| Contents Notes |
Notation -- 1. Introduction -- 2. Frequency distribution -- Tabulation of data -- Frequency grouping -- Cumulative frequency -- Graphical representation -- Solved problems -- Problems -- 3. Characteristics of distributions : central tendency -- Averages -- Arithmetic mean -- Median -- Mode -- Skewness -- Quantiles -- Geometric mean -- Solved problems -- Problems -- 4. Characteristics of distributions : dispersion -- Variance -- Standard deviation -- Simplified computation of standard deviation -- Mean deviation -- Coefficient of variation -- Range -- Solved problems -- Problems -- 5. Permutations, combinations, and probability -- Permutations -- Combinations -- Probability -- Solved problems -- Problems -- 6. Samples : accuracy of the mean -- Sampling -- Mean of sample means -- Distribution of sample means -- Standard deviation of the mean -- Problems -- 7. Binomial distribution -- Derivation -- Pascal's triangle -- Mean and standard deviation -- Comparison of experimental and binomial distributions -- Solved problems -- Problems -- 8. Poisson distribution -- Terms of the Poisson distribution -- Derivation from binomial distribution -- Mean and standard deviation -- Poisson distribution as an approximation to binomial distribution -- Significance of Poisson distribution -- Poisson probability paper -- Solved problems -- Problems -- 9. Normal distribution -- Errors -- Gauss function -- Derivation of the function -- The normal curve -- Physical significance of standard deviation -- Area under the normal curve -- Solved problems -- Problems -- 10. Use of normal distribution -- Limits of practical distributions -- Some important probabilities -- Fitting a normal curve -- Probability paper -- Mean deviation in normal distribution -- Central limit theorem -- Transformation to a normally distributed variate -- Binomial approximation -- Level of significance -- Specifying a minimum value -- Solved problems -- Problems -- 11. Rejection of outliers -- Reasons for outliers -- Rejection on basis of estimated variance -- Chauvenet's criterion -- Problems -- 12. The chi-squared test -- Null hypothesis -- Significance of test -- Degrees of freedom -- Minimum class frequency -- Continuity correction -- Contingency tables -- Too good a fit -- X2 as a measure of goodness of fit -- Solved problems -- Problems -- 13. Comparison of means -- Inference errors -- Normal distribution test -- The t test -- One-sided and two-sided tests -- t test for paired data -- Interpretation of results -- Case of nonhomogeneous variances -- Solved problem -- Problems -- 14. Comparison of variances and their properties -- F test -- Bartlett's test -- Standard deviation of various statistics -- Propagation of errors -- Confidence limits for variance -- Comparison of standard deviations of large samples -- Solved problems -- Problems -- 15. Method of least squares and regression -- Method of least squares -- Regression line -- Limitations of method -- Confidence limits of regression estimates -- Significance test for slope -- Use of method of least squares in surveying -- Nonlinear relations -- Rectification -- Solved problems -- Problems -- 16. Correlation -- Correlation coefficient -- Correlation and causation -- Solved problem -- Problems -- 17. Multiple linear regression -- Regression equation -- Shorter computation -- Use of matrices -- Confidence limits of a partial regression coefficient -- Significance of multiple regression as a whole -- Multiple-correlation coefficient -- Solved problem -- Problems -- 18. Analysis of variance -- Method of analysis -- Usual method of computation -- Test on homogeneity of variances -- Simplifying the computations -- Multifactor analysis -- Solved problems -- Problems -- 19. Tolerance and control charts -- Specification and tolerance limits -- Stability of a process -- Warning and action limits -- Mean chart -- Range chart -- Scheme of operation -- Charts using attributes -- Advantages of quality control -- Solved problems -- Problems -- 20. Introduction to the design of experiments -- Choice of sample size -- Construction of the power curve -- Distribution of strength of accepted and rejected batches -- Simplified case -- Sampling of attributes -- Randomized blocks -- Latin squares -- Balanced incomplete blocks -- Multiple factor experiments -- Classical three-factor experiment -- Factorial three-factor experiment -- Partitioning the treatments sum of squares -- The main effects A, B, and C -- The interactions A x B, B x C, A x C, A x B x C -- Meaning of the main and interaction effects -- Graphical interpretation -- Random numbers -- Solved problem -- Problems -- Appendices -- Tables -- Index. |
