Sampling : Error and bias
Sampling definitions 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 Probability sampling Also called formal sampling or random sampling 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 Simple random sampling (SRS) Systematic random sampling Stratified sampling Cluster sampling Multi-stage sampling
Questions for sampling design 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 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 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 Prevalence Point estimate from survey 40% Total error True population value 50% 0% 100% Nonsampling bias Sampling bias Sampling error
Nonsampling bias Is present even if sampling and analysis done correctly Would 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 Types: Sampling frame is not equal to population to which you want to generalize (sampling universe) Sampling frame out of date Non-response among sampling units in sampling frame Measurement error Tape incorrectly fixed to height board Scale consistently reads low by 0.5 kg Failure to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Nonsampling bias Source of bias Sampling frame out of date Non-response Measurement error Prevention or cure Use current sampling frame Limit generalizations Minimize non-response Use various statistical methods to weight data 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 Failure to weight analysis of unequal probability sample In sum, you have not sampled people with equal probability and you have not accounted for this in your analysis!
Sampling bias 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 Failure to do weighting Prevention or cure ALWAYS ask yourself "Will this choice enhance representativeness or reduce it"? Calculate the probabilities of selection Apply appropriate statistical weights if selection probabilities unequal
Sampling error Difference between survey result and population value due to random selection of sample Influenced by: Sample size Sampling scheme 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 Use these measures to: Calculate sample size prior to sampling Determine how sure we are of result after analysis
Bias and sampling error Nonsampling bias Sampling bias Sampling error Bias Sampling error
In sum Bias Includes nonsampling bias and sampling bias Is due to mistakes which can be avoided Cannot be precisely measured Control and prevention requires careful attention Sampling error Is unavoidable if sampling < 100% of population Can be controlled by selecting appropriate sample size and sampling method 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: 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: Reliability 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 Sampling error 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 How can you tell which situation you have? Result of single survey 95% confidence limits Result of single survey 95% confidence limits
Precision, bias, and sample size Precision vs. bias 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 Quality control is more difficult the larger the sample size Therefore, you may be better off with smaller sample size, less precision, but much less bias.