Hypothesis Study Guide

📖 Core Concepts Hypothesis – a testable, reproducible explanation for a phenomenon, grounded in observation. Working hypothesis – a provisional idea used to steer research; discarded when better explanations appear. Scientific hypothesis requirements – educated guess, operational definition, falsifiability, and reproducibility. Types of hypotheses Mathematical model – expressed with equations. Existential – claims a particular instance has a property. Universal – claims every instance has a property. Entrepreneurial – tested by verifiable/falsifiable experiments. Evaluation criteria – testability/falsifiability, parsimony (Occam’s Razor), scope, fruitfulness, conservatism. Statistical hypothesis testing – compares a null hypothesis (H₀) (no effect/relationship) with an alternative hypothesis (H₁) (effect exists). Significance level (α) – pre‑chosen probability of wrongly rejecting H₀ (commonly .10, .05, .01). Effect size – quantitative magnitude of a result (small, medium, large) used to gauge practical importance. --- 📌 Must Remember A hypothesis must be falsifiable (Popper). Parsimony: fewer assumptions = stronger hypothesis, all else equal. Scope: broader applicability = higher value, but may reduce parsimony. Null vs. Alternative H₀: no relationship/effect. H₁: some relationship/effect (two‑sided if direction unknown, one‑sided if direction predicted). α must be set before data collection; never after looking at results. Power depends on α, effect size, and sample size – larger N → higher power. Effect‑size categories (Cohen’s d, r, etc.) are context‑specific; define them for each test. --- 🔄 Key Processes Formulating a hypothesis Observe → generate educated guess → write in operational, testable terms. Evaluating a hypothesis (criteria checklist) Is it falsifiable? → Is it parsimonious? → What is its scope? → Is it fruitful? → Does it align with existing knowledge (conservatism)? Statistical testing workflow State H₀ and H₁. Choose α before data collection. Determine required sample size for desired power (often 0.80). Collect data, compute test statistic. Compare p‑value to α → reject or fail to reject H₀. Report effect size and confidence interval. --- 🔍 Key Comparisons Existential vs. Universal Existential: “∃ x  such that P(x)” (at least one case). Universal: “∀ x , P(x)” (all cases). Working hypothesis vs. Theory Working: provisional, guides next steps, may be discarded. Theory: robust, repeatedly confirmed, explains many phenomena. Two‑sided vs. One‑sided alternative Two‑sided: tests for any difference (↑ or ↓). One‑sided: tests for a specific direction; higher power but risk of missing opposite effect. Parsimony vs. Scope Parsimony: fewer entities → preferred. Scope: wider applicability → higher value but may require more complexity. --- ⚠️ Common Misunderstandings “A hypothesis is a guess” → It must be educated and testable; random speculation is not a scientific hypothesis. “If H₀ is not rejected, it is proven true” → Failure to reject only means insufficient evidence; H₀ remains tentative. “Higher α = better” → Larger α raises Type I error risk (false positive). “A statistically significant result equals a large effect” → Significance only speaks to probability; effect size measures magnitude. “One‑sided tests are always superior” → Use only when theory a priori predicts direction; otherwise you invite bias. --- 🧠 Mental Models / Intuition Falsifiability filter: Imagine a hypothesis as a door; if any experiment can smash the door down, it passes the filter. Parsimony balance beam: Picture a scale with “simplicity” on one side and “explanatory power” on the other; the best hypothesis balances them. Null hypothesis as a default setting: Treat H₀ like a computer’s default state—only change it when evidence clearly pushes you away. --- 🚩 Exceptions & Edge Cases Non‑falsifiable statements (e.g., “the universe is infinite”) are philosophical, not scientific hypotheses. Small sample, huge effect: May achieve significance but be unreliable; beware of over‑interpreting. Multiple comparisons: Each additional test inflates overall Type I error; apply corrections (Bonferroni, FDR). --- 📍 When to Use Which Use a working hypothesis when exploring a new area and need a guiding framework. Adopt a universal hypothesis if theory predicts a rule that should hold for all instances. Choose a one‑sided alternative only when prior theory strongly predicts direction and a two‑sided test would waste power. Select a larger α (e.g., .10) for exploratory pilot studies; use .05 or .01 for confirmatory research. Apply parsimonious models for initial testing; expand scope only after basic validation. --- 👀 Patterns to Recognize “No relation” wording in a question usually signals H₀. Effect‑size language (“small/medium/large”) hints that you must report magnitude, not just p‑value. Scope clues (“applies to all species”) indicate a universal hypothesis. “Pre‑specify” language (α, sample size) flags a well‑designed experiment. --- 🗂️ Exam Traps Trap 1: Selecting a one‑sided test when the question never specified direction → penalty for unjustified power increase. Trap 2: Confusing “failure to reject H₀” with “prove H₀ true.” Trap 3: Ignoring the need to define effect‑size categories; exam may ask for Cohen’s d interpretation. Trap 4: Choosing α after seeing the data (e.g., “p‑value is .06, so I’ll set α=.07”) – invalid. Trap 5: Overlooking parsimony; picking a complex model when a simpler one explains data equally well. ---