Analysis of survey results - United Nations Office on ... · Analysis of survey results Estimation, Weighting & Non-response “Training Course on Victimization Surveys” for Asia-Pacific,

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Analysis of survey results

Estimation, Weighting & Non-response

“Training Course on Victimization Surveys” for Asia-Pacific, 29 May - 2 June 2017

Chris Ryan

Statistics Division, ESCAP


Overview of Presentation

• What is a survey estimate

• What is a survey weight, and how to

calculate a survey weight

• Different basic estimation formula

• Dealing with non-response


What is a survey estimate?

• When we run a survey and base the results on

just a sample of the population, the results

are referred to as “estimates”

• Why? We don’t know the true value,

because we took just a sample of the

population


What is a survey weight?

• Survey weights help the results of the sample

represent the population

• Lets look at how this works with an example

Example

• Population (N) = 1,000 people

• Sample (n) = 50 people

• We want to estimate how many people in the

population of 1,000 were victims of an assault in the

last year, by asking the 50 people in the sample


What is a survey weight? (cont)

• Based on the 50 people in the sample survey, 12 reported they were a victim of an assault in the last year

• The question now is “how many of the 1,000 people in the

population do we estimate were victims?”

• Each person in the sample represents (N/n) people in the

population = (1,000/50) = 20 = weight

• We thus estimate the number of people in the population who

was a victim = wt * # cases of assault in the sample

= 20 * 12

= 240



Important Note

The survey weight is the inverse of the sample fraction

That means, if the survey weight = 20

Then

The sample fraction = 1/20 = 5%



• What happens if we want to simply report what

“proportion” of people in the population were victims

of an assault in the last year?

• The weight in this example is no longer important

because:

(12/50) = (240/1,000) = 24%


Sample surveys with different weights

• What happens if we have two stratum, urban and rural,

and we take a different sample fraction from each?

Example

• Urban: N = 10,000 n = 250 wt = 10,000/250 = 40

• Rural: N = 10,000 n = 100 wt = 10,000/100 = 100

• In the urban population, 100 of the 250 people in

sample were victim of an assault

• In the rural population, 15 of the 100 people in sample

were victim of an assault


Sample surveys with different weights

If we ignore the weights

• The estimated proportion of people who were a victim

of an assault from the population is:

115/350 = 32.9%

If we don’t ignore the weights

• The estimated proportion of people who were a victim

of an assault from the population is:

[(100 * 40) + (15 * 100)] / (20,000) = 27.5%


Types of estimates required from the survey

Number of crimes

EG: What number of households in Country X,

experienced a burglary in the last 2 years?

𝑋 =𝑁

𝑛

𝑖=1

𝑛

𝑥𝑖

𝑋 =

ℎ=1

𝐻𝑁ℎ

𝑛ℎ

𝑖=1

𝑛ℎ

𝑥𝑖

1 stratum

More than 1 stratum

𝑥𝑖=1 if crime

0 if not


Types of estimates required from the survey

Proportion of crimes

What proportion of people were a victim of a

physical assault in the last 12 months?

1 stratum

More than 1 stratum

𝑥𝑖=1 if crime

0 if not

𝑃 =

𝑖=1

𝑛

𝑥𝑖 /𝑛

𝑃 =

ℎ=1

𝐻𝑁ℎ

𝑛ℎ

𝑖=1

𝑛ℎ

𝑥𝑖 /

ℎ=1

𝐻

𝑁ℎ


Dealing with non-response

• As already discussed earlier, not all units

(households/people) will respond to the

survey.

• We need to account for this in estimation

𝑋 =𝑁

𝑛

𝑖=1

𝑛

𝑥𝑖 𝑋 =𝑁

𝑛𝑟

𝑖=1

𝑛𝑟

𝑥𝑖

Documents

Analysis of survey results - United Nations Office on ... · Analysis of survey results Estimation, Weighting & Non-response “Training Course on Victimization Surveys” for Asia-Pacific,