Elementary Statistical Analysis

✍ Scribed by Samuel Stanley Wilks

• Publisher: Princeton University Press
• Year: 2015
• Tongue: English
• Leaves: 296
• Series: Princeton Legacy Library; 1956
• Category: Library

✦ Synopsis

A beginning text especially designed for those who probably will not go in to statistics professionally but who plan to go into the physical, biological, and social sciences. The material presupposes only one semester of elementary mathematical analysis.

Originally published in 1948.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

✦ Table of Contents

PREFACE
CONTENTS
CHAPTER 1. INTRODUCTION
1.1 General Remarks
1.2 Quantitative Statistical Observations
1.3 Qualitative Statistical Observations
CHAPTER 2. FREQUENCY DISTRIBUTIONS
2.1 Frequency Distributions for Ungrouped Measurements
2.2 Frequency Distributions for Grouped Measurements
2.3 Cumulative Polygons Graphed on Probability Paper
2.4 Frequency Distributions — General
CHAPTER 3. SAMPLE MEAN AND STANDARD DEVIATION
3.1 Mean and Standard Deviation for the Case of Ungrouped Measurements
3.11 Definition of the mean of a sample (ungrouped)
3.12 Definition of the standard deviation of a sample (ungrouped)
3.2 Remarks on the Ifiterpretation of the Mean and Standard Deviation of a Sample
3.3 The Mean and Standard Deviation for the Case of Grouped Data
3.31 An example
3.32 The general case
3.4 Simplified Computation of Mean and Standard Deviation
3.41 Effect of adding a constant
3.42 Examples of using a working origin
3.43 Fully coded calculation of means, variances and standard deviations
CHAPTER 4. ELEMENTARY FROBiiBILITY
4.1 Preliminary Discussion and Definitions
4.2 Probabilities in Simple Repeated Trials
4.3 Permutations
4.4 Combinations
4.41 Binomial coefficients
4.5 Calculation of Probabilities
4.51 Complementation
4.52 Addition of probabilities for mutually exclusive events
4.53 Multiplication of probabilitiss for independent events
4.54 Multiplication of probabilities when events are not independent; conditional probabilities
4.55 Addition of probabilities when events are not mutually exclusive
4.56 Euler diagrams
4.57 General remarks about calculating probabilities
4.6 Mathematical Expectation
4.7 Geometric Probability
CHAPTER 5. PROBABILITY DISTRIBUTIONS
5.1 Discrete Probability Distributions
5.11 Probability tables and graphs
5.12 Remarks on the statistical interpretation of a discrete probability distribution
5.13 Means, variances and standard deviations of discrete chance quantities
5.2 Continuous Probability Distributions
5.21 A simple continuous probability distribution
5.22 More general continuous probability distributions
5.3 Mathematical Manipulation of Continuous Probability Distributions
5.31 Probability density functions — a simple case
5.32 Probability density functions — a more general case
5.33 Continuous probability distributions — the general case
5.34 The mean and variance of a continuous probability distribution
5.35 Remarks on the statistical interpretation of continuous probability distributions
CHAPTER 6. THE BINOMIAL DISTRIBUTION
6.1 Derivationof the Binomial Distribution
6.2 The Mean and Standard Deviation of the Binomial Distribution
6.3 "Fitting" a Binomial Distribution to a Sample Frequency Distribution
CHAPTER 7. THE POISSON DISTRIBUTION
7.1 The Poisson Distribution as a Limiting Case of the Binomial Distribution
7.2 Derivation of the Poisson Distribution
7.3 The Mean and Variance of a Poisson Distribution
7.4 "Fitting" a Poisson Distribution to a Sample Frequency Distribution
CHAPTER 8. THE NORMAL DISTRIBUTION
8.1 General Properties of the Normal Distribution
8.2 Some Applications of the Normal Distribution
8.21 "Fitting" a cumulative distribution of measurements in a sample by a -cumulative normal distribution
8.22 "Fitting" a cumulative binomial distribution by a cumulative normal distribution
8.3 The Cumulative Normal Distribution on Probability Graph Paper
CHAPTER 9. ELEMENTS OF SAMPLING
9.1 Introductory Remarks
9.2 Sampling from a Finite Population
9.21 Experimental sampling from a finite population
9.22 Theoretical sampling from a finite population
9.23 The mean and standard deviation of means of all possible samples from a finite population
9.24 Approximation of distribution of sample means by normal distribution
9.3 Sampling from an Indefinitely Large Population
9.31 Mean and standard deviation of theoretical distributions of means and sums, of samples from an indefinitely large population
9.32 Approximate normality of distribution of sample mean in large samples from an indefinitely large population
9.35 Remarks on the binomial distribution as a theoretical sampling distribution
9.4 The Theoretical Sampling Distributions of Sums and Differences of Sample Means
9.41 Differences of sample means
9.42 Sums of sample means
9.43 Derivations
CHAPTER 10. CONFIDENCE LIMITS OF POPULATION PARAMETERS
10.1 Introductory Remarks
10.2 Confidence Limits of p in a Binomial Distribution
10.21 Confidence interval chart for p
10.22 Remarks on sampling from a finite binomial population
10.3 Confidence Limits of Population Means Determined from Large Samples
Remarks about confidence limits of means of finite populations
10.4 Confidence Limits of Means Determined from Small Samples
10.5 Confidence Limits of Difference between Population Means Determined from Large Samples
10.51 Confidence limits of the difference p-p' in two binomial populations
10.52 Confidence limits of the difference of two population means in case of small samples
CHAPTER 11. STATISTICAL SIGNIFICANCE TESTS
11.1 A Simple Significance Test
11.2 Significance Tests by Using Confidence Limits
11.3 Significance Tests without the Use of Population Parameters
CHAPTER 12. TESTING RANDOiaiESS IN SAMPLES
12.1 The Idea of Random Sampling
12.2 Runs
12.3 Quality Control Charts
CHAPTER 13. ANALYSIS OF PAIRS OF MEa.SUREi;ENTS
13.1 Introductory Comments
13.2 The Method of Least Squares for Fitting Straight Lines
13.21 An example
13.22 The general case
13.23 The variance of estimates of Y from X
13.24 Remarks on the sampling -variability of regression lines
13.25 Remarks on the correlation coefficient
13.3 Simplified Computation of Coefficients for Regression Line
13.31 Computation by using a working origin
13.32 Computation by using a fully coded scheme
13.4 Generality of the Method of Least Squares
13.41 Fitting a line through the origin by least squares
13.42 Fitting parabolas and higher degree polynomials
13.43 Fitting exponential functions
INDEX