Statistical methods/ George W. Snedecor, William G. Cohran.

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 (<t known)
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 <r from the sample range
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