Practical Statistics and Experimental Design for Plant and Crop Science

by Clewer, Alan G.; Scarisbrick, David H.

• ISBN13: 9780471899099
• ISBN10: 0471899097
• Edition: 1st
• Format: Paperback
• Copyright: 2001-02-08
• Publisher: WILEY

Summary

Presents readers with a user-friendly, non-technical introduction to statistics and the principles of plant and crop experimentation. Avoiding mathematical jargon, it explains how to plan and design an experiment, analyse results, interpret computer output and present findings. Using specific crop and plant case studies, this guide presents: * The reasoning behind each statistical method is explained before giving relevant, practical examples * Step-by-step calculations with examples linked to three computer packages (MINITAB, GENSTAT and SAS) * Exercises at the end of many chapters * Advice on presenting results and report writing Written by experienced lecturers, this text will be invaluable to undergraduate and postgraduate students studying plant sciences, including plant and crop physiology, biotechnology, plant pathology and agronomy, plus ecology and environmental science students and those wanting a refresher or reference book in statistics.

Author Biography

Alan G. Clewer and David H. Scarisbrick T. H. Huxley School of Environment, Earth Sciences and Engineering, Imperial College at Wye, Ashford, Kent, UK

Table of Contents

Preface	xi
Basic Principles of Experimentation	1	(8)
Introduction	1	(1)
Field and glasshouse experiments	1	(2)
Choice of site	3	(1)
Soil testing	4	(1)
Satellite mapping	5	(1)
Sampling	6	(3)
Basic Statistical Calculations	9	(7)
Introduction	9	(1)
Measurements and type of variable	9	(1)
Samples and populations	10	(6)
Basic Data Summary	16	(8)
Introduction	16	(1)
Frequency distributions (discrete data)	16	(2)
Frequency distributions (continuous data)	18	(4)
Descriptive statistics	22	(2)
The Normal Distribution, the t-Distribution and Confidence Intervals	24	(14)
Introduction to the normal distribution	24	(1)
The standard normal distribution	25	(2)
Further use of the normal tables	27	(2)
Use of the percentage points table (Appendix 2)	29	(1)
The normal distribution in practice	29	(2)
Introduction to confidence intervals	31	(1)
Estimation of the population mean	31	(1)
The sampling distribution of the mean, μ	32	(1)
Confidence limits for μ when σ is known	32	(2)
Confidence limits for μ when σ is unknown---use of the t-distribution	34	(2)
Determination of sample size	36	(1)
Estimation of total crop yield	36	(2)
Introduction to Hypothesis Testing	38	(11)
The standard normal distribution and the t-distribution	38	(1)
The single sample t-test	39	(3)
The P-value	42	(1)
Type I and Type II errors	43	(1)
Choice of level of significance	44	(1)
The usefulness of a test	45	(1)
Estimation versus hypothesis testing	46	(1)
The paired samples t-test	46	(3)
Comparison of Two Independent Sample Means	49	(14)
Introduction	49	(2)
The Independent Samples t-test	51	(4)
Confidence intervals	55	(1)
The theory behind the t-test	55	(3)
The F-test	58	(1)
Unequal sample variances	59	(1)
Determination of sample size for a given precision	60	(3)
Linear Regression and Correlation	63	(24)
Basic principles of Simple Linear Regression (SLR)	63	(3)
Experimental versus observational studies	66	(1)
The correlation coefficient	67	(1)
The least squares regression line and its estimation	67	(4)
Calculation of residuals	71	(1)
The goodness of fit	72	(2)
Calculation of the correlation coefficient	74	(1)
Assumptions, hypothesis tests and confidence intervals for simple linear regression	75	(8)
Testing the significance of a correlation coefficient	83	(4)
Curve Fitting	87	(15)
Introduction	87	(1)
Polynomial fitting	87	(2)
Quadratic regression	89	(4)
Other types of curve	93	(7)
Multiple linear regression	100	(2)
The Completely Randomised Design	102	(30)
Introduction	102	(1)
Design construction	103	(2)
Preliminary analysis	105	(3)
The one-way analysis of variance model	108	(2)
Analysis of variance	110	(8)
After Anova	118	(5)
Reporting results	123	(1)
The completely randomised design---unequal replication	124	(4)
Determination of number of replicates per treatment	128	(4)
The Randomised Block Design	132	(17)
Introduction	132	(3)
The analysis ignoring blocks	135	(1)
The analysis including blocks	136	(1)
Using the computer	136	(1)
The effect of blocking	137	(1)
The randomised blocks model	138	(3)
Using a hand calculator to find the sums of squares	141	(1)
Comparison of treatment means	142	(2)
Reporting the results	144	(1)
Deciding how many blocks to use	144	(2)
Plot sampling	146	(3)
The Latin Square Design	149	(10)
Introduction	149	(2)
Randomisation	151	(2)
Interpretation of computer output	153	(2)
The Latin square model	155	(1)
Using your calculator	156	(3)
Factorial Experiments	159	(23)
Introduction	159	(1)
Advantages of factorial experiments	160	(3)
Main effects and interactions	163	(2)
Varieties as factors	165	(1)
Analysis of a randomised blocks factorial experiment with two factors	166	(10)
General advice on presentation	176	(1)
Experiments with more than two factors	177	(2)
Confounding	179	(1)
Fractional replication	180	(2)
Comparison of Treatment Means	182	(31)
Introduction	182	(1)
Treatments with no structure	182	(9)
Treatments with structure (factorial structure)	191	(4)
Treatments with structure (levels of a quantitative factor)	195	(7)
Treatments with structure (contrasts)	202	(11)
Checking the Assumptions and Transformation of Data	213	(13)
The assumptions	213	(6)
Transformations	219	(7)
Missing Values and Incomplete Blocks	226	(12)
Introduction	226	(1)
Missing values in a completely randomised design	226	(3)
Missing values in a randomised block design	229	(5)
Other types of experiment	234	(1)
Incomplete block designs	234	(4)
Split Plot Designs	238	(18)
Introduction	238	(1)
Uses of this design	238	(2)
The skeleton analysis of variance tables	240	(2)
An example with interpretation of computer output	242	(8)
The growth cabinet problem	250	(2)
Other types of split plot experiment	252	(1)
Repeated measures	252	(4)
Comparison of Regression Lines and Analysis of Covariance	256	(16)
Introduction	256	(1)
Comparison of two regression lines	256	(4)
Analysis of covariance	260	(1)
Analysis of covariance applied to a completely randomised design	260	(5)
Comparing several regression lines	265	(5)
Conclusion	270	(2)
Analysis of Counts	272	(21)
Introduction	272	(1)
The binomial distribution	272	(3)
Confidence intervals for a proportion	275	(2)
Hypothesis test of a proportion	277	(2)
Comparing two proportions	279	(1)
The chi-square goodness of fit test	280	(4)
r x c contingency tables	284	(2)
2 x c contingency tables: comparison of several proportions	286	(1)
2 x 2 contingency tables: comparison of two proportions	287	(2)
Association of plant species	289	(1)
Heterogeneity chi-square	290	(3)
Some Non-parametric Methods	293	(14)
Introduction	293	(1)
The Sign test	294	(2)
The Wilcoxon single-sample test	296	(1)
The Wilcoxon matched pairs test	297	(2)
The Mann-Whitney U test	299	(3)
The Kruskal-Wallis test	302	(2)
Friedman's test	304	(3)
Appendix 1: The normal distribution function	307	(1)
Appendix 2: Percentage points of the normal distribution	308	(1)
Appendix 3: Percentage points of the t-distribution	309	(1)
Appendix 4a: 5 per cent points of the F-distribution	310	(2)
Appendix 4b: 2.5 per cent points of the F-distribution	312	(2)
Appendix 4c: 1 per cent points of the F-distribution	314	(2)
Appendix 4d: 0.1 per cent points of the F-distribution	316	(2)
Appendix 5: Percentage points of the sample correlation coefficient (r) when the population correlation coefficient is 0 and n is the number of X, Y pairs	318	(1)
Appendix 6: 5 per cent points of the Studentised range, for use in Tukey and SNK tests	319	(2)
Appendix 7: Percentage points of the chi-square distribution	321	(1)
Appendix 8: Probabilities of S or fewer successes in the binomial distribution with n `trials' and p=0.5	322	(1)
Appendix 9: Critical values of T in the Wilcoxon signed rank or matched pairs test	323	(1)
Appendix 10: Critical values of U in the Mann-Whitney test	324	(3)
References	327	(1)
Further reading	328	(1)
Index	329