# Sampling Error and bias Sampling definitions Sampling universe

Sampling : Error and bias

Sampling definitions Ø Ø Ø Ø Sampling universe Sampling frame Sampling unit Basic sampling unit or elementary unit Sampling fraction Respondent Survey subject Unit of analysis

Sampling types Two basic categories of sampling Ø Probability sampling • Also called formal sampling or random sampling Ø Non-probability sampling • Also called informal sampling

Probability sampling What is probability sampling? A selection of elements in a population, such that every element has a known, non-zero probability of being selected.

Types of probability sampling Ø Ø Ø Simple random sampling (SRS) Systematic random sampling Stratified sampling Cluster sampling Multi-stage sampling

Questions for sampling design Ø Presampling choices • What is the nature of the study: exploratory, descriptive, analytical? • What are the outcomes of interest? • What are the target populations? • Do you want estimates for subpopulations or just for the entire population? • How will the data be collected? • Is sampling necessary and appropriate?

Questions for sampling design Ø Sampling choices • What listing will be used as the sampling frame? • What is the desired precision? • What type of samping will be done? • Will the probability of selection be equal or unequal? • What is the sample size?

Questions for sampling design Ø Postsampling choices • How can the effect of nonresponse be assessed? • Is weighted analysis necessary? • What are the confidence limits for the major estimates?

But… Result from survey is never exactly the same as the actual value in the population WHY?

Components of total error Point estimate from survey 40% True population value 50% Total error Prevalence 0% 100% Nonsampling bias Sampling error Sampling bias

Nonsampling bias ØIs present even if sampling and analysis done correctly ØWould still be present if survey measured outcome in ENTIRE sampling frame In sum, you have either sampled the wrong people or screwed up your measurements!

Nonsampling bias Ø Types: • Sampling frame is not equal to population to which you want to generalize (sampling universe) • • • Sampling frame out of date Non-response among sampling units in sampling frame Measurement error • • • Tape incorrectly fixed to height board Scale consistently reads low by 0. 5 kg Failure to remove heavy clothing before weighing Misleading questions Recall bias

Nonsampling bias Source of bias Sampling frame out of date Prevention or cure Use current sampling frame Limit generalizations Non-response Minimize non-response Use various statistical methods to weight data Measurement error Standardize instruments Write clear & simple questions Train survey workers Supervise survey workers

Sampling bias Selection of nonrepresentative sample, i. e. , the likelihood of selection not equal for each sampling unit Ø Failure to weight analysis of unequal probability sample Ø In sum, you have not sampled people with equal probability and you have not accounted for this in your analysis!

Sampling bias Ø Examples • Nonrepresentative sample Selecting youngest child in household • Choosing households close to the road • Using a different sampling fraction in different provinces Failure to do statistical weighting • •

Sampling bias Source of bias Nonrepresentative sampling Prevention or cure ALWAYS ask yourself "Will this choice enhance representativeness or reduce it"? Calculate the probabilities of selection Failure to do weighting Apply appropriate statistical weights if selection probabilities unequal

Sampling error Difference between survey result and population value due to random selection of sample Ø Influenced by: • Sample size • Sampling scheme Ø Unlike nonsampling bias and sampling bias, it can be predicted, calculated, and accounted for.

Sampling error Measures of sampling error: • Confidence limits • Standard error • Coefficient of variance • P values • Others Ø Use these measures to: • Calculate sample size prior to sampling • Determine how sure we are of result after analysis Ø

Bias and sampling error Nonsampling bias Bias Sampling bias Sampling error

In sum… Bias Ø Includes nonsampling bias and sampling bias Ø Is due to mistakes which can be avoided Ø Cannot be precisely measured Ø Control and prevention requires careful attention Sampling error Ø Is unavoidable if sampling < 100% of population Ø Can be controlled by selecting appropriate sample size and sampling method Ø Can be precisely calculated after-the-fact

Essential concepts Bias & Accuracy Sampling error & Precision

Accuracy What is accuracy? The degree to which a measurement, or an estimate based on measurements, represents the true value of the attribute that is being measured. Last. A Dictionary of Epidemiology. 1988 In short, obtaining results close to the TRUTH.

Accuracy Associated terms: Ø Validity

Precision What is precision? Precision in epidemiologic measurements corresponds to the reduction of random error. Rothman. Modern Epidemiology. 1986. In short, obtaining similar results with repeated measurement

Precision Associated terms: Ø Reliability Ø Reproducability

Accuracy vs. precision Accuracy: obtaining results close to truth Survey 1 Survey 2 Survey 3 Real population value

Accuracy vs. precision Precision: obtaining similar results with repeated measurement (may or may not be accurate)

Accuracy vs. precision Poor precision (from small sample size) with reasonable accuracy (without bias):

Accuracy vs. precision Good precision (from small sample size) with reasonable accuracy (without bias):

Accuracy vs. precision Good precision (from large sample size), but with poor accuracy (with bias):

In sum… Ø Sampling error • • • Ø Difference between survey result and population value due to random selection of sample Greater with smaller sample sizes Induces lack of precision Bias • • Difference between survey result and population value due to error in measurement, selection of non-representative sample or other factors Due to factors other than sample size Therefore, a large sample size cannot guarantee absence of bias Induces lack of accuracy, even with good precision

Usual situation after a survey Result of single survey 95% confidence limits

Usual situation after a survey Result of single survey 95% confidence limits

Usual situation after a survey Result of single survey 95% confidence limits

Usual situation after a survey Ø How can you tell which situation you have? Result of single survey 95% confidence limits

Precision, bias, and sample size Precision vs. bias Ø Larger sample size increases precision • It does NOT guarantee absence of bias • Bias may result in very incorrect estimate • If little sampling error, may have confidence in this wrong estimate Ø Quality control is more difficult the larger the sample size Ø Therefore, you may be better off with smaller sample size, less precision, but much less bias.

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