Plausible values and Plausibility
Range
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Prevalence of FSWs in some west African
Countries
0.1%
4.3%
2
Plausible values
• In west African countries, prevalence of FSWs ranged 0.1% to
4.3%.
• Suppose you implement a study in another country in this
region, and get a prevalence of 10%.
• How plausible this figure is?
• Did you implement the study in high risk locations?
• What are the potential biases in your study (selection of
respondents, data collection, …)?
• What are the main cultural and socioeconomic differences
between this country and others?
3
Comparison of prevalence across risk
zones
• Suppose, we have stratified the country into low, intermediate
and high risk zones.
• We have selected one province from each zone.
• The prevalence in low zone was higher than that of high zone.
• How plausible it is?
• Have you implemented standard approach in all provinces?
• Have you trained the interviewers of the study?
• Have you used the right criteria to define the risk zones?
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Point Estimate vs. plausible range
• One of the aims of statistics is estimating population
parameters from sample statistics
• For example, in a randomly selected sample of prisoners, 25
out of 200 ones reports sharing of injection equipment
• Thus in the sample, 12.5% of the prisoners share injection
equipments
• This value of 12.5% is called a point estimate of the
population proportion
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Sampling Variation
• Point estimate is a value derived from one randomly selected
sample
• We use it as the best guess for the population parameter
• What would happen if we select another random sample?
• If you repeat the mapping or the NSU survey, do you expect to
get the same estimates?
• What is the impact of respondents, locations, and time …
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Construction of a Range
• It is preferred to report a range of possible values, instead of a
single point estimate
• It is conventional to create 95% range which means that 95% of
the time constructed range contains the true value of the
parameter of interest
• The width of the range provides some idea about uncertainty of
the unknown parameter
• A very wide interval may indicate that more data should be
collected before anything very definite can be said about the
parameter.
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Advantages of Reporting a Range
• A smaller confidence interval is always more desirable than a
larger one because it shows that the population parameter
can be estimated more accurately
• Point estimation gives us a particular value as an estimate of
the population parameter
• Interval estimation gives us a range of values which is likely to
contain the population parameter
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Interpretation of Range
• The upper and lower bounds of the interval give us
information on how big or small the true parameter might be
• Wide range indicates great uncertainty in the true value of the
parameter
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Different Names for Range
• Statistical terminology
– Confidence Interval
– Uncertainty Limit
– Credibility Interval
• Non-statistical terminology (in this course)
– Plausibility Range
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How to Construct Statistical Ranges?
• Standard Formulas Based on Normal approximation
• Monte Carlo
• Bootstrapping
– Works based on resampling with replacement from the original
sample
– Estimation of parameter of interest in each sample
– Use of 2.5 and 97.5 percentiles at lower and upper bounds
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Application of available formulas
• To estimate number of IDUs, capture-recapture study has
been implemented:
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How to Construct Non-Statistical
Ranges?
• In the following slides we introduce some approaches
followed by other researchers
• In addition, we introduce some other approaches based on
common sense
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Other Countries Experience
• Indonesia applied the following formula:
__
( X i  X )2
n 1
– x(i) =
estimated size in district (i)
__
–X
=
–n =
mean of district sizes
number of districts
• Probably they used this statistics as SE and applied normal
approximation theory
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Ad Hoc Methods (1)
• In other study, time-varying parameters were assigned
uncertainty bounds in the model up to ± 50% of the best
parameter estimates.
• Parameter estimates:50000
• 20%*50000=10000
• uncertainty bounds: 50000 ± 10000
• (40000, 60000)
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Ad Hoc Methods (2)
• Ask respondents to provide a range, instead of a single value
• For example, in NSU, ask respondents to count minimum and
maximum of FSWs they know
• Analysis lower bound data should provide the lower bound of
the plausibility range
• Analyzing the upper bound data should provide the upper
bound of the plausibility range
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