Populations, Sampling Methods, and Representativeness

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sampling populations generalizability representativeness

Core Idea

The population is the full set to which inferences are desired; the sample is the subset studied. Probability sampling (random, stratified, systematic) provides known inclusion probabilities and supports statistical inference. Non-probability sampling (convenience, purposive) sacrifices representativeness but is practical. Sample representativeness on key variables enhances generalizability; bias in sampling limits it.

How It's Best Learned

Specify a research population and design probability and non-probability sampling schemes. Evaluate how different sampling methods affect validity and generalizability. Calculate what percentage of a population you've sampled.

Common Misconceptions

Explainer

Every empirical study begins with a fundamental question: who are we studying, and who do we want our conclusions to apply to? The population is the full set of individuals, events, or observations to which you want to generalize. The sample is the subset you actually study. The relationship between them — and how that relationship was constructed — determines the generalizability of everything you conclude.

Probability sampling methods give each member of the population a known, nonzero probability of being selected. Simple random sampling is the foundation: every individual has an equal chance of selection, which allows you to use standard inferential statistics — sampling distributions, confidence intervals, and significance tests — in their textbook form, because the theoretical assumptions underlying those tools require random selection. Stratified sampling divides the population into subgroups (strata such as age, gender, or region) and samples randomly within each, ensuring proportional representation of key variables even with moderate sample sizes. Systematic sampling selects every kth person from an ordered list — practical when a list exists and the ordering is unrelated to the outcome. All probability methods share a crucial property: selection is governed by chance, not judgment, so sample estimates are unbiased estimates of population parameters.

Non-probability sampling includes convenience samples (whomever is available and willing), purposive samples (selected for specific characteristics), and snowball samples (participants recruit others from their networks). These are common in psychology — undergraduate participant pools, clinic populations, online panels — and they are not inherently invalid. But they require honesty about generalizability limits. A convenience sample of university students may generalize well to similar populations but poorly to older adults, rural communities, non-Western cultures, or people with limited education. The now-famous WEIRD critique (Western, Educated, Industrialized, Rich, Democratic) of psychology's participant base is fundamentally a sampling argument: if most published research draws from a narrow slice of humanity, conclusions cannot be claimed to describe universal human psychology.

The most important misconception to overcome is confusing large sample size with representativeness. A famous historical example: the Literary Digest predicted a landslide win for Alf Landon in the 1936 US presidential election based on a survey of 10 million people — one of the largest polls ever conducted. Franklin Roosevelt won by the largest Electoral College margin in over a century. The poll failed not because it was too small but because it drew from telephone directories and car registration lists, systematically oversampling wealthy, Republican-leaning voters. Representativeness is a question of *who* is selected and how, not how many. A well-drawn random sample of 1,000 routinely outperforms a convenience sample of 1,000,000 for accurate population inference.

Practice Questions 5 questions

Prerequisite Chain

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsCombining Like TermsOne-Step EquationsTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIndefinite IntegralsBasic Integration RulesRiemann SumsDefinite Integral DefinitionProbability Density Functions and Continuous DistributionsCumulative Distribution FunctionsContinuous Random VariablesNormal DistributionCentral Limit TheoremConfidence Intervals for MeansZ-Tests and T-Tests for MeansOne-Sample Z-Test for MeansOne-Sample and Two-Sample T-TestsInferential Statistics in PsychologyEffect Size and Statistical PowerSample Size Determination in Research PlanningLiterature Review and Research SynthesisHypothesis Construction: Directional and Nondirectional PredictionsOperationalizing Independent and Dependent VariablesConstruct Definition and Measurement DevelopmentConstruct Validity and Measurement ValidityConstruct Validity and Operationalization of Psychological ConstructsVariables: Definition, Operationalization, and MeasurementSelecting and Matching Research Designs to QuestionsPopulations, Sampling Methods, and Representativeness

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