# Controlled rounding

Rounding is performed independently on each cell (including subtotals or grand total). See Step 3 below. Here is a simple example of how rounding is performed:

Suppose we have a survey of 10 people representing a population of 1,205 and let 100 be the rounding base used by the RTRA.

## Microdata

Table 1
Controlled rounding using sex and marital status
Unit Sex Marital status Weight
(pounds)
1 Male Married 120.5
2 Male Widowed 120.5
3 Male Married 120.5
4 Male Divorced 120.5
5 Male Married 120.5
6 Female Married 120.5
7 Female Married 120.5
8 Female Widowed 120.5
9 Female Widowed 120.5
10 Female Married 120.5

## Step 1

The RTRA modified SAS procedure creates the following table:

Table 2
Controlled rounding using sex and marital status
Married Divorced Widowed Total
Male 361.5 120.5 120.5 602.5
Female 361.5 0.0 241.0 602.5
Total 723.0 120.5 361.5 1,205.0

## Step 2

The RTRA system applies conventional rounding to the inner cells, and then sums up totals and subtotals.

Table 3
Controlled rounding using sex and marital status
Married Divorced Widowed Total
Male 362 121 121 603
Female 362 0 241 603
Total 724 121 362 1,207

## Step 3

The RTRA system sends these counts into the controlled random rounding program. We obtain the following:

Table 4
Controlled rounding using sex and marital status1
Married Divorced Widowed Total
Male 400 100 100 600
Female 300 0 300 600
Total 700 100 400 1,200

Note that lines and columns are additives. This last table is then sent to the researcher.

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