Statistical methods/
George W. Snedecor, William G. Cohran.
- 8th edition
- New Delhi : Rajkamal Electric Press , 1989.
- xx, 503 p. : ill. ; 26 cm.
Chapter 1. Introduction 1.1 Introduction 1.2 Purpose of this chapter 1.3 Examples of sample surveys 1.4 Problems of sampling 1.5 Biased sampling 1.6 Random sampling 1.7 Tables of random digits 1.8 Sampling distributions of estimates 1.9 Studies of the comparative effects of different agents 1.10 Problems in drawing conclusions from comparative studies 1.11 Effectiveness of the Salk polio vaccine 1.12 Death rates of different smoking groups 1.13 Observational studies 1.14 Summary Chapter 2. Frequency Distributions 2.1 Quantitative data 2.2 Frequency distributions 2.3 Grouped frequency distributions 2.4 Class limits 2.5 Cumulative frequency distributions 2.6 Probability distributions Chapter 3. The Mean and Standard Deviation 3.1 Arithmetic mean 3.2 Population mean 3.3 Population standard deviation 3.4 Two-class populations 3.5 Sample standard deviation _ 3.6 Use of frequency distributions to calculate X and s 3.7 Numerical example 3.8 Coefficient of variation Chapter 4. The Normal Distribution 4.1 Normally distributed populations 4.2 Reasons for use of the normal distribution 4.3 Tables of the normal distribution 4.4 Standard deviation of sample meitns 4.5 Frequency distribution of sample .means 4.6 Three illustrations 4.7 Confidence limits for /t when a is known 4.8 Size of sample 4.9 Student's t distribution 4.10 Confidence limits for n based on th« t distribution 4.11 Experinrental sampling of the r dist ribution 4.12 Sample check on confidence interva 1 statements 4.13 Probability plots 4.14 A finite population simulating the normal Chapter 5. T^ts of Hypothecs 5.1 Introduction 5.2 A test of the mean of a normal population (5.3 Tests of significance and confidence intervals 5.4 Practical uses of tests of significance 5.5 One-sided or one-tailed tests 5.6 Power of a test of significance 5.7 Testing a mean when a is not known 5.8 Other tests of significance 5.9 Frequency distribution of 5.10 Interval estimates of 5.11 Test of a null hypothesis value of a' 5.12 The test of goodness of fit 5.13 Test of skewness 5.14 Test for kurtosis Chapter 6. The Comparison of Two Samples 6.1 Estimates and tests of differences 6.2 A simulated paired experiment 6.3 Example of a paired experiment 6.4 Conditions for pairing 6.7 A pooled estimate of variance 6.10 Precautions against bias; randomization 6.11 Analysis ot inaepenaeni samples wnen ax f aj 6.12 A test of the equality of two variances 6.13 Paired versus independent samples 6.14 Sample size in comparative experiments Chapter 7. The Binomial Distribution 7.1 Introduction 7.2 Some simple rules of probability 7.3 The binomial distribution 7.4 Sampling the binomial distribution 7.5 Probability of at least one success 7.6 The normal approximation and the correction for. continuity 7.7 Test of significance of a binomial proportion 7.8 Confidence limits for a binomial proportion 7.9 Comparison of proportions in paired samples 7.10 Comparison of proportions in independent samples: the 2 X 2 table 7.11 The test in a 2 X 2 contingency table 7.12 Test of the independence of two attributes 7.13 Sample size for comparing two proportions 7.14 The Poisson distribution Chapter 8. Shortcut and Nonparametric Methods 8.1 Introduction 8.2 Sample median 8.3 Estimation of 8.4 Sign test 8.5 Signed-rank test 8.6 The rank sum test for two independent samples 8.7 Comparison of rank and normal tests 8.8 Nonparametric confidence limits 8.9 Discrete scales with limited values: randomization test Chapter 9. Regression 9.1 Introduction 9.2 Calculations for fitting a linear regression 9.3 The mathematical model in linear regression 9.4 Analysis of variance for linear regression 9.5 The method of least squares 9.6 Regression in observational studies 9.7 Apple example 9.8 Estimation of the mean of Y for a given X 9.9 Prediction of an individual new V 9.10 Prediction of a sample mean of K 9.11 Testing a deviation that looks suspiciously large 9.12 Prediction of from Y: linear calibration 9.13 Gabon's use of the term "regression" 9.14 Regression when A'is subject to error 9.15 Fitting a straight line through the origin Chapter 10. Correlation 10.1 The sample correlation coefficient r 10.2 Properties of r 10.3 Bivariate normal distribution 10.4 Some uses of the correlation coefficient 10.5 Testing the null hypothesis, p - 0 10.6 Confidence limits and tests of hypotheses about p 10.7 Variance of a linear function 10.8 Comparison of two correlated variances in paired samples 10;9 Nonparametric methods: rank correlation Chapter 11. Analysis of Frequencies in One-way and Two-way Class&cations 11.1 Introduction 11.2 Single classifications with more than two classes 11.3 Single classifications with equal expectations 11.4 Test that Poisson samples have the same mean 11.5 Additional tests 11.6 Two-way classifications: the 2 x C contingency table 11.7 Test for homogeneity of binomial samples 11.8 Ordered classifications 11.9 Test for a linear trend in proportions 11.10 The/? X Ccontingency table 11.11 Sets of 2 X 2 tables Chapter 12. One-way Classifications: Analysis of Variance 12.1 Extension from two samples to many 12.2 An experiment with four samples 12.3 Analysis of variance: model I (fixed effects) 12.4 Effect of differences between population class means 12.5 The F test 12.6 Analysis of variance with only two classes 12.7 Proof of the algebraic identity in the analysis of variance 12.8 Planned comparisons among class means 12.9 Orthogonal comparisons 12.10 Samples of unequal sizes 12.11 Weighted linear regression 12.12 Testing effects suggested by the data 12.13 Inspwtion of all differences between pairs of means Chapter 13. Analysis of Variance: The Random Effects Model 13.1 Model 11: random effects 13.2 Relation between model II and model I 13.3 Use of model II in problems of measurement 13.4 Structure of model II illustrated by sampling 13.5 Intraclass correlation 13.6 Confidence limits related to variance components 13.7 Random effects with samples of unequal sizes 13.8 Extension to three stages of sampling 13.9 Three stages with mixed model 13.10 Tests of homogeneity of variance 13.11 Levene's test of homogeneity of variance Chapter 14. Two-way Classifications 14.1 Introduction 14.2 Experiment in randomized blocks 14.3 Comparisons among means 14.4 Notation and mathematical model 14.5 Method of estimation: least squares I4!6 Deviations from the model i 4.7 Efficiency of blocking 14.8 Two-way classifications with n observations per cell 14^9 Balancing the order in which treatments are given 14.10 Latin squares Chapter 15. Failures in the Assumptions 15.1 Introduction 15.2 The problem of missing data 15!3 More than one missing value 15.4 Extreme observations 15.5 Suspected outliers in one-way or two-way classifications 15.6 Correlations between the errors 15.7 The role of transformations 15.8 A test for nonadditivity 15.9 Application to an experiment 15.10 Variance-stabilizing transformations 15^11 Square root transformation for counts 15.12 Arc sine transformation for proportions 15! 13' Logarithmic transformation 15.14 Nonadditivity in a Latin square 15.15 Simultan^us study of different effects of a transformation Chapter 16. Factorial Experiments '16.1 Introduction 16.2 The single-factor approach 16.3 The factorial approach 16.4 Analysis of the 2^ factorial experiment 16.5 The 2^ factorial when interaction, is present 16.6 The general two-factor experiment 16.7 Polynomial response curves 16.8 Response curves in two-factor experiments 16.9 An example with both factors quantitative 16.10 Fitting the response surface 16.11 Three-factor experiments: the 2' 16.12 Yates'algorithm 16.13 Three-factor experiments: a 2 x 3 x 4 16.14 Expected values of mean squares 16.15 Split-plot design 16.16 Experiments with repeated measurements Chapter 17. Multiple Linear Regression 17.1 Introduction 17.2 Estimation of the coefficients 17.3 The analysis of variance 17.4 Extension of the analysis of variance 17.5 Variances and covariances of the regression coefficients 17.6 Relationship between univariate and multivariate regression 17.7 Examination of residuals 17.8 Standard errors of predicted values 17.9 Interpretation of regression coefficients 17.10 Omitted A-variables 17.11 Effects possibly causal 17.12 Relative importance of different A'-variables 17.13 Selection of variables for prediction 17.14 Partial correlation Appendix to chapter 17: matrix algebra Chapter 18. Analysts of Covariance 18.1 Introduction 18.2 Covariance in a completely randomized experiment 18.3 The F test of the adjusted means 18.4 Covariance in a two-way classification 18.5 Use of regression adjustments in observational studies 18.6 Problems with regression adjustments 18.7 Covariance in interpreting differences between classes 18.8 Comparison of regression lines 18.9 Multiple covariance Chapter 19. Nonlinear Relations 19.1 Introduction 19.2 The exponential growth cur\'e 19.3 The second degree polynomial 19.4 Data having several Ks for each X 19.5 Test of departure from linear regression in covariance analysis 19.6 Orthogonal polynomials 19.7 A general method of fitting nonlinear regressions 19.8 Fitting an asymptotic regression Chapter 20. Two-way Tables with Unequal Numbers and Proportions 20.1 Introduction 20.2 Methods of attack 20.3 Inspection of cell means 20.4 Unweighted analysis of cell means 20.5 Analysis by proportional numbers 20.6 Least squares fitting of the additive model 20.7 Analysis of proportions in two-way tables 20.8 Analysis in the p scale: a 3 x 2 table Chapter 21. Sample Surveys 21.1 Introduction 21.2 An example of simple random sampling 21.3 An example of stratified random sampling 21.4 Probability sampling 21.5 Standard errors for simple random sampling 21.6 Size of sample 21.7 Standard errors for stratified random sampling 21.8 Choice of sample sizes in the strata 21.9 Systematic sampling 21.10 Two-stage sampling 21.11 Sampling with probability proportional to size 21.12 Ratio estimators 21.13 Nonsampling errors 21.14 Further reading