Sampling Design, Sample Size, and Their Importance
Sampling Design, Sample Size, and Their Importance Prof. Bhisma Murti, dr, MPH, MSc, PhD Institute of Health Economic and Policy Studies (IHEPS), Department of Public Health, Faculty of Medicine, Universitas Sebelas Maret Types of Population • • • • Target population is the population a researcher wants to make inference about Source population (accessible population) is a subset of the target population that is accessible to the researcher, from which the samples are drawn. Study sample is a group of subjects chosen from the source population for study to represent the target population External population is the population larger than the target population that the researcher may still want to generalize results Target population Internal Validity External population Source population Sampling Statistical inference Sample External Validity Internal Validity and External Validity • Internal validity refers to the extent to which the sample estimate reflects the true value of the association/ effect under study in the target population • External validity refers to the Internal Validity extent to which the sample estimate is generalizable to the (larger) external population. The internal validity is a prerequisite for the external validity Target population External population Source population Sampling Statistical inference Sample External Validity What is Sampling and Why • Sampling is the selection of a subset of individuals from within a population to estimate characteristics of the whole population, e.g. – Prevalence of tuberculosis – The relationship between smoking and the risk of stroke • Researchers rarely study the entire population because the cost of a census is too high. Properties of a Good Research • • • A good research is one that makes a valid, precise, and consistent estimate of characteristics or difference/ association/ effect of variables under study in the population The validity of a study is inversely related to the degree of systematic error. The precision and consistency of an estimate are inversely related to the degree of random error Validity Validity Systematic Error • A systematic error or bias occurs when there is a deviation between the true value (in the target population) and the observed value (in the study sample) • A systematic error results from an error in the selection of sample (selection bias), faulty measurement of variables (information bias), and/ or mixed effect by a third variable (confounding factor) Random Error • Random error occurs due to random variation in sampling and/ or measurement of variables • Random error is always present in a measurement. It is caused by inherently unpredictable fluctuations in measuring the variables under study. • The distribution of random errors follows a Gaussian-shape "bell" curve. They are scattered about the true value, and tend to have null value when a measurement is repeated several times with the same instrument. • Therefore increasing sample size can reduce random error. Systematic Error The observed values of the characteristics in the sample Per Cent 14 12 10 The true values of the characteristics in the target population 8 6 4 2 0 0 5 10 15 20 Size of induration, mm 25 30 Random Error The true values of the characteristics in the target population Per Cent 14 12 10 The observed values of the characteristics in the sample 8 6 4 2 0 0 5 10 15 20 25 Size of induration, mm 30 35 Why is Sampling Design Important? • Incorrect selection of a sample leads to bias estimate of a study • Analysis of data from a sample that is biased or unrepresentative to population will result in wrong conclusion about the characteristics of the population Why is Sample Size Important? • Choosing a sample size that is too small may not give a statistically significant conclusion nor precise estimate about difference/ relationship/ effect of the variables under study • Too large a sample size is wasteful and sometimes impossible to complete. Valid, Not valid, Valid, Not valid, Sample Size, Systematic Error, and Random Error • The larger sample size, the smaller random error • But sample size does not affect systematic error Systematic error, • Larger sample size does random error not reduce systematic error • Systematic error is more serious than random error, as it cannot be corrected by increasing sample size Random error Systematic error Sample size Sample Size and Random Error (Sampling Error, Margin of Error) Larger sample size reduces random variation, therefore increases precision Sampling Design • Random sampling: – Simple random sampling – Stratified random sampling – Cluster random sampling • Non-random sampling: A. Convenient sampling B. Purposive (judgmental ) sampling: • • Fixed disease sampling Fixed exposure sampling etc. Types of Random Sampling • Random sampling is a sampling method in which all member of a population (universe) have a known and independent chance of being selected. • Simple random sampling is a sampling method in which all member of a population have an equal chance of being selected. • Stratified random sampling selects independent samples at random from subpopulations, groups or strata within the population. • Cluster (random) sampling selects the sample units at random in groups (called cluster, eg. neighborhood). Choose groups (cluster) at random Study all members of the groups selected Types of Non-Random Sampling • Purposive sampling uses expert judgment to select a sample that adequately represents the target population on factors that might influence the population: e.g. socio-economic status, intelligence, access to education, environmental factors, etc. • Convenience sampling is a nonprobability sampling technique where subjects are selected because of their convenient accessibility and proximity to the researcher. This sampling design is poor, it very unlikely gives a representative sample Fixed Exposure Sampling and Fixed Disease Sampling • • Fixed exposure sampling selects a fixed number of subjects from each exposure category (exposed and nonexposed groups). This design is primary used in a cohort study, but can also be used in a cross-sectional study Fixed disease sampling select a fixed number of subjects from each disease category (case and control groups). This design is primary used in a case control study, but can also be used in a cross-sectional study. Since cases are rare, it will be efficient to include all available cases for the study, while subjects in the control group can be selected at random from the available non-diaseased population Minimum Sample Size Formulas • Formula for Testing/ Estimating One Population: 1. Mean 2. Proportion 3. Correlation coefficient • Formula for Testing/ Estimating Two Populations: 1. Difference in Two (or More) Population Means 2. Difference in Two (or More) Population Proportion Examples of Sample Size Formula • Sample size for a study that tests proportion difference between two (or more) populations: Z n 1α/2 2 P 1 P Z1β P1 1 P1 P2 1 P2 P P 2 2 1 2 • Sample size for a study that tests mean difference between two (or more) populations: n 2σ 2 Z 1α/2 Z1β μ1 μ 2 2 2 Determinants of a Sample Size Estimation • Minimum sample size calculated by any formula is only a statistical estimate. It is dependent on the researcher’s choice of acceptable random error and on findings from previous studies. Time, cost, and ethics should also be considered. • The researcher’s choice of acceptable random error: 1. 2. 3. Tipe I error (α). Arbritary, but conventional choice: α= 0.05 Type 2 Error (β) or statistical power (1- β). Arbritary, but conventional choice: β = 0.20 Degree of precision or margin of error (e.g. +/- 5%) • Findings from previous or preliminary studies: 1. 2. 3. Difference in population means and their variances Difference in population proportions Correlation coeficient from one population Using Statistical Program to Calculate Minimum Sample Size Use of OpenEpi to calculate sample size Final Words: Important Reminder • The sample should be selected by correct (unbiased) sampling design so that it accurately represents the population. Incorrect sampling design will cause systematic error, which leads to an estimate of the characteristics or the association/ effect of variables in the population that is not valid. • The sample size should be large enough to achieve statistically significant results (i.e. consistency) and precise estimate. Small sample size will increase random error, therefore will cause non-statistically significant and imprecise results.
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