Statistics

Cover
Title Page
Copyright Page
Dedication
Preface to the Sixth Edition
Preface to the Fourth Edition
Preface to the Third Edition
Preface to the Second Edition
Contents
Chapter 1 Variables and Graphs
	Statistics
	Population and Sample; Inductive and Descriptive Statistics
	Variables: Discrete and Continuous
	Rounding of Data
	Scientific Notation
	Significant Figures
	Computations
	Functions
	Rectangular Coordinates
	Graphs
	Equations
	Inequalities
	Logarithms
	Properties of Logarithms
	Logarithmic Equations
Chapter 2 Frequency Distributions
	Raw Data
	Arrays
	Frequency Distributions
	Class Intervals and Class Limits
	Class Boundaries
	The Size, or Width, of a Class Interval
	The Class Mark
	General Rules for Forming Frequency Distributions
	Histograms and Frequency Polygons
	Dot Plots and Box Plots
	Relative-Frequency Distributions
	Cumulative-Frequency Distributions and Ogives
	Relative Cumulative-Frequency Distributions and Percentage Ogives
	Frequency Curves and Smoothed Ogives
	Types of Frequency Curves
Chapter 3 The Mean, Median, Mode, and Other Measures of Central Tendency
	Index, or Subscript, Notation
	Summation Notation
	Averages, or Measures of Central Tendency
	The Arithmetic Mean
	The Weighted Arithmetic Mean
	Properties of the Arithmetic Mean
	The Arithmetic Mean Computed from Grouped Data
	The Median
	The Mode
	The Empirical Relation Between the Mean, Median, and Mode
	The Geometric Mean G
	The Harmonic Mean H
	The Relation Between the Arithmetic, Geometric, and Harmonic Means
	The Root Mean Square
	Quartiles, Deciles, and Percentiles
	Software and Measures of Central Tendency
Chapter 4 The Standard Deviation and Other Measures of Dispersion
	Dispersion, or Variation
	The Range
	The Mean Deviation
	The Semi-Interquartile Range
	The 10–90 Percentile Range
	The Standard Deviation
	The Variance
	Short Methods for Computing the Standard Deviation
	Properties of the Standard Deviation
	Charlier’s Check
	Sheppard’s Correction for Variance
	Empirical Relations Between Measures of Dispersion
	Absolute and Relative Dispersion; Coefficient of Variation
	Standardized Variable; Standard Scores
	Software and Measures of Dispersion
Chapter 5 Moments, Skewness, and Kurtosis
	Moments
	Moments for Grouped Data
	Relations Between Moments
	Computation of Moments for Grouped Data
	Charlier’s Check and Sheppard’s Corrections
	Moments in Dimensionless Form
	Skewness
	Kurtosis
	Population Moments, Skewness, and Kurtosis
	Software Computation of Skewness and Kurtosis
Chapter 6 Elementary Probability Theory
	Definitions of Probability
	Conditional Probability; Independent and Dependent Events
	Mutually Exclusive Events
	Probability Distributions
	Mathematical Expectation
	Relation Between Population, Sample Mean, and Variance
	Combinatorial Analysis
	Combinations
	Stirling’s Approximation to n!
	Relation of Probability to Point Set Theory
	Euler or Venn Diagrams and Probability
Chapter 7 The Binomial, Normal, and Poisson Distributions
	The Binomial Distribution
	The Normal Distribution
	Relation Between the Binomial and Normal Distributions
	The Poisson Distribution
	Relation Between the Binomial and Poisson Distributions
	The Multinomial Distribution
	Fitting Theoretical Distributions to Sample Frequency Distributions
Chapter 8 Elementary Sampling Theory
	Sampling Theory
	Random Samples and Random Numbers
	Sampling With and Without Replacement
	Sampling Distributions
	Sampling Distribution of Means
	Sampling Distribution of Proportions
	Sampling Distributions of Differences and Sums
	Standard Errors
	Software Demonstration of Elementary Sampling Theory
Chapter 9 Statistical Estimation Theory
	Estimation of Parameters
	Unbiased Estimates
	Efficient Estimates
	Point Estimates and Interval Estimates; Their Reliability
	Confidence-Interval Estimates of Population Parameters
	Probable Error
Chapter 10 Statistical Decision Theory
	Statistical Decisions
	Statistical Hypotheses
	Tests of Hypotheses and Significance, or Decision Rules
	Type I and Type II Errors
	Level of Significance
	Tests Involving Normal Distributions
	Two-Tailed and One-Tailed Tests
	Special Tests
	Operating-Characteristic Curves; the Power of a Test
	p-Values for Hypotheses Tests
	Control Charts
	Tests Involving Sample Differences
	Tests Involving Binomial Distributions
Chapter 11 Small Sampling Theory
	Small Samples
	Student’ts Distribution
	Confidence Intervals
	Tests of Hypotheses and Significance
	The Chi-Square Distribution
	Confidence Intervals for σ
	Degrees of Freedom
	The F Distribution
Chapter 12 The Chi-Square Test
	Observed and Theoretical Frequencies
	Definition of X2
	Significance Tests
	The Chi-Square Test for Goodness of Fit
	Contingency Tables
	Yates’ Correction for Continuity
	Simple Formulas for Computing X2
	Coefficient of Contingency
	Correlation of Attributes
	Additive Property of X2
Chapter 13 Curve Fitting and the Method of Least Squares
	Relationship Between Variables
	Curve Fitting
	Equations of Approximating Curves
	Freehand Method of Curve Fitting
	The Straight Line
	The Method of Least Squares
	The Least-Squares Line
	Nonlinear Relationships
	The Least-Squares Parabola
	Regression
	Applications to Time Series
	Problems Involving More Than Two Variables
Chapter 14 Correlation Theory
	Correlation and Regression
	Linear Correlation
	Measures of Correlation
	The Least-Squares Regression Lines
	Standard Error of Estimate
	Explained and Unexplained Variation
	Coefficient of Correlation
	Remarks Concerning the Correlation Coefficient
	Product-Moment Formula for the Linear Correlation Coefficient
	Short Computational Formulas
	Regression Lines and the Linear Correlation Coefficient
	Correlation of Time Series
	Correlation of Attributes
	Sampling Theory of Correlation
	Sampling Theory of Regression
Chapter 15 Multiple and Partial Correlation
	Multiple Correlation
	Subscript Notation
	Regression Equations and Regression Planes
	Normal Equations for the Least-Squares Regression Plane
	Regression Planes and Correlation Coefficients
	Standard Error of Estimate
	Coefficient of Multiple Correlation
	Change of Dependent Variable
	Generalizations to More Than Three Variables
	Partial Correlation
	Relationships Between Multiple and Partial Correlation Coefficients
	Nonlinear Multiple Regression
Chapter 16 Analysis of Variance
	The Purpose of Analysis of Variance
	One-Way Classification, or One-Factor Experiments
	Total Variation, Variation Within Treatments, and Variation Between Treatments
	Shortcut Methods for Obtaining Variations
	Mathematical Model for Analysis of Variance
	Expected Values of the Variations
	Distributions of the Variations
	The F Test for the Null Hypothesis of Equal Means
	Analysis-of-Variance Tables
	Modifications for Unequal Numbers of Observations
	Two-Way Classification, or Two-Factor Experiments
	Notation for Two-Factor Experiments
	Variations for Two-Factor Experiments
	Analysis of Variance for Two-Factor Experiments
	Two-Factor Experiments with Replication
	Experimental Design
Chapter 17 Nonparametric tests
	Introduction
	The Sign Test
	The Mann–Whitne U Test
	The Kruskal–Wallis H Test
	The H Test Corrected for Ties
	The Runs Test for Randomness
	Further Applications of the Runs Test
	Spearman’s Rank Correlation
Chapter 18 Statistical Process Control and Process Capability
	General Discussion of Control Charts
	Variables and Attributes Control Charts
	X-bar and R Charts
	Tests for Special Causes
	Process Capability
	P- and NP-Charts
	Other Control Charts
	Answers to Supplementary Problems
Appendixes
	I Ordinates (Y) of the Standard Normal Curve at z
	II  Areas Under the Standard Normal Curve from 0 to z
	III  Percentile Values (tp) for Student’s t Distribution with Degrees of Freedom
	IV  Percentile Values (X2p) for the Chi-Square Distribution with Degrees of Freedom
	V 95th Percentile Values for the F Distribution
	VI 99th Percentile Values for the F Distribution
	VII Four-Place Common Logarithms
	VIII Values of e-λ
	IX Random Numbers
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	K
	L
	M
	N
	O
	P
	Q
	R
	S
	T
	U
	V
	W
	X
	Y
	Z