Statistical Methods

, by Snecdecor, George W.; Cochran, William G.

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ISBN: 9780813815619 | 0813815614
Cover: Hardcover
Copyright: 1/16/1991

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Summary

Author Biography

Supplemental Materials

Offers a comprehensive update of this classic statistics textbook, with careful adherence to the intent, approach, and style of the original authors.

Preface to the Eighth Edition

xiii

Preface to the First Edition

Symbols Frequently Used

xix

Introduction

(1)

Purpose of this chapter

(1)

Examples of sample surveys

(1)

Problems of sampling

(1)

Biased sampling

(1)

Random sampling

(2)

Tables of random digits

(1)

Sampling distributions of estimates

(2)

Studies of the comparative effects of different agents

(1)

Problems in drawing conclusions from comparative studies

(1)

Effectiveness of the Salk polio vaccine

(1)

Death rates of different smoking groups

(1)

Observational studies

(1)

Summary

(3)

Frequency Distributions

Quantitative data

(1)

Frequency distributions

(1)

Grouped frequency distributions

(2)

Class limits

(1)

Cumulative frequency distributions

(3)

Probability distributions

(3)

The Mean and Standard Deviation

Arithmetic mean

(1)

Population mean

(2)

Population standard deviation

(1)

Two-class populations

(1)

Sample standard deviation

(3)

Use of frequency distributions to calculate X and s

(1)

Numerical example

(2)

Coefficient of variation

(2)

The Normal Distribution

Normally distributed populations

(2)

Reasons for use of the normal distribution

(1)

Tables of the normal distribution

(3)

Standard deviation of sample means

(1)

Frequency distribution of sample means

(1)

Three illustrations

(5)

Confidence limits for μ when σ is known

(2)

Size of sample

(1)

Student's t distribution

(2)

Confidence limits for μ based on the t distribution

(2)

Experimental sampling of the t distribution

(1)

Sample check on confidence interval statements

(1)

Probability plots

(3)

A finite population simulating the normal

(2)

Tests of Hypotheses

Introduction

(1)

A test of the mean of a normal population (σ known)

(2)

Tests of significance and confidence intervals

(1)

Practical uses of tests of significance

(1)

One-sided or one-tailed tests

(1)

Power of a test of significance

(3)

Testing a mean when σ is not known

(2)

Other tests of significance

(1)

Frequency distribution of s2

(2)

Interval estimates of σ2

(1)

Test of a null hypothesis value of σ2

(1)

The Χ2 test of goodness of fit

(3)

Test of skewness

(1)

Test for kurtosis

(3)

The Comparison of Two Samples

Estimates and tests of differences

(1)

A simulated paired experiment

(2)

Example of a paired experiment

(2)

Conditions for pairing

(1)

Comparison of the means of two independent samples

(1)

Variance of a difference

(2)

A pooled estimate of variance

(1)

An experiment comparing two samples of equal size

(2)

Samples of unequal sizes

(2)

Precautions against bias: randomization

(1)

Analysis of independent samples when σ1 ν σ2

(2)

A test of the equality of two variances

(1)

Paired versus independent samples

(3)

Sample size in comparative experiments

102

(5)

The Binomial Distribution

Introduction

107

(1)

Some simple rules of probability

107

(3)

The binomial distribution

110

(3)

Sampling the binomial distribution

113

(2)

Probability of at least one success

115

(2)

The normal approximation and the correction for continuity

117

(3)

Test of significance of a binomial proportion

120

(1)

Confidence limits for a binomial proportion

121

(1)

Comparison of proportions in paired samples

121

(3)

Comparison of proportions in independent samples: the 2 x 2 table

124

(1)

The Χ2 test in a 2 x 2 contingency table

125

(3)

Test of the independence of two attributes

128

(1)

Sample size for comparing two proportions

129

(1)

The Poisson distribution

130

(5)

Shortcut and Nonparametric Methods

Introduction

135

(1)

Sample median

135

(2)

Estimation of σ from the sample range

137

(1)

Sign test

138

(2)

Signed-rank test

140

(2)

The rank sum test for two independent samples

142

(2)

Comparison of rank and normal tests

144

(1)

Nonparametric confidence limits

145

(1)

Discrete scales with limited values: randomization test

146

(3)

Regression

Introduction

149

(1)

Calculations for fitting a linear regression

149

(3)

The mathematical model in linear regression

152

(4)

Analysis of variance for linear regression

156

(2)

The method of least squares

158

(2)

Regression in observational studies

160

(1)

Apple example

161

(2)

Estimation of the mean of Y for a given X

163

(2)

Prediction of an individual new Y

165

(3)

Prediction of a sample mean of Y

168

(1)

Testing a deviation that looks suspiciously large

169

(1)

Prediction of X from Y: linear calibration

170

(2)

Galton's use of the term ``regression''

172

(1)

Regression when X is subject to error

173

(1)

Fitting a straight line through the origin

174

(3)

Correlation

The sample correlation coefficient r

177

(1)

Properties of r

178

(2)

Bivariate normal distribution

180

(3)

Some uses of the correlation coefficient

183

(3)

Testing the null hypothesis, ρ = 0

186

(1)

Confidence limits and tests of hypotheses about ρ

187

(3)

Variance of a linear function

190

(2)

Comparison of two correlated variances in paired samples

192

(1)

Nonparametric methods: rank correlation

193

(3)

Analysis of Frequencies in One-way and Two-way Classifications

Introduction

196

(1)

Single classifications with more than two classes

196

(3)

Single classifications with equal expectations

199

(1)

Test that Poisson samples have the same mean

199

(2)

Additional tests

201

(1)

Two-way classifications: the 2 x C contingency table

202

(1)

Test for homogeneity of binomial samples

203

(3)

Ordered classifications

206

(2)

Test for a linear trend in proportions

208

(2)

The R x C contingency table

210

(2)

Sets of 2 x 2 tables

212

(5)

One-way Classifications: Analysis of Variance

Extension from two samples to many

217

(1)

An experiment with four samples

217

(2)

Analysis of variance: model I (fixed effects)

219

(3)

Effect of differences between population class means

222

(1)

The F test

223

(1)

Analysis of variance with only two classes

224

(1)

Proof of the algebraic identity in the analysis of variance

225

(1)

Planned comparisons among class means

226

(2)

Orthogonal comparisons

228

(2)

Samples of unequal sizes

230

(2)

Weighted linear regression

232

(2)

Testing effects suggested by the data

234

(1)

Inspection of all differences between pairs of means

235

(2)

Analysis of Variance: The Random Effects Model

Model II: random effects

237

(1)

Relation between model II and model I

237

(1)

Use of model II in problems of measurement

238

(3)

Structure of model II illustrated by sampling

241

(1)

Intraclass correlation

242

(2)

Confidence limits related to variance components

244

(1)

Random effects with samples of unequal sizes

245

(2)

Extension to three stages of sampling

247

(2)

Three stages with mixed model

249

(2)

Tests of homogeneity of variance

251

(1)

Levene's test of homogeneity of variance

252

(2)

Two-way Classifications

Introduction

254

(1)

Experiment in randomized blocks

255

(1)

Comparisons among means

256

(1)

Notation and mathematical model

257

(2)

Method of estimation: least squares

259

(1)

Deviations from the model

260

(3)

Efficiency of blocking

263

(1)

Two-way classifications with n observations per cell

264

(2)

Balancing the order in which treatments are given

266

(2)

Latin squares

268

(5)

Failures in the Assumptions

Introduction

273

(1)

The problem of missing data

273

(2)

More than one missing value

275

(3)

Extreme observations

278

(2)

Suspected outliers in one-way or two-way classifications

280

(1)

Correlations between the errors

281

(1)

The role of transformations

282

(1)

A test for nonadditivity

282

(2)

Application to an experiment

284

(2)

Variance-stabilizing transformations

286

(1)

Square root transformation for counts

287

(2)

Arc sine transformation for proportions

289

(1)

Logarithmic transformation

290

(1)

Nonadditivity in a Latin square

291

(3)

Simultaneous study of different effects of a transformation

294

(3)

Factorial Experiments

Introduction

297

(1)

The single-factor approach

297

(1)

The factorial approach

298

(1)

Analysis of the 22 factorial experiment

299

(2)

The 22 factorial when interaction is present

301

(2)

The general two-factor experiment

303

(3)

Polynomial response curves

306

(2)

Response curves in two-factor experiments

308

(2)

An example with both factors quantitative

310

(2)

Fitting the response surface

312

(2)

Three-factor experiments: the 23

314

(2)

Yates' algorithm

316

(1)

Three-factor experiments: a 2 x 3 x 4

317

(2)

Expected values of mean squares

319

(5)

Split-plot design

324

(5)

Experiments with repeated measurements

329

(4)

Multiple Linear Regression

Introduction

333

(1)

Estimation of the coefficients

333

(7)

The analysis of variance

340

(3)

Extension of the analysis of variance

343

(4)

Variances and covariances of the regression coefficients

347

(3)

Relationship between univariate and multivariate regression

350

(1)

Examination of residuals

351

(2)

Standard errors of predicted values

353

(1)

Interpretation of regression coefficients

354

(1)

Omitted X-variables

355

(3)

Effects possibly causal

358

(1)

Relative importance of different X-variables

359

(1)

Selection of variables for prediction

360

(3)

Partial correlation

363

(11)

Appendix to chapter 17: matrix algebra

366

(8)

Analysis of Covariance

Introduction

374

(1)

Covariance in a completely randomized experiment

375

(4)

The F test of the adjusted means

379

(1)

Covariance in a two-way classification

380

(4)

Use of regression adjustments in observational studies

384

(1)

Problems with regression adjustments

385

(4)

Covariance in interpreting differences between classes

389

(1)

Comparison of regression lines

390

(3)

Multiple covariance

393

(5)

Nonlinear Relations

Introduction

398

(2)

The exponential growth curve

400

(4)

The second degree polynomial

404

(2)

Data having several Ys for each X

406

(3)

Test of departure from linear regression in covariance analysis

409

(1)

Orthogonal polynomials

409

(4)

A general method of fitting nonlinear regressions

413

(2)

Fitting an asymptotic regression

415

(5)

Two-way Tables with Unequal Numbers and Proportions

Introduction

420

(1)

Methods of attack

421

(1)

Inspection of cell means

422

(2)

Unweighted analysis of cell means

424

(2)

Analysis by proportional numbers

426

(1)

Least squares fitting of the additive model

427

(1)

Analysis of proportions in two-way tables

427

(2)

Analysis in the p scale: a 3 x 2 table

429

(2)

Sample Surveys

Introduction

431

(1)

An example of simple random sampling

432

(1)

An example of stratified random sampling

433

(1)

Probability sampling

434

(1)

Standard errors for simple random sampling

435

(3)

Size of sample

438

(2)

Standard errors for stratified random sampling

440

(3)

Choice of sample sizes in the strata

443

(3)

Systematic sampling

446

(1)

Two-stage sampling

447

(3)

Sampling with probability proportional to size

450

(2)

Ratio estimators

452

(2)

Nonsampling errors

454

(1)

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Statistical Methods

Summary

Author Biography

Table of Contents

Supplemental Materials

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Statistical Methods

Summary

Author Biography

Table of Contents

Supplemental Materials

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