Inferential statistics

2 artículos

Sampling Point estimation Confidence interval Hypothesis testing P value Type i and ii errors Maximum likelihood Statistical inference Frequentist inference Statistical hypothesis test Statistical hypothesis testing Null hypothesis Alternative hypothesis Significance level Type i and type ii errors Statistical power Power statistics Credible interval Prediction interval Tolerance interval Interval estimation Likelihood interval Pivotal quantity One and two tailed tests Multiple comparisons Family wise error rate False discovery rate Uniformly most powerful test Neyman pearson lemma Likelihood function Likelihood ratio Monotone likelihood ratio Whittle likelihood Sampling distribution Standard error Effect size Statistical significance Misuse of statistics Statistical theory Statistical model Statistical parameter Nuisance parameter Statistical classification Elementary statistics Statistical assumption Ancillary statistic Sufficient statistic Acceptance sampling Acceptance sampling plan for attributes Acceptance sampling plan for variables Adaptive sampling Anderson darling statistic Auto regression Bayes formula Bayes thomas Bayesian approach Bayesian approach empirical Bayesian decision function Bayesian estimator Bayesian numerical analysis Best linear unbiased estimation in linear models Best linear unbiased estimator Biased estimator Boltzmann statistics Bose einstein statistics Confidence estimation Conventional distance sampling Correlation function in statistical mechanics Covariance analysis Cox regression model Discrete systems in statistical mechanics Edge of regression Efficiency of a statistical procedure Efficient estimator Equivariant estimator Exponential sum estimates Fermi dirac statistics Generalized quasi likelihood Gibbs statistical aggregate Hypereffective estimator Inefficient statistic Interval estimator Invariance of a statistical procedure Invariant statistic L space of a statistical experiment Likelihood equation Linear estimator Maximum likelihood method Model based geostatistics Multi dimensional statistical analysis Neyman method of confidence intervals Non parametric methods in statistics Nonparametric regression using kernel and spline methods Parabolic regression Pitman estimator Point estimator Power of a statistical test Rank statistic Regression Regression coefficient Risk of a statistical procedure Sampling from finite populations Shannon sampling theorem Similar statistic Statistical acceptance control Statistical approaches to protecting confidentiality in public use data Statistical ensemble Statistical estimation Statistical estimator Statistical experiments method of Statistical game Statistical hypotheses verification of Statistical hypothesis Statistical mechanics mathematical problems in Statistical modelling Statistical physics mathematical problems in Statistical quality control Statistical sum Statistics in insurance Superefficient estimator Test statistics The significance test controversy and the bayesian alternative Two sided estimate Unbiased estimator Vinogradov estimates

Probability & Statistics GradoExplicación10 min

Three Points from a Thousand People, and the Two Roundings That Cancel

The 95 percent margin on a proportion is almost exactly 1 over the square root of the sample size, because p(1-p) is flat enough near its peak to call a quarter and 1.96 is close enough to 2, and those two roundings are reciprocal so they annihilate. At N = 1000 the shortcut gives 3.16 percent against an exact 3.04, and it always errs on the conservative side. Reporting one standard error instead, 1.55 percent, describes a 68 percent interval rather than a 95 percent one.

Probability & Statistics GradoAnálisis9 min

Five Numbers, Two Answers, and the Divisor Nobody Asks About

The standard deviation of 1, 2, 3, 4, 5 is either 1.4142 or 1.5811, and offering one of them without asking which question you are answering is the only wrong move. The sum of squared deviations is 10 either way, so everything turns on whether you divide it by 5 or by 4. Bessel's correction makes the variance unbiased and leaves the standard deviation biased low by about six percent at this sample size, and a third divisor beats both of them if you optimise for mean squared error instead.