Sampling : Error and bias definitions

‹ Sampling universe ‹ Sampling frame ‹ Sampling unit ‹ Basic sampling unit or elementary unit ‹ Sampling fraction ‹ Respondent ‹ 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 ‹ ‹ ‹ 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 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

Point True estimate population from survey value 40% 50% Total error Prevalence 0% 100%

Nonsampling Sampling bias error Sampling bias 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Types: • Sampling frame is not equal to population to which you want to generalize (sampling universe) • Sampling frame out of date • Non-response among sampling units in sampling frame • Measurement error • Tape incorrectly fixed to height board • Scale consistently reads low by 0.5 kg •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Source of bias Prevention or cure Sampling frame out of date Use current sampling frame Limit generalizations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 ‹ 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 Prevention or cure Nonrepresentative sampling 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 ‹ 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 • • 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 Bias Sampling bias

Sampling error Sampling error In sum…

Bias Sampling error ‹ Includes nonsampling bias ‹ Is unavoidable if sampling and sampling bias < 100% of population ‹ Is due to mistakes which ‹ Can be controlled by can be avoided selecting appropriate ‹ Cannot be precisely sample size and sampling measured method ‹ Control and prevention ‹ Can be precisely requires careful attention 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 . 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 Result of single survey 95% confidence limits 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.