Schaum's Outline of 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