Philosophy of Science
What science is, how it advances, and how different philosophical approaches understand it — each topic on its own page.
Philosophy of Science Approaches
- 01What Is Science?What distinguishes science from other kinds of knowledge?
- 02The Scientific MethodThe cycle of observation, hypothesis, test and revision
- 03The Problem of InductionHume's challenge to reasoning from past to future
- 04The Hypothetico-Deductive MethodDeriving testable consequences from hypotheses
- 05The Demarcation ProblemWhat separates science from pseudoscience?
- 06PositivismKnowledge only from observable facts
- 07Logical Positivism (Vienna Circle)Verifiability as the criterion of meaning
- 08Falsificationism (Popper)Science advances by attempts to refute, not to confirm
- 09Paradigms and Scientific Revolutions (Kuhn)Normal science, anomaly, crisis and paradigm shift
- 10Scientific Research Programmes (Lakatos)Hard core, protective belt, progressive vs degenerating programmes
- 11Epistemological Anarchism (Feyerabend)"Anything goes" — there is no single scientific method
- 12Scientific Realism and Anti-RealismDo theories describe the world, or merely work?
- 13Scientific Explanation (the DN Model)Explanation as deduction of the event from laws
- 14Bayesian Philosophy of ScienceDegrees of belief updated by evidence
- 15Research ParadigmsPositivism, interpretivism, pragmatism, critical realism
- 16Reproducibility and Open ScienceThe replication crisis, preregistration and transparency
Statistical & Methodological Foundations
- 01Hypothesis: Null and AlternativeThe logic of statistical hypothesis testing
- 02The Central Limit TheoremWhy the sample mean tends toward a normal distribution
- 03Sampling MethodsProbability and non-probability sampling
- 04Statistical Significance and the p-valueWhat the p-value does and does not tell you
- 05Type I and Type II ErrorsFalse positives, false negatives and power
- 06Statistical Errors and BiasSampling error, non-sampling error, bias vs variance
- 07Confidence IntervalsInterval estimation and its correct interpretation
- 08Effect SizeThe magnitude of an effect, independent of sample size
- 09Descriptive vs Inferential StatisticsSummarizing data vs generalizing to a population
- 10Variable Types and Levels of MeasurementNominal, ordinal, interval, ratio
- 11Validity and ReliabilityThe two core dimensions of measurement quality
- 12Correlation vs CausationAssociation does not imply causation
- 13Measures of Central TendencyMean, median and mode
- 14Measures of DispersionHow spread out the data are
- 15Skewness and KurtosisThe shape of a distribution
- 16Foundations of ProbabilityEvents, conditional probability and Bayes
- 17The Normal DistributionThe bell curve and z-scores
- 18Common Probability Distributionst, F, chi-square, binomial, Poisson
- 19The Sampling DistributionHow a statistic varies across samples
- 20Standard Error vs Standard DeviationTwo often-confused quantities
- 21Degrees of FreedomThe number of values free to vary
- 22Parametric vs Non-parametric TestsWhich family of test, and when
- 23Statistical AssumptionsNormality, homogeneity, independence
- 24One-tailed vs Two-tailed TestsDirectional vs non-directional hypotheses
- 25The Multiple Comparisons ProblemMany tests inflate false positives
- 26Bootstrapping and ResamplingInference without distributional assumptions
- 27Bayesian vs Frequentist InferenceTwo philosophies of statistics
- 28Statistical Power and Sample SizeThe chance of detecting a real effect
- 29Choosing the Right Statistical TestA practical test-selection guide
- 30Missing Data MechanismsMCAR, MAR, MNAR
- 31Outliers and Influential ObservationsDetecting and handling them sensibly
- 32Data Transformation and StandardizationLog, square-root, z, min-max
Statistical Literacy
- 01Sensitivity and SpecificityHow well a test catches positives and negatives
- 02Predictive Values (PPV and NPV)The real probability given a test result
- 03ROC Curves and AUCThreshold-independent classifier performance
- 04The Confusion MatrixThe basis of all classification metrics
- 05Classification Metrics: Accuracy, Precision, Recall, F1Evaluating a classifier correctly
- 06Likelihood RatiosHow a test result updates the odds
- 07Cohen's d and the Standardized Mean DifferenceThe magnitude of a difference between two means
- 08Variance Explained: Eta-squared and R-squaredHow much variability the model explains
- 09The Odds RatioA measure of association for categorical outcomes
- 10Relative Risk and Risk DifferenceComparing risk as a ratio and as a difference
- 11Number Needed to Treat (NNT)How many patients for one extra good outcome
- 12The Hazard RatioComparing instantaneous risk over time
- 13Measures of Association for Categorical DataEffect size after a chi-square test
- 14Overfitting and UnderfittingA model's ability to generalize
- 15The Bias–Variance TradeoffThe tension between two sources of error
- 16Training, Validation, and Test SetsSplitting data for honest evaluation
- 17RegularizationPreventing overfitting with a penalty
- 18Model Selection and Information CriteriaChoosing among competing models
- 19Goodness-of-Fit and Model ErrorHow well a model fits the data
- 20Regression DiagnosticsChecking the assumptions of a regression
- 21Interaction EffectsWhen one effect depends on another variable
- 22Random VariablesMapping outcomes to numbers
- 23Expected Value and VarianceA distribution's centre and spread
- 24The Law of Large NumbersWhy the sample mean converges to the truth
- 25Bayes' TheoremUpdating beliefs in light of evidence
- 26Joint, Marginal, and Conditional DistributionsHow several variables behave together
- 27How to Conduct a Hypothesis TestThe step-by-step testing procedure
- 28Checking Statistical Assumptions in PracticeWhat to do when assumptions fail
- 29Reporting Statistical ResultsReporting findings fully and honestly
- 30Interpreting p-values, Confidence Intervals, and Effect Sizes TogetherReading the whole picture, not one number