Basic Statistics - Raykov, Tenko

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Résumé :
Preface 1. Statistics and data. 1.1.Statistics as a science. 1.2.Collecting data. 1.3.Why study statistics? 2. An introduction to descriptive statistics: Data description and graphical representation. 2.1. What is descriptive statistics? 2.2. Graphical means of data description. 2.2.1. Reading data into R. 2.2.2. Graphical representation of data. 2.2.2.1. Pie-charts and bar-plots. 2.2.2.2. Histograms and stem-and-leaf plots. 3. Data description: Measures of central tendency and variability. 3.1. Measures of central tendency. 3.1.1. The mode. 3.1.2. The median. 3.1.3. The mean. 3.2. Measures of variability. 3.3. The box-plot. 3.3.1. Quartiles. 3.3.2. Definition and empirical construction of a box-plot. 3.3.3. Box-plots and comparison of groups of scores. 4. Probability. 4.1. Why be interested in probability? 4.2. Definition of probability. 4.2.1. Classical definition. 4.2.2. Relative frequency definition. 4.2.3. Subjective definition. 4.3. Evaluation of event probability. 4.4. Basic relations between events and their probabilities. 4.5. Conditional probability and independence. 4.5.1. Defining conditional probability. 4.5.2. Event independence. 4.6. Bayes' formula (Bayes' theorem). 5. Probability distributions of random variables. 5.1. Random variables. 5.2. Probability distributions for discrete random variables. 5.2.1. A start up example. 5.2.2. The binomial distribution. 5.2.3. The Poisson distribution. 5.3. Probability distributions for continuous random variables. 5.3.1. The normal distribution. 5.3.1.1. Definition. 5.3.1.2. Graphing a normal distribution. 5.3.1.3. Mean and variance of a normal distribution. 5.3.1.4. The standard normal distribution. 5.3.2. z-scores. 5.3.3. Model of congeneric tests. 5.4. The normal distribution and areas under the normal density curve. 5.5. Percentiles of the normal distribution. 6. Random sampling distributions and the central limit theorem. 6.1. Random sampling distribution. 6.1.1. Random sample. 6.1.2. Sampling distribution. 6.2. The random sampling distribution of the mean (sample average). 6.2.1. Mean and variance of the RSD of the sample average. 6.2.2. Standard error of the mean. 6.3. The central limit theorem. 6.3.1. The central limit theorem as a large-sample statement. 6.3.2. When does normality hold for a finite sample? 6.3.3. How large a sample size is 'sufficient' for the central limit theorem to be valid? 6.3.4. Central limit theorem for sums of random variables. 6.3.5. A revisit of the random sampling distribution concept. 6.3.6. An application of the central limit theorem. 6.4. Assessing the normality assumption for a population distribution. 7. Inferences about single population means. 7.1. Population parameters. 7.2. Parameter estimation and hypothesis testing. 7.3. Point and interval estimation of the mean. 7.3.1. Point estimation. 7.3.2. Interval estimation. 7.3.3. Standard normal distribution quantiles for use in confidence intervals. 7.3.4. How good is an estimate, and what affects the width of a confidence interval? 7.4. Choosing sample size for estimating the mean. 7.5. Testing hypotheses about population means. 7.5.1. Statistical testing, hypotheses, and test statistics. 7.5.2. Rejection regions. 7.5.3. The 'assumption' of statistical hypothesis testing 7.5.4. A general form of a z-test. 7.5.5. Significance level. 7.6. Two types of error in statistical hypothesis testing. 7.6.1. Type I and Type II errors. 7.6.2. Statistical power. 7.6.3. Type I error rate and significance level. 7.6.4. Have we proved the null or alternative hypothesis? 7.6.5. One-tailed tests. 7.6.5.1. Alternative hypothesis of mean larger than a pre-specifie...

Biographie:
Tenko Raykov is professor of measurement and quantitative methods at Michigan State University....

Sommaire:
By Tenko Raykov and George A. Marcoulides...