Analysis of survey results - United Nations Office on ... · Analysis of survey results Estimation,...
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Statistics Divisionhttp://www.unescap.org/our-work/statistics
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
Statistics Divisionhttp://www.unescap.org/our-work/statistics
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
Statistics Divisionhttp://www.unescap.org/our-work/statistics
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
Statistics Divisionhttp://www.unescap.org/our-work/statistics
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
Statistics Divisionhttp://www.unescap.org/our-work/statistics
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
Statistics Divisionhttp://www.unescap.org/our-work/statistics
What is a survey weight? (cont)
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%
Statistics Divisionhttp://www.unescap.org/our-work/statistics
What is a survey weight? (cont)
• 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%
Statistics Divisionhttp://www.unescap.org/our-work/statistics
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
Statistics Divisionhttp://www.unescap.org/our-work/statistics
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%
Statistics Divisionhttp://www.unescap.org/our-work/statistics
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
Statistics Divisionhttp://www.unescap.org/our-work/statistics
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
Statistics Divisionhttp://www.unescap.org/our-work/statistics
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