Why a Small "n"

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Why a Small "n" is Surrounded by
Confidentiality Ensuring Confidentiality and
Reliability in Microdatabases and Summary Tables.
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Glynn D. Ligon Barbara S. Clements Vicente
Paredes Evaluation Software Publishing,
Incorporated Austin, Texas
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There are two angles.
1. Control access to databases, and protect the
identity of individuals in databases extracted
for others.
2. Avoid reporting a statistic that can be
linked to an individual.
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00000000000001000000000000000000000000000000000000
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Problem 1 An individual is identified in the
database.
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There are two angles.
1. Control access to databases, and protect the
identity of individuals in databases extracted
for others.
2. Avoid reporting a statistic that can be
linked to an individual.
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Data Problem 176993445
Small Cell Size
An individuals data are captured by the
report. An individual is the only one in a
group.
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Data Problem n
The n Crowd
Internal disclosure to people in the
know. Someone with additional information can
identify individuals.
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Data Problem X
X-ternal Disclosure
External disclosure to people with good math
skills. Using marginal totals, individual cell
values can be calculated.
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Bad News
Data Problems 100 0
Good News
100 are Low Income.
0 are Low Income!
All or None Make the Grade.
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Typical PR Decision...
Bad News is
Good News is
Confidential!
NEWS!
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Data Problem mm
m
Mean
Minimum
m
Median
Maximum
Mean or Median Equals Min or Max. When the mean
or median equals the minimum or maximum value,
then all values in the cell are the same.
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Data Problem 6
Reliability (p) is based upon frequency (n) and
standard deviation.
Small Inns
1
2
2
3
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WELCOME TO MOTEL 6
OFFICE
Reliability of the data is low.
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Natural Persons
Most Organizations All personal data typically
protected
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Name
Natural Persons
Test Scores
School Location
Handicapping Conditions
Family Income
Public Education Some personal data protected
Salary
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Most Organizations All unit data typically
protected
Collective Units
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Public Education Almost no unit data protected
Collective Units
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Perturbing the Data
Statisticians change data to mask identities but
maintain statistical integrity.
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Perturbing the Data
ROUNDING
3 5
NOISE False data added.
1 0
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Data Swapping

• Any frequency of 1 combines with a frequency of
  2.
• If 3 frequencies of 1, the central cell is set to
  3, others set to 0.
• Any frequency of 1 combines with the greatest
  frequency.
• 1 is subtracted from the greatest frequency and
  added to any frequency of 2.
• A frequency of 2 is split up.

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What if our text says, Every gender and ethnic
group was represented in the awards!
Data swapping creates a dilemma.
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Suppressing the Data

• Any frequency less than 3 is suppressed.
• Complementary cells for any suppressed are
  suppressed.
• Complementary tables are masked.
• Whole tables are suppressed.

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What if our text says, Every gender and ethnic
group was represented in the awards!
Suppression creates mysteries.
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What do we call a cell that has been suppressed?
Quell
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Glynn D. Ligon Barbara S. Clements Vicente
Paredes Evaluation Software Publishing,
Incorporated 1510 West 34th Street Suite
200 Austin, Texas 78703 512-458-8364 Fax
512-371-0520 gligon_at_evalsoft.com www.evalsoft.com