عنوان

A concise guide to statistics

electronic

Kaltenbach, Hans-Michael.

A concise guide to statistics

Heidelberg ; New York

Springer

c2012

xiii, 111 p. : ill. ; 24 cm.

Springerbriefs in statistics

Includes bibliographical references and index

Hans-Michael Kaltenbach

1. Basics of probability theory -- Probability and events -- Random variables -- The normal distribution -- Important distributions and their relations -- Quantiles -- Moments -- Expectation -- Variance and standard deviation -- Z-scores -- Covariance and independence -- General moments : skewness and kurtosis -- Important limit theorems -- Visualizing distributions -- Summaries -- Plotting empirical distributions -- Quantile-quantile plots -- Barplots and boxplots -- 2. Estimation -- Introduction -- Constructing estimators -- Maximum-likelihood -- Least-squares -- Properties of estimators -- Confidence intervals -- The bootstrap -- Robust estimation -- Location : median and k-trimmed mean -- Scale : MAD and IQR -- Minimax estimation and missing observations -- Loss and risk -- Minimax estimators -- Fisher-information and Cramف‌r-Rao bound -- 3. Hypothesis testing -- Introduction -- The general procedure -- Testing the mean of normally distributed data -- Known variance -- Unknown variance : t-tests --Testing equality of distributions : Kolmogorov-Smirnov -- Testing for normality : Shapiro-Wilks -- Testing location : Wilcoxon -- Testing multinomial probabilities -- Testing goodness-of-fit -- Sensitivity and specificity -- Multiple testing -- Bonferroni-Correction -- False-Discovery-Rate )FDR( -- Combining results of multiple experiments -- 4. Regression -- Introduction -- Classes of regression problems -- Linear regression : one covariate -- Linear regression : multiple covariates -- Robust regression -- Analysis-of-variance -- Interpreting error bars

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