Introductory Statistics

PrefaceIntroduction1 Presentation of Sets of Measurements 1.1 Sampling 1.2 Ordering the Sample 1.3 Grouping 1.4 Diagrammatic Representation 1.5 The Arithmetic Mean and Its Calculation 1.6 Inadequacy of Arithmetic Mean 1.7 Measures of Spread: Range and Mean Deviation 1.8 Measures of Spread: Standard Deviation and Variance 1.9 Sample Estimates 1.10 Calculation of Standard Deviation and Variance Summary Examples 1A.11 Other Measures: Median and Mode 1A.12 Further Measures: Quartiles and Coefficient of Variability 1A.13 Moments and Other Coefficients 1A.14 Formula for Calculation of Standard Deviation Summary Examples2 Normal Distribution 2.1 Frequency Distributions 2.2 Frequency Curves 2.3 Normal Distribution 2.4 Applications of Normal Distribution 2.5 Alternative Form of Normal-Deviate Table Summary Examples 2A.6 Theoretical Distributions: The Binomial 2A.7 Application of Normal Approximation to Binomial Distribution 2A.8 Accuracy of an Estimated Proportion 2A.9 Theoretical Distributions: The Poisson Summary Examples 2A.10 A Rough Estimate of The Standard Deviation3 Comparison of Two Sets of Measurements 3.1 Method of Comparison 3.2 Variance-Ratio Test 3.3 Examples of Use of Variance-Ratio Test 3.4 Pooling of Variances 3.5 Accuracy of Arithmetic Mean 3.6 Examples of Determination of Accuracy of Arithmetic Mean 3.7 Comparison of Arithmetic Means 3.8 Examples of Test of Difference Between Means 3.9 The t Test 3.Summary 3.Examples 3A.10 Calculation of Number of Observations Necessary for a Given Accuracy 3A.11 Relative Precision and Combination of Experimental Results 3A.12 Estimation of Variance From Observations of Differing Precision 3A.13 Proof of Formula for Variance of Sum of Independent Measurements Summary Examples4 Comparison of Several Sets of Measurements 4.1 The Problem and Its Solution 4.2 Analysis of Variance 4.3 Further Examples of Analysis of Variance 4.4 Orthogonality and Interaction of Effects 4.5 Randomized Block Analysis 4.6 Examples of Randomized Block Analysis 4.7 Latin and Graeco-Latin Squares 4.8 Analysis of A Latin Square Summary Examples 4A.9 Testing Particular Comparisons 4A.10 Test for Interaction 4A.11. Examples of Test for Interaction 4A.12. Higher Order Interactions and Factorial Principle 4A.13. Confounding Summary Examples5 Attributes and Comparison of Proportions 5.1 Measurement of Attributes 5-2 Comparison of Several Groups 5.3 The Chi-Squared Test 5.4 An Alternative Computational Procedure 5.5 Comparison of Several Proportions 5.6 Testing 2 x 2 Tables 5.7 Yates' Correction for Continuity 5.8 Testing Goodness of Fit 5.9 Goodness of Fit With Estimated Constants Summary Examples 5A.10 Components of Chi-Squared 5A.11 Combination of Tests of Significance 5A.12 Exact Testing of 2 x 2 Tables Summary Examples6 Interrelations of Sets of Measurements 6.1 Associated Measurements 6.2 Diagrammatic Presentation 6.3 General Test for Association 6.4 Measures of Joint Variation 6.5 Fitting Straight Lines 6.6 Regression Lines 6.7 Correlation Coefficients Summary Examples 6A.8 Theory of Minimal Variance 6A.9 Example of Multiple Regression 6A.10 Significance of Particular Variates 6A.11 Partial Correlation Coefficients 6A.12 Curvilinear Regression Summary Examples7 Concomitant Observations 7.1 Comparison of Regression Coefficients 7.2 Comparison of Regressions 7.3 Concomitant Observations 7.4 Analysis of Covariance 7.5 Use of Analysis of Covariance in Estimation of Associations 7.6 Regression of Group Means Summary Examples 7A.