| Description |
1 online resource (xiii, 111 pages) : illustrations |
| Series |
SpringerBriefs in statistics, 2191-544X |
|
SpringerBriefs in statistics. 2191-544X
|
| Contents |
880-01 Basics of Probability Theory -- Estimation -- Hypothesis Testing -- Regression |
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880-01/(S Machine generated contents note: 1. Basics of Probability Theory -- 1.1. Probability and Events -- 1.2. Random Variables -- 1.3. Normal Distribution -- 1.4. Important Distributions and Their Relations -- 1.5. Quantiles -- 1.6. Moments -- 1.6.1. Expectation -- 1.6.2. Variance and Standard Deviation -- 1.6.3. Z-Scores -- 1.6.4. Covariance and Independence -- 1.6.5. General Moments; Skewness and Kurtosis -- 1.7. Important Limit Theorems -- 1.8. Visualizing Distributions -- 1.8.1. Summaries -- 1.8.2. Plotting Empirical Distributions -- 1.8.3. Quantile--Quantile Plots -- 1.8.4. Barplots and Boxplots -- 1.9. Summary -- 2. Estimation -- 2.1. Introduction -- 2.2. Constructing Estimators -- 2.2.1. Maximum-Likelihood -- 2.2.2. Least-Squares -- 2.2.3. Properties of Estimators -- 2.3. Confidence Intervals -- 2.3.1. Bootstrap -- 2.4. Robust Estimation -- 2.4.1. Location: Median and k-Trimmed Mean -- 2.4.2. Scale: MAD and IQR -- 2.5. Minimax Estimation and Missing Observations -- 2.5.1. Loss and Risk -- 2.5.2. Minimax Estimators -- 2.6. Fisher-Information and Cramer-Rao Bound -- 2.7. Summary -- 3. Hypothesis Testing -- 3.1. Introduction -- 3.2. General Procedure -- 3.3. Testing the Mean of Normally Distributed Data -- 3.3.1. Known Variance -- 3.3.2. Unknown Variance: t-Tests -- 3.4. Other Tests -- 3.4.1. Testing Equality of Distributions: Kolmogorov-Smirnov -- 3.4.2. Testing for Normality: Shapiro-Wilks -- 3.4.3. Testing Location: Wilcoxon -- 3.4.4. Testing Multinomial Probabilities: Pearson's Χ2 -- 3.4.5. Testing Goodness-of-Fit -- 3.5. Sensitivity and Specificity -- 3.6. Multiple Testing -- 3.6.1. Bonferroni-Correction -- 3.6.2. False-Discovery-Rate (FDR) -- 3.7. Combining Results of Multiple Experiments -- 3.8. Summary -- Reference -- 4. Regression -- 4.1. Introduction -- 4.2. Classes of Regression Problems -- 4.3. Linear Regression: One Covariate -- 4.3.1. Problem Statement -- 4.3.2. Parameter Estimation -- 4.3.3. Checking Assumptions -- 4.3.4. Linear Regression Using R -- 4.3.5. On the "Linear" in Linear Regression -- 4.4. Linear Regression: Multiple Covariates -- 4.4.1. Problem Statement -- 4.4.2. Parameter Estimation -- 4.4.3. Hypothesis Testing and Model Reduction -- 4.4.4. Outliers -- 4.4.5. Robust Regression -- 4.5. Analysis-of-Variance -- 4.5.1. Problem Statement -- 4.5.2. Parameter Estimation -- 4.5.3. Hypothesis Testing -- 4.6. Interpreting Error Bars -- 4.7. Summary -- Reference |
| Summary |
The text gives a concise introduction into fundamental concepts in statistics. Chapter 1: Short exposition of probability theory, using generic examples. Chapter 2: Estimation in theory and practice, using biologically motivated examples. Maximum-likelihood estimation in covered, including Fisher information and power computations. Methods for calculating confidence intervals and robust alternatives to standard estimators are given. Chapter 3: Hypothesis testing with emphasis on concepts, particularly type-I, type-II errors, and interpreting test results. Several examples are provided. T-tests are used throughout, followed important other tests and robust/nonparametric alternatives. Multiple testing is discussed in more depth, and combination of independent tests is explained. Chapter 4: Linear regression, with computations solely based on R. Multiple group comparisons with ANOVA are covered together with linear contrasts, again using R for computations |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Statistics.
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Statistics as Topic
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statistics.
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MATHEMATICS -- Applied.
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MATHEMATICS -- Probability & Statistics -- General.
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Statistics
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| Form |
Electronic book
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| ISBN |
9783642235023 |
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3642235026 |
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