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Triangulation: Convergent Validity and Method Confirmation

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triangulation convergence validity multiple-methods

Core Idea

Triangulation uses multiple methods, data sources, or investigators to examine questions from different angles. Convergent findings increase confidence; divergence prompts investigation. Divergence often proves more informative than convergence.

Explainer

From your mixed-methods work, you know that each individual method carries its own vulnerabilities — surveys may suffer from social desirability bias, interviews from recall error, administrative records from bureaucratic categorization artifacts. Triangulation is the strategy of using multiple methods so that the weaknesses of one are compensated by the strengths of another. The underlying logic borrows from measurement theory: if two independent measures of the same construct reach the same conclusion, the probability that both are wrong in the same way is lower than the probability that either is wrong alone. This is convergent validity — confidence in a finding grows when methods with different error structures agree.

There are four distinct forms triangulation can take. Data triangulation uses multiple data sources — interviewing different stakeholders, sampling from different time periods, or drawing on records from different agencies. Investigator triangulation uses multiple researchers to code, analyze, or interpret the same material, testing whether findings are specific to one analyst's perspective. Theory triangulation applies multiple theoretical frameworks to the same data, asking what each lens makes visible and obscures. Methodological triangulation — the most common — combines qualitatively different methods such as a survey and an ethnography or a regression and a case study. Each type increases confidence for different reasons.

The methodologically surprising insight, however, is that divergence is not failure. When a survey shows that 60% of employees report high job satisfaction while ethnographic fieldwork reveals chronic workplace frustration, the divergence is a finding, not a problem. It prompts deeper questions: perhaps the survey elicits socially acceptable answers that respondents feel unsafe revising in an anonymous questionnaire; perhaps the ethnographic sample over-represents a particular department; perhaps satisfaction and frustration genuinely coexist for different aspects of work life. Divergence forces the researcher to interrogate the assumptions each method smuggles in, and those interrogations often produce more sophisticated theoretical accounts than either method alone would have generated.

The practical discipline is to plan triangulation prospectively, not retrospectively. Retroactively assembling convergent evidence after seeing results is a form of confirmation bias — you select the sources that agree and quietly set aside the ones that diverge. Good triangulation specifies in advance what counts as convergence, what counts as divergence, and what inference each pattern will support. It also requires honest reporting: when your survey and your interviews disagree, you must report both and theorize the disagreement rather than privileging one source because it aligns with your hypothesis. This connects triangulation to the broader norms of mixed-methods design: methodological pluralism is a commitment to letting reality surprise you.

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Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Introduction to Exponents → Order of Operations → Integer Order of Operations → Variable Expressions → The Distributive Property → Variables and Expressions Review → Introduction to Polynomials → Adding and Subtracting Polynomials → Multiplying Polynomials → Factorial → Permutations → Combinations → Counting Principles: Addition and Multiplication Rules → Introduction to Graph Theory → Propositional Logic Foundations → Logical Equivalences → Boolean Algebra → Introduction to Propositional Logic → Introduction to Predicate Logic (First-Order Logic) → First-Order Logic Syntax → Terms and Atomic Formulas in FOL → Variable Binding and Scope → Open and Closed Formulas in First-Order Logic → Variable Substitution and Capture-Avoidance in First-Order Logic → Quantifier Instantiation Rules in First-Order Proof Systems → Universal Quantification: Meaning and Scope → Free Variables and Bound Variables → Substitution and Instantiation in Predicate Logic → Terms and Atomic Formulas → Formulas and Well-Formed Expressions → Structures and Interpretations → Model Interpretation and Satisfaction → Interpretation, Truth, and Satisfaction of Formulas → Logical Consequence and Entailment → Soundness Theorem and Validity of Proof Systems → Deductive Reasoning and Formal Proof Systems → First-Order Resolution → Propositional Resolution → Semantic Tableaux (Propositional) → Semantic Tableaux (First-Order) → Decidable Fragments of First-Order Logic → Gödel's Completeness Theorem for First-Order Logic → Gödel's Incompleteness Theorems → Introduction to Intuitionistic Logic → Introduction to Modal Logic → Compatibilism → Moral Responsibility → Moral Psychology → Moral Sentiments and Emotions → Care Ethics → Rational Choice and Ethics → Contractarian Moral Foundations → Moral Foundations and Intuitions → Moral Relativism → Introduction to Applied Ethics → Bioethics: Foundations → Medical Ethics & Patient Autonomy → Informed Consent & Research Ethics → Research Ethics: Human Subjects Protection → Ethnographic Fieldwork: Positionality and Research Ethics → Ethnographic Interviewing and Qualitative Data Collection → Advanced Ethnographic Methods → Mixed Methods Research Integration → Triangulation: Convergent Validity and Method Confirmation

Longest path: 116 steps · 975 total prerequisite topics

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