01
Target
What population quantity or model feature is unknown?
Define the estimand or hypothesis before seeing a convenient statistic. The target might be a mean, proportion, difference, effect, or model parameter.
Samples · estimands · standard errors · evidence
Statistical Inference
Statistical inference uses sample data and an uncertainty model to make bounded claims about a larger population or process. The strength of an inference depends on how the data were generated, what is being estimated, and which assumptions connect the sample to the target.
Inference pipeline
Inference begins before the calculation, with the target and the design.
A precise standard error cannot repair a biased sampling process, an irrelevant target, or a model whose assumptions disconnect it from the data-generating mechanism.
02
Sample
How was information selected or generated?
Sampling design, randomization, missingness, measurement, and dependence determine what uncertainty model is defensible.
03
Uncertainty
How much would the statistic vary across repeated data?
Sampling distributions, standard errors, bootstrap procedures, and probability models quantify variation induced by the data-generating process.
04
Inference
Which conclusions remain compatible with the data and assumptions?
Intervals, tests, estimates, model comparisons, and predictions translate sample evidence into bounded claims about a larger target.
Repeated confidence-interval lab
Toy model: independent normal observations, population σ = 10 known, true mean μ = 50.
Sample size
Confidence level
blue = covers μred = misses μeach row = new sample
Interpretation guardrails
An inferential output has a narrower meaning than its everyday wording suggests.
Confidence, significance, and evidence are technical ideas. Translating them carelessly into certainty, truth, importance, or causality creates statistical errors even when the arithmetic is flawless.
01Confidence interval
A procedure that produces intervals with a specified repeated-sampling coverage under the model. Wider intervals usually reflect more uncertainty.
02p-value
Under a specified null model, the probability of obtaining a test statistic at least as incompatible with the null as the observed one. It is not the probability that the null hypothesis is true.
03Statistical significance
A decision threshold applied to a test statistic or p-value. It does not measure practical importance, effect size, replication probability, or truth by itself.
04Generalizability
Whether an inference extends beyond the observed sample depends on sampling, design, context, and assumptions, not merely on a small standard error.