Introductory Statistics is an elementary non-mathematical manual on statistics and provides a connected account of the more common statistical tests. It is divided into two parts: the first part introduces the reader to elementary applications of statistical methods and the line of reasoning involved in their use, and the second part covers elementary parts of statistical theory and more advanced applications. This book consists of nine chapters and opens with a discussion on the presentation of sets of measurements, touching on topics such as sampling, grouping, measures of spread, and standard deviation. The following chapters deal with normal distribution and its applications; comparison of two or several sets of measurements; attributes and comparison of proportions; and interrelations of sets of measurements. Concomitant observations are also considered, along with transformations and non-normal distributions. The final chapter is devoted to sampling methods, including the ratio method and the regression method. This monograph is written primarily for students of statistics and aims to help research workers gain a fuller understanding of the methods used in the analysis of their results.
Inhalt
Preface
Introduction
1 Presentation of Sets of Measurements
1.1 Sampling
1.2 Ordering the Sample
1.3 Grouping
1.4 Diagrammatic Representation
1.5 The Arithmetic Mean and Its Calculation
1.6 Inadequacy of Arithmetic Mean
1.7 Measures of Spread: Range and Mean Deviation
1.8 Measures of Spread: Standard Deviation and Variance
1.9 Sample Estimates
1.10 Calculation of Standard Deviation and Variance
Summary
Examples
1A.11 Other Measures: Median and Mode
1A.12 Further Measures: Quartiles and Coefficient of Variability
1A.13 Moments and Other Coefficients
1A.14 Formula for Calculation of Standard Deviation
Summary
Examples
2 Normal Distribution
2.1 Frequency Distributions
2.2 Frequency Curves
2.3 Normal Distribution
2.4 Applications of Normal Distribution
2.5 Alternative Form of Normal-Deviate Table
Summary
Examples
2A.6 Theoretical Distributions: The Binomial
2A.7 Application of Normal Approximation to Binomial Distribution
2A.8 Accuracy of an Estimated Proportion
2A.9 Theoretical Distributions: The Poisson
Summary
Examples
2A.10 A Rough Estimate of The Standard Deviation
3 Comparison of Two Sets of Measurements
3.1 Method of Comparison
3.2 Variance-Ratio Test
3.3 Examples of Use of Variance-Ratio Test
3.4 Pooling of Variances
3.5 Accuracy of Arithmetic Mean
3.6 Examples of Determination of Accuracy of Arithmetic Mean
3.7 Comparison of Arithmetic Means
3.8 Examples of Test of Difference Between Means
3.9 The t Test
3.Summary
3.Examples
3A.10 Calculation of Number of Observations Necessary for a Given Accuracy
3A.11 Relative Precision and Combination of Experimental Results
3A.12 Estimation of Variance From Observations of Differing Precision
3A.13 Proof of Formula for Variance of Sum of Independent Measurements
Summary
Examples
4 Comparison of Several Sets of Measurements
4.1 The Problem and Its Solution
4.2 Analysis of Variance
4.3 Further Examples of Analysis of Variance
4.4 Orthogonality and Interaction of Effects
4.5 Randomized Block Analysis
4.6 Examples of Randomized Block Analysis
4.7 Latin and Graeco-Latin Squares
4.8 Analysis of A Latin Square
Summary
Examples
4A.9 Testing Particular Comparisons
4A.10 Test for Interaction
4A.11. Examples of Test for Interaction
4A.12. Higher Order Interactions and Factorial Principle
4A.13. Confounding
Summary
Examples
5 Attributes and Comparison of Proportions
5.1 Measurement of Attributes
5-2 Comparison of Several Groups
5.3 The Chi-Squared Test
5.4 An Alternative Computational Procedure
5.5 Comparison of Several Proportions
5.6 Testing 2 x 2 Tables
5.7 Yates' Correction for Continuity
5.8 Testing Goodness of Fit
5.9 Goodness of Fit With Estimated Constants
Summary
Examples
5A.10 Components of Chi-Squared
5A.11 Combination of Tests of Significance
5A.12 Exact Testing of 2 x 2 Tables
Summary
Examples
6 Interrelations of Sets of Measurements
6.1 Associated Measurements
6.2 Diagrammatic Presentation
6.3 General Test for Association
6.4 Measures of Joint Variation
6.5 Fitting Straight Lines
6.6 Regression Lines
6.7 Correlation Coefficients
Summary
Examples
6A.8 Theory of Minimal Variance
6A.9 Example of Multiple Regression
6A.10 Significance of Particular Variates
6A.11 Partial Correlation Coefficients
6A.12 Curvilinear Regression
Summary
Examples
7 Concomitant Observations
7.1 Comparison of Regression Coefficients
7.2 Comparison of Regressions
7.3 Concomitant Observations
7.4 Analysis of Covariance
7.5 Use of Analysis of Covariance in Estimation of Associations
7.6 Regression of Group Means
Summary
Examples
7A.7 Analysis of Covariance With Two or More Sets of Concomitant Observations
7A.8 Dummy Variates
7A.9 Non-Orthogonality
7A.10 Non-Orthogonal Comparisons When Interaction Exists
7A.11 Discriminant Functions
Summary
Examples
8 Transformations and Non-Normal Distributions
8.1 Reasons for Transformations
8.2 Transformations To Equalize Variances
I Logarithmic Transformation
II Square Root Transformation
III Sin- 1 vP Transformation
Iv 1/ßsinh-1ßvx Transformation
V Reciprocal Transformation
8.3 Transformations To Achieve Normality
I Logarithmic, Square Root and Reciprocal Transformation
II Transformation of Ranks To Normal Scores
8.4 Numerical Presentation of Transformed Data
8.5 Graphical Presentation of Transformed Data
Summary
Examples
8A.6 Additive Transformations
I Logarithmic Transformation
II Probit Transformation
III -Log(1-p) Transformations
8A.7 Theoretical Variances of Transformed Data
8A.8 Transformations of Statistical Measures
I Estimated Variances and Standard Deviations
II Variance Ratios
III Correlation Coefficients
IV Estimated Deviate
8A.9 Test for Homogeneity of Variance
8A.10 Testing for Normality
8A.11 Serial Correlation
Summary
Examples
9 Sampling Methods
9.1 Random Selection
9.2 Use of Tables of Random Numbers<…