Scientific method Study Guide

📖 Core Concepts Scientific Method – An empirical, iterative cycle: Observation → Hypothesis → Prediction → Experiment → Analysis → Revision. Not a rigid sequence; steps can be reordered. Falsifiability – A hypothesis is scientific only if a conceivable observation could refute it (Popper). Hypothesis Types – Deductive: derives specific predictions from a general principle. Inductive: infers a general rule from many observations. Abductive: proposes the most plausible explanation for an unexpected fact. Strong Inference – Form several mutually exclusive hypotheses, then design decisive experiments that eliminate all but one. Peer Review & Replication – Community checks for errors, bias, and ensures reproducibility. Biases – Confirmation bias, theory‑laden observation, narrative fallacy; they distort data collection and interpretation. Statistical Inference – Uses sampling, uncertainty estimates, p‑values, confidence intervals, and Bayesian updating to judge if data support a prediction. 📌 Must Remember Falsifiable ⇔ Testable – If you cannot imagine a refuting experiment, the claim isn’t scientific. Prediction must be unknown – Known consequences do not test a hypothesis. Control Variables – Isolate causal factors; without controls you cannot attribute effects. p‑value misuse – Low p‑value ≠ proof; it only indicates low probability of data under the null if all assumptions hold. Bayes’ theorem: $$ P(H|E) = \frac{P(E|H)P(H)}{P(E)} $$ Updates prior belief \(P(H)\) with new evidence \(E\). Occam’s Razor – Prefer the explanation with the fewest assumptions that still fits the data. Strong inference rule – At least three competing hypotheses → design experiment that can eliminate two. 🔄 Key Processes Formulate Research Question – Identify the unknown and its relevance. Gather Existing Evidence – Literature review, define variables, measure precisely. Develop Hypothesis – Use creativity, inductive reasoning, or Bayesian inference. Derive Testable Predictions – Quantitative (e.g., \(v = \sqrt{gh}\)) or qualitative. Design Experiment Choose controls, replicates, blind procedures. Pre‑register analysis plan to limit researcher degrees of freedom. Conduct Experiment & Record Data – Detailed logs for reproducibility. Statistical Analysis – Correlation, regression, factor analysis; compute uncertainties. Interpret Results – Accept, refine, or reject hypothesis; note alternative explanations. Publish & Peer Review – Provide full methods, data, and discuss limitations. Replication – Independent labs repeat the study; failure to replicate signals error or fraud. 🔍 Key Comparisons Deduction vs. Induction Deduction: true premises → necessarily true conclusion. Induction: many observations → probable generalization (not guaranteed). Falsifiability vs. Confirmation Falsifiability: single contrary result can discard a theory. Confirmation: many supporting results increase credibility but never prove. Strong Inference vs. Simple Hypothesis Testing Strong Inference: multiple rival hypotheses, decisive experiments. Simple testing: one hypothesis, often only looks for support. Bayesian vs. Frequentist Statistics Bayesian: updates prior probabilities; yields posterior probability of a hypothesis. Frequentist: focuses on long‑run error rates (p‑values, confidence intervals). ⚠️ Common Misunderstandings “A true prediction proves a hypothesis.” – It only corroborates; the hypothesis remains provisional. “If a result is statistically significant, it must be important.” – Significance does not imply practical relevance or large effect size. “Science provides absolute truth.” – All knowledge is provisional; new data can overturn even well‑supported theories. “Observations are neutral.” – Theory‑laden observation means our expectations shape what we notice. 🧠 Mental Models / Intuition The “Falsification Funnel” – Imagine a funnel where each experiment removes a slice of the hypothesis space; the narrower the funnel, the stronger the remaining theory. Control‑Bias Balance – Think of an experiment as a balance scale: controls on one side keep the scale from tipping due to hidden variables. Bayesian Updating as a “Weight of Evidence” – Each new piece of data adds or subtracts weight from the belief scale. 🚩 Exceptions & Edge Cases Big‑Data Predictive Models – May achieve high accuracy without explicit falsifiable hypotheses; violates traditional falsifiability. Serendipitous Discoveries – Up to 50 % of breakthroughs arise unintentionally; the method still works after the fact via retrospective hypothesis formation. Hard‑to‑Vary Explanations – Some theories (e.g., certain cosmological models) are robust under many transformations, making falsification difficult. 📍 When to Use Which Use Strong Inference when multiple plausible mechanisms exist and decisive experiments are feasible. Choose Bayesian analysis when prior information is strong or when you need a direct probability of a hypothesis. Apply Frequentist tests for regulatory or conventional settings where long‑run error rates are required. Employ Abductive reasoning early in exploratory research to generate the most plausible hypothesis from sparse data. 👀 Patterns to Recognize Control‑only differences – If an experiment’s only change is a control variable, any effect points to that variable’s causal role. Replication failures – Repeated non‑replication often signals systematic bias or hidden confounders. “Too good to be true” effect sizes – Very large effects in small studies frequently indicate p‑hacking or selective reporting. Narrative coherence without data – Stories that fit all known facts but lack new predictions are likely narrative fallacies. 🗂️ Exam Traps Distractor: “Confirmation proves a theory.” – Remember only falsification can decisively reject; confirmation is never definitive. Distractor: “A single experiment can establish a law.” – Robust laws require repeated, independent confirmation and reproducibility. Distractor: “All statistical significance equals real-world importance.” – Look for effect size, confidence intervals, and practical relevance. Distractor: “If a hypothesis is elegant, it must be true.” – Elegance is a heuristic, not a criterion for truth. Distractor: “Observation is objective.” – Theory‑laden observation means expectations shape what is seen; bias checks are essential.