Fundamentals of Statistics

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Harvard University Press, 1947 - 755 pàgines
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
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