Introductory Statistics

Introductory Statistics

1st Edition - January 1, 1966

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  • Author: M.H. Quenouille
  • eBook ISBN: 9781483140384

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Description

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.

Table of Contents


  • 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 √P Transformation

    Iv 1/ßsinh-1ß√x 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

    9.3 Randomization In Experimentation

    9.4 Methods of Sampling

    9.5 Analysis of Stratified Random Samples

    9.6 Analysis of Systematic Samples

    9.7 Sampling from Finite Populations

    9.8 Sampling Efficiency

    Summary

    Examples

    9.9 Multi-Stage Sampling

    9.10 Ratio Method in Sampling

    9.11 Regression Method in Sampling

    Summary

    Examples

    Bibliography

    Appendix of Statistical Tables

    I Table of The Percentage of Observations Exceeding A Given Normal Deviate d

    II Table of Limits for The Deviate d Corresponding to a Given Percentage

    III Variance-Ratio Table 5 per cent Points

    IV Variance-Ratio Table 1 per cent Points

    V Table Giving The Percentage of Trials in Which a Given Estimated Deviate t is Exceeded

    VI Table of χ2 Distribution

    VII Table of Random Numbers

    VIII Tables of Common Logarithms and Natural Logarithms

    IX Values of Sin-1√p

    X Values of Sinh-1√x

    XI Table of Squares and Square Roots

    Index

Product details

  • No. of pages: 262
  • Language: English
  • Copyright: © Pergamon 1969
  • Published: January 1, 1966
  • Imprint: Pergamon
  • eBook ISBN: 9781483140384

About the Author

M.H. Quenouille

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