Cross table Cross area Table based on off Mee cs Correct Rank on off We al Correct Class on off Ne Correct Neighbouring Class on off 1 Cell based measures of fit cell_exp on off W230 Cell_obs on off wO cell_changed on off 0 Cell_TE on off Ww 0 Cell_Z on off we 0 Cell_NFC on off We SO Cell_Z2m on off Wee o Cell_NFCm on off Ww 0 Cell_Summary Max on off mao Cell_Summary 95 tile on off 1 Cell_Summary mean on off Wo l Cell_Summary 5 tile on off 1 Cell_Summary min on off Moet Table based measures of fit Table_frequency of cell type on off Table_n_changed on off wy Table_p changed on off Table_max_change on off Me Table_maxPchange on off m Table Totalirror on off we Table_TAE on off Me Table_RAE on off Ty Table_SAE on off Wa Table_Sq_Error on off wi Table_RMSE on off ua Table_SSZ on off We Table_NFC on off wy Table_NFT on off wae Table_SSZm on off Wy Table _NFCm on off wa Table_NFTm on off ee Table_Gibsons_D on off Mie Table _Cramers_V on off s Table_PearsonsR on off Mi Table_ChiSquare on off We Table_TVCC on off my Table_v_expcells
35. rsons LS 94 4 0 0 3 0 0 12 0 2 gi 0 4 6 5 0 0 0 0 0 0 1 0 0 0 5 15 5 3 0 0 0 0 0 0 2 0 0 0 16 29 52 44 1 0 0 0 0 0 5 0 2 5 30 lt pa 42 36 2 0 0 3 0 0 1 0 0 0 Pa and 9 5 0 0 0 1 0 0 3 0 0 2 over In the above table the original total persons counts in each row and column are based upon the sum of various interior counts Additional information is required to map the contribution of table counts to each column and row table marginal In this case the appropriate table description would be NR Oo ors PRN 2 304 5 67 8 9 10 21 0 23000 Description Row 1 6 rows by 12 columns Description Row 2 Row mapping first number 1 column 1 is a row marginal 1 columns 2 through 11 sum to give total in column 1 values gt 0 12 column does not contribute to row marginal 0 Description Row 3 Column mapping first number 2 row 1 is a column marginal 1 rows 2 and 3 sum to give total in column 1 values gt 0 Example 4 Table with multiple dependent row and column table marginals This final example is based upon a complex table containing multiple totals and sub totals see next page Given that all table marginals are based on the sum of the relevant interior counts to be found in the body of the table this table requires mappings for one row marginal and six column marginals 28 11 1 12345 678 9 100 2 OST 3 4 gt 5 6 28 O 0 OP 0 0 OQ 08 Or 08 Oe 08 Or 0 0 08 20 0 0 O 0 2 Ob Ou 0s 08 FOC
36. sure control variant It is recommended but not essential that 0 is used to indicate files containing the original unperturbed counts E g User_supplied_table_v0 fmt Within each file it is recommended that counts are laid out in rows and tables as per the published version although supply of counts in vector format is also supported The counts including marginals should be space or comma separated no commas at ends of rows For example the table SAS Table 06 Ethnic group of Residents by Age and by Sex Enumeration District BYFAO1 Sex Ethnic group Persons and Total Black Black Black Other groups born in Age Persons White C bean African other Indian P stani B deshi Chinese Asian Other Ireland Total Persons 115 94 4 0 0 3 0 0 12 0 2 7 Males 54 45 1 0 0 0 0 0 6 0 2 1 Females 61 49 3 0 0 3 0 0 6 0 0 6 0 4 6 5 0 0 0 0 0 0 1 0 0 0 5 15 3 0 0 0 0 0 0 2 0 0 0 16 29 52 44 At 0 0 0 0 0 5 0 2 5 30 lt pa 42 36 2 0 0 3 0 0 1 0 0 0 Pa and 9 5 0 0 0 1 0 0 3 0 0 2 over would be represented in the file s06_v0 fmt as s06_v0_s1l fmt 115 94 4 0 0 3 0 0 12 0 2 7 54 45 1 0 0 0 0 0 6 0 2 A 61 49 3 0 0 3 0 0 6 0 0 6 6 5 0 0 0 0 0 0 al 0 0 0 5 3 0 0 0 0 0 0 2 0 0 0 52 44 ah 0 0 0 0 0 5 0 2 5 42 36 2 0 0 3 0 0 1 0 0 0 9 5 0 0 0 1 0 0 3 0 0 2 Or s06a_v0_s1 fmt 115 694 4 lt 0 0 3 O 20 22 0 2 9 54 45 i Ose HO o 602 Oe 805
37. t data InputCounts Pre and post adjustment cell counts to be compared TableMappings Table mappings describing layout of each input table required StrataData Data to be used for creation of stratified samples optional RunParameters Files containing program run time parameters required The file input_and_output_paths txt lists these input output sources each followed by a pathname defined relative to the program execution root folder pointing to the relevant user specified folder StrataDataPath Strata Data TableMappingsPath Table mappings RunParametersPath Parameters InputCountsPath SDCi Input Counts Note that if modifying the default settings above the quote marks comma and the first and final backward slash at the start and end of each pathname should all be retained 2 Pre perturbation counts Stored in the nputCounts folder pointed to in Input_and_output_paths txt One file per table containing the original table counts prior to the application of statistical disclosure control for 1 1000 areas samples A sample 1 or more areas previously selected at random and aggregated if appropriate from a larger set of user supplied areas These files may be supplied by the user or produced using Create Aggregates Files supplied directly by the user should use the following naming convention lt table name gt _vn fmt where n is any user specified number indicating a particular disclo
38. ted above and once in a stand alone section as illustrated below Cross table Cross area Table based report mean Cell type no of contributing cells Measure Distrib Marginal Internal All 1 2 3 10 20 frequency Count 16 32 48 32 11 2 A 1 n_changed Mean 14 400000 26 000000 40 400000 26 000000 10 000000 1 800000 1 600000 1 000000 p_changed Mean 90 000000 81 250000 84 166667 81 250000 90 909091 90 000000 80 000000 100 000000 Sb viii Correct Rank If this flag is switched on and use counts percentages lt gt 0 a report is generated indicating the extent to which the ranking of input areas by observed post disclosure control percentages matches the ranking of input areas by expected original percentages The process of ranking and assessment of correct rank is repeated for each percentage identified via percentage mapping see 8 below An example of the output produced for two percentages only follows Subsequent percentages would appear as additional columns in the output To aid readability the example output below has been edited to ensure column alignment The raw space separated output is best viewed particularly when many percentages are involved via a spreadsheet Correct Rank percentages pltill pltiti pItrir punemp punemp punemp CorrectRank Samples _correct CorrectRank Samples _correct 6 10 60 00 10 10 100 00 15 In SDC_Direct_Impacts Samples is synonymous with input areas Hence the a
39. the distribution of user requested table based measures across all input areas samples on a table by table basis For example the user might require the mean maximum and minimum across all user supplied input areas of the number and percentage of cells changed within each user supplied input table as a result of disclosure control Table specific Cross area Table based report user requested s71 Cell type no of contributing cells Measure Distrib Marginal Internal All i 3 n_changed Maximum 2 000000 8 000000 10 000000 8 000000 2 000000 n_changed Mean 1 800000 7 000000 8 800000 7 000000 1 800000 n_changed Minimum 1 000000 6 000000 8 000000 6 000000 1 000000 p_changed Maximum 100 000000 80 000000 63333333 80 000000 100 000000 p_changed Mean 90 000000 70 000000 73 333333 70 000000 90 000000 p_changed Minimum 50 000000 60 000000 66 666667 60 000000 50 000000 Note that as for table specific area specific table based reports see 5b iii above each table is considered as comprising a number of versions each based on aggregations of cells of the same type A separate column is produced for each table cell type The full range of tabular measures and distributional summary statistics available are set out below see section 5 d below headed Table based measures If multiple distributional measures are requested including the mean the report output will include report the mean twice once in conjunction
40. ue of V represents only an approximate measure of fit PearsonsR 7 O On Ei Em 2 O On Z E En for i 1 ton where On O n and En E n i IfFE Oi On 0 or X O O 0 setr 0 ii If number of cells in table 1 r 9 undefined ChiSquare 7 O E E fori 1 ton TVCC TVCC for all i where E lt gt O v_expcells XZ x E for i 1 ton v_obscells XO x O for i 1 ton 3 Cross table measures for count data In definitions given in this section amp X sum indicated measure X across all input tables N_changed x NC P_changed XNC in Max_change Maximum MNC MaxPchange Maximum MPC TotalError TE TAE TAE 25 RAE 100 TAE X TVCC SAE TAE Ei for i 1 to n SqError LE RMSE x RMSE SSZ x SSZ NFC NFC NFT x NFT SSZm x SSZm NFCm x NFCm NFTm x NFTm GibsonsD As for tabular measure but for i 1 to n Cramers_V V T where T no of tables an approximation required because min 7 1 c 1 is a meaningless concept across multiple tables PearsonsR As for tabular measure but for i 1 to n ChiSquare Ly df n TVCC x TVCC v_expcells As for tabular measure but for i 1 to n v_obscells As for tabular measure but for i 1 to n 4 Measures for use with percentages The following measures of fit are inappropriate for use with percentage data Cellular Z NFC Zm NFCm Tabular SSZ NFC NFT SSZm
41. und 4 Percentile 60 class 3 lLower bound 5 Upper bound 6 Percentile 80 class 4 lLower bound 7 Upper bound 8 Percentile 100 class 5 lLower bound 9 Upper bound 10 Correct Class 5 quantiles percentages Percentage pltill pltill pltill punemp punemp punemp Class Correct_Class no _in_class _Correct Correct_Class no _in_class _Correct 1 1 2 50 00 2 2 100 00 2 0 2 0 00 2 2 100 00 3 1 2 50 00 2 2 100 00 4 2 2 100 00 2 2 100 00 5 2 2 100 00 2 2 100 00 All Correct_Class no _in_sample _Correct Correct_Class no _in_sample _Correct classes 6 10 60 00 10 10 100 00 Quantile boundaries 10 classes percentages Percentile 10 class 1 Lower bound 1 Upper bound 1 Percentile 20 class 2 Lower bound 2 Upper bound 2 Percentile 30 class 3 Lower bound 3 Upper bound 3 Percentile 40 class 4 Lower bound 4 Upper bound 4 Percentile 50 class 5 Lower bound 5 Upper bound 5 Percentile 60 class 6 Lower bound 6 Upper bound 6 Percentile 70 class 7 Lower bound 7 Upper bound 2 Percentile 80 class 8 Lower bound 8 Upper bound 8 Percentile 90 class 9 Lower bound 9 Upper bound 9 Percentile 100 class 10 Lower bound 10 Upper bound 10 Ets The report Correct Class appears between any table specific and cross table reports requested 16 5b x Correct Neighbouring Class If this flag is switched on and use counts percentages lt gt 0 the number of areas placed into the same or an adjacent pre
42. user supplied input tables Summary and tabular measures reported are specified by the user A full list of the tabular and summary measures available is listed below 5d i The report output format follows that of table specific area specific table based reports Sb iii with a separate output column for each table cell type For example Cross table Cross area Table based report user requested Cell type no of contributing cells Measure Distrib Marginal Internal All 1 2 3 10 20 frequency Count 16 32 48 32 11 2 2 q n_changed Maximum 16 000000 28 000000 42 000000 28 000000 11 000000 2 000000 2 000000 1 000000 n_changed Mean 14 400000 26 000000 40 400000 26 000000 10 000000 1 800000 1 600000 1 000000 n_changed Minimum 13 000000 24 000000 38 000000 24 000000 9 000000 1 000000 0 000000 1 000000 p_changed Maximum 100 000000 87 500000 87 500000 87 500000 100 000000 100 000000 100 000000 100 000000 p_changed Mean 90 000000 81 250000 84 166667 81 250000 90 909091 90 000000 80 000000 100 000000 p_changed Minimum 81 250000 75 000000 79 166667 75 000000 81 818182 50 000000 0 000000 100 000000 reports the mean maximum and minimum across all user supplied areas and tables of the number and percentage of table cells changed by disclosure control If multiple distributional measures are requested including the mean the report output will include report the mean twice once in conjunction with the other requested measures as illustra
43. w in the section 5 d headed table based measures For example if the number of cells changed by disclosure control n_ changed is requested the resulting output would look like Table specific Area specific Table based report for s06a Cell type no of contributing cells count depends upon Sample Measure Marginal Internal All J 2 10 20 1 n_changed 14 000000 17 000000 31 000000 17 000000 11 000000 2 000000 1 000000 2 n_changed 13 000000 20 000000 33 000000 20 000000 10 000000 2 000000 1 000000 3 n_changed 11 000000 20 000000 31 000000 20 000000 10 000000 0 000000 1 000000 4 n_changed 12 000000 20 000000 32 000000 20 000000 9 000000 2 000000 1 000000 5 n_changed 13 000000 19 000000 32 000000 19 000000 10 000000 2 000000 1 000000 12 Each input area sample is represented by a row whilst each cell type is represented by a column Cell type no of cells on which a cell s value depends Please note that the column headed cell type 1 is the direct equivalent of the column headed internal If two measures of tabular fit are requested no and of table cells changed by disclosure control the output will look like Table specific Area specific Table based report for s06a Cell type no of contributing cells count depends upon Sample Measure Marginal Internal All 1 2 10 20 1 n_changed 14 000000 17 000000 31 000000 17 000000 11 000000 2 000000 1 000000 1 p_changed 100 000000 77 272727 86 111111
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