# Fundamentals of Statistics

Harvard University Press, 1947 - 755 pŕgines
This book provides a broad general survey of the principles of scientific method, and a substantial basic knowledge of statistics particularly in its application to scientific research and with special relevance to the fields of the social and biological sciences. The introductory chapters aim to place statistical procedures in the reader's general philosophy and experience, and to show him their logical importance and practical utility. Mr. Kelley then develops a detailed presentation of essential statistics. Finally, he makes a serious but admittedly initial attempt to release the niceties of middle and advanced mathematics to the peculiar problems that may be found in a given issue and with given data. His book will be of particular value in the teaching of elementary statistics in that it provides a broad scientific and logical approach. Yet, while its earlier chapters constitute a complete first semester course and the later chapters a reference handbook for one going no further, these later chapters also provide the basic topics, procedures and formulas for incorporation into second and third semester courses in applied statistics.

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### Continguts

 THE DIGNITY OF DATA AND 3 Historical Antecedents of Modern Statis 10 The Mathematical Background of Students 24 Plan of Study 46 STATISTICAL SERIES 62 Temporal Series 63 Types of Statistical Processes 74 STATISTICAL TABLES 84
 Comparable Measures 499 Quotients 501 The Most Reliable Weighted Average of Independent Measures 505 Fitting of Curves to Observations 506 The Variance Error of a Statistic Derived from One Having a known Vari ance Error 523 The Variance Error of a Coefficient Corrected for Attenuation 526 The EquiProbable and the Mean Ranges for Samples of Different Size Drawn from a Normal Population 529 The Optimal Size of Interval for Histo gram or Frequency Polygon 531

 Problems 95 Quantitative Series 135 Qualitative Series 154 Graphic Portrayal in Three Dimensions 166 THE STABLE FEATURES OF PHENOMENA 185 Temporal Data 193 MEASURES OF VARIABILITY 199 Degrees of Freedom 205 Cumulants and kStatistics 215 Decimal Places to be kept in Published 222 The Effect of Form of Distribution Upon 234 The Geometric Mean 248 THE NORMAL DISTRIBUTION 275 The Normal Distribution as Related 284 Certain Properties of the Normal Distri 290 The Significance of Differences Between 300 The Relationship of ChiSquare 306 ChiSquare 318 Transformations No rhializing the Vari 325 AND CORRELATION 332 Findings Resulting from Galtons Graphic 339 Derivation of Computational Formulas 348 The Regression Equation and the Analysis 354 Averaging Correlation coefficients 363 Biserial Correlation 370 TwoByTwofold Correlation 379 Adjustments for Coarseness of Grouping 388 Correlations and Other Statistics 395 The Effect of Variability in Pange Upon 425 ThreeVariable Multiple Correlation 433 Nonlinear Regression 442 The Correlation Ratio 449 THE GENERAL MULTIPLE LINEAR REGRESSION PROBLEM 454 458 1 A Statement of Relationships in Connec tion with Standard Score Varia... 454 A Modi fied Doolittle Solution 3 The Determinantal Expression of the Solution of Normal Equations 471 The Use of Matrices in Expressing Mul tiple Correlation Relationships 471 475 SUNDRY STATISTICAL ISSUES AND PROCEDURES 482 492 497 499 501 482 Lead and Lag in Time Series 492 Imposed Conditions 497
 Direct and Inverse Interpolation 538 The Machine Extraction of Square and Cube Roots 543 Occasional Formulas 545 Sequential Analysis 565 MATHEMATICS THE MENTOR OF STATISTICAL INGENUITY 1 Ingenuity in Research 571 Matrices and Determinants 573 Determinant al Solution of Simultaneous Equa tions 580 The Point Binomial 581 The Poisson Distribution 582 The Hypergeometric Series 583 Factorials and the Gamma Function 585 The Numerical Solution of Higher Degree Parabolic and of Exponential Equations 589 The Numerical Solution of complicated Simul taneous Equations 591 Transforming Rank and Percentage Posi tions into Quantitative Scores 592 Transforming Rank or Percentage Position into Equally Reliable Deviation Scores 593 The Square Root Transformation 598 The Cube Root Transformation 599 Expanding A Table By Interpolating Values 601 Trigonometric Functions of Sums and Di fferences 603 Space of Three or More Dimensions 605 LaGrange Multipliers 607 Growth Curves 608 The Binomial Theorem 609 Fourier Series 610 Selected References 612 Lagrangi an Interpolation Coefficients 627 Normal Probability Functions 639 538 640 555 641 APPENDIX A MATHEMATICAL 659 Scoring Keys 673 NonLiteral Symbols 693 References 729 Dwight TABLES OF INTEGRALS AND OTHER 731 CORRELATION CHART 745 619 746 Copyright