Experimental Statistics using Minitab

Abstract

Includes index. From the Publisher: Experimental Statistics using Minitab exploits the availability of the statistical computer package Minitab to explain advanced statistical concepts related to the design and analysis of experiments in an intuitive and easily comprehended manner. This is achieved with a minimum of mathematical knowledge using the data generating and analyzing features of Minitab. Detailed instructions for the use of Minitab are given throughout making the book particularly useful for in-class use. Examples are drawn from a wide range of scientific fields. Dr Colin Weatherup formerly held the joint appointment of head of Biometrics Division of the Department of Agriculture for Northern Ireland and head of the Biometrics Department of the Queens University, Belfast. He has taught statistics to students in Agriculture, Biomedicine, Food Technology and in a range of other scientific subjects since 1970. In retirement he is currently an Associate Lecturer in the Open University. Preface -- 1: Basic Statistics -- 1-1: Interpretation of experimental data -- 1-2: Probability -- 1-3: Expected or the "long-run" value -- 1-4: Distributions -- 1-5: Use of distributions -- 1-6: Location and spread -- 1-7: Boxplots -- 1-8: Introduction to minitab -- 1-9: Minitab practical -- A: Frequency table -- B: Histogram -- C: Boxplot -- D: Display basic statistics -- 2: Normal Distribution -- 2-1: Definion of the normal distribution -- 2-2: Central limit theorem -- 2-3: Areas under the standard normal distribution -- 2-4: Minitab practical -- A: Demonstration of the central limit theorem -- B: One sided areas under the normal distribution -- C: Two sided areas under the normal distribution -- D: To draw a normal distribution with shaded areas -- 3: Normal Probability Plot And Properties Of The Mean And Variance -- 3-1: Normal probability plot -- 3-2: Transforming to normality -- 3-3: Properties of means and variances -- 3-4: Minitab practical -- A: Construction of normal probability plots and comparison with histograms -- B: Demonstration of the properties of the variance -- 4: Distribution Of Sample Means -- 4-1: Standard error -- 4-2: Confidence intervals -- 4-3: Paired comparisons using confidence intervals -- 4-4: Minitab practical -- A: Demonstration of the relationship between standard errors and standard deviations -- B: Calculation of confidence intervals -- C: Determination of the 2 sided t value for a specified probability and DF -- D: Determination of the 2 sided probability for a specified t value and DF -- 5: Laws Of Probability, The Binomial Distribution And Significance Testing -- 5-1: Laws of probability -- 5-2: Binomial distribution -- 5-3: Significance testing -- 5-4: One sided and two sided test of significance -- 5-5: Minitab practical -- A: Demonstration of the binomial distribution -- B: Use of minitab to obtain theoretical probabilities for the binomial distribution -- C: Calculation of the probabilities of occurrence of a range of numbers of survivals out of 20 cases using survival probabilities of 0_5 and 0_7 -- 6: Student's t Test, The Power Of A Test And Sample Size Estimation -- 6-1: Comparisons between population means using samples -- 6-2: Assumptions for the t test -- 6-3: Student's t test -- 6-4: Power of a test -- 6-5: Sample size calculation -- 6-6: Minitab practical -- A: Demonstration of a t test -- B: T-test using data from example 6-1 -- C: Sample size calculation -- 7: Non-Parametric Tests -- 7-1: Need for non-parametric tests -- 7-2: Testing the assumptions of a parametric test -- 7-3: Use of transformations -- 7-4: Wilcoxon signed rank test -- 7-5: Mann-Whitney U test -- 7-6: Minitab practical -- A: Wilcoxon signed rank test -- B: Mann-Whitney U test -- C: Use of minitab to determine critical F ratios for specified DF's -- D: Use of minitab to obtain F ratio probabilities -- 8: Analysis Of Proportions And Associations -- 8-1: Use of normal distribution with proportions -- 8-2: Comparison between two proportions -- 8-3: Sample size calculation to compare two proportions -- 8-4: Analysis of contingency tables -- 8-5: Minitab practical -- A: Demonstration of a normal fit to the binomial distribution -- B: Sample size calculation -- C: Analysis of a contingency table -- D: Determination of critical X2 values. 9: Analysis Of Variance (ANOVA) -- 9-1: Comparison of means from more than two populations -- 9-2: Mathematical model -- 9-3: Analysis of variance -- 9-4: Summary of variance estimates -- 9-5: Significance test for the F ratio -- 9-6: Standard error (SE) of a treatment mean -- 9-7: Comparison between two treatment means -- 9-8: Least significant difference (LSD) -- 9-9: Making several comparisons among pairs of treatment means -- 9-10: Complete analysis of variance table -- 9-11: Minitab practical -- A: Demonstration of analysis of variance -- B: Analysis of data from example 9-1: with joint types in one column -- C: Re-analysis of data from example 9-1: with joint types in different columns -- 10: Randomized Block Designs -- 10-1: Blocking -- 10-2: Randomised block model -- 10-3: Randomised block analysis -- 10-4: Significance levels -- 10-5: Residuals -- 10-6: Missing values -- 10-7: Minitab practical -- A: Demonstration of the randomised block design -- B: Analysis of data from example 10-1 -- C: Analysis of data from example 10-1 with a missing value -- 11: Factorial Experiments -- 11-1: Definition of a factorial experiment -- 11-2: Definitions -- 11-3: Main effect means -- 11-4: Interaction means -- 11-5: Reasons for using a factorial treatment structure -- 11-6: Statistical analysis of a randomised block factorial experiment -- 11-7: Analysis of a 3 factor experiment -- 11-8: Minitab practical -- A: Analysis of data from 11-1 and 11-2 -- B: Analysis of data from example 11-3 -- C: Designing and analysing a factorial experiment -- D: Recording data using the Microsoft Excel spreadsheet program for input into minitab -- 12: Split-Plot Designs -- 12-1: Definition of a split-plot experimental design -- 12-2: Split-model -- 12-3: Analysis of a split-plot design -- 12-4: Use of split-plot experiments -- 12-5: Minitab practical -- A: Simulation of a split-plot experiment -- B: Analysis of data -- 13: Fitting A Straight Line To Data -- 13-1: Regression line -- 13-2: Fitting a regression line to a set of points -- 13-3: Determining how good a fit has been obtained -- 13-4: Regression and analysis of variance -- 13-5: Proportion of total variation explained by regression -- 13-6: Prediction using a regression line -- 13-7: Correlation coefficient -- 13-8: Minitab practical -- A: Demonstration of regression analysis -- B: Analysis of the data given in example 13-1 -- 14: Comparing Regression Lines -- 14-1: Alternative regression models -- 14-2: Selection of best model to fit data -- 14-3: Minitab practical -- A: Demonstration of model with 2 regression lines -- B: Analysis of data from example 14-1 -- 15: Analysis Of Covariance -- 15-1: Covariance model -- 15-2: Use of a covariate to salvage an experiment -- 15-3: Mathematical model for a covariance analysis -- 15-4: Comparisons following a covariance analysis -- 15-5: Minitab practical -- A: Demonstration of a covariance analysis -- B: Analysis of experimental data -- C: Graphical presentation of results -- 16: Design Of Experiments And Validation Of Data -- 16-1: Introduction -- 16-2: Experimental unit -- 16-3: Use of a control treatment -- 16-4: Replication -- 16-5: Randomisation -- 16-6: Blocking -- 16-7: Paired comparisons -- 16-8: Meeting the assumptions of the analysis -- 16-9: Factors -- 16-10: Split-plots -- 16-11: Use of a covariate -- 16-12: Multiple comparisons following a significant F test -- 16-13: data validation -- 16-14: Redi's experiment -- Index.