Practical Statistics and Experimental Design for Plant and Crop Science

Cover......Page 1
Practical Statistics and Experimental Design for Plant and Crop Science......Page 5
©......Page 6
Contents......Page 7
Preface......Page 13
1.2 Field and glasshouse experiments......Page 17
1.3 Choice of site......Page 19
1.4 Soil testing......Page 20
1.5 Satellite mapping......Page 21
1.6 Sampling......Page 22
2.2 Measurements and type of variable......Page 25
2.3 Samples and populations......Page 26
3.2 Frequency distributions (discrete data)......Page 32
3.3 Frequency distributions (continuous data)......Page 34
3.4 Descriptive statistics......Page 38
4.1 Introduction to the normal distribution......Page 40
4.2 The standard normal distribution......Page 41
4.3 Further use of the normal tables......Page 43
4.5 The normal distribution in practice......Page 45
4.7 Estimation of the population mean, µ......Page 47
4.9 Confidence limits for µ when σ is known......Page 48
4.10 Confidence limits for µ when σ is unknownuse—of the t-distribution......Page 50
4.12 Estimation of total crop yield......Page 52
5.1 The standard normal distribution and the t-distribution......Page 54
5.2 The single sample t-test......Page 55
5.3 The P-value......Page 58
5.4 Type I and Type II errors......Page 59
5.5 Choice of level of significance......Page 60
5.6 The usefulness of a test......Page 61
5.8 The paired samples t-test......Page 62
6.1 Introduction......Page 65
6.2 The Independent Samples t-test......Page 67
6.4 The theory behind the t-test......Page 71
6.5 The F-test......Page 74
6.6 Unequal sample variances......Page 75
6.7 Determination of sample size for a given precision......Page 76
7.1 Basic principles of Simple Linear Regression (SLR)......Page 79
7.2 Experimental versus observational studies......Page 82
7.4 The least squares regression line and its estimation......Page 83
7.5 Calculation of residuals......Page 87
7.6 The goodness of fit......Page 88
7.7 Calculation of the correlation coefficient......Page 90
7.8 Assumptions, hypothesis tests and confidence intervals for simple linear regression......Page 91
7.9 Testing the significance of a correlation coefficient......Page 99
8.2 Polynomial fitting......Page 103
8.3 Quadratic regression......Page 105
8.4 Other types of curve......Page 109
8.5 Multiple linear regression......Page 116
9.1 Introduction......Page 118
9.2 Design construction......Page 119
9.3 Preliminary analysis......Page 121
9.4 The one-way analysis of variance model......Page 124
9.5 Analysis of variance......Page 126
9.6 After ANOVA......Page 134
9.7 Reporting results......Page 139
9.8 The completely randomised design—unequal replication......Page 140
9.9 Determination of number of replicates per treatment......Page 144
10.1 Introduction......Page 148
10.2 The analysis ignoring blocks......Page 151
10.4 Using the computer......Page 152
10.5 The effect of blocking......Page 153
10.6 The randomised blocks model......Page 154
10.7 Using a hand calculator to find the sums of squares......Page 157
10.8 Comparison of treatment means......Page 158
10.10 Deciding how many blocks to use......Page 160
10.11 Plot sampling......Page 162
11.1 Introduction......Page 165
11.2 Randomisation......Page 167
11.3 Interpretation of computer output......Page 169
11.4 The Latin square model......Page 171
11.5 Using your calculator......Page 172
12.1 Introduction......Page 175
12.2 Advantages of factorial experiments......Page 176
12.3 Main effects and interactions......Page 179
12.4 Varieties as factors......Page 181
12.5 Analysis of a randomised blocks factorial experiment with two factors......Page 182
12.6 General advice on presentation......Page 192
12.7 Experiments with more than two factors......Page 193
12.8 Confounding......Page 195
12.9 Fractional replication......Page 196
13.2 Treatments with no structure......Page 198
13.3 Treatments with structure (factorial structure)......Page 207
13.4 Treatments with structure (levels of a quantitative factor)......Page 211
13.5 Treatments with structure (contrasts)......Page 218
14.1 The assumptions......Page 229
14.2 Transformations......Page 235
15.2 Missing values in a completely randomised design......Page 242
15.3 Missing values in a randomised block design......Page 245
15.5 Incomplete block designs......Page 250
16.2 Uses of this design......Page 254
16.3 The skeleton analysis of variance tables......Page 256
16.4 An example with interpretation of computer output......Page 258
16.5 The growth cabinet problem......Page 266
16.7 Repeated measures......Page 268
17.2 Comparison of two regression lines......Page 272
17.4 Analysis of covariance applied to a completely randomised design......Page 276
17.5 Comparing several regression lines......Page 281
17.6 Conclusion......Page 286
18.2 The binomial distribution......Page 288
18.3 Confidence intervals for a proportion......Page 291
18.4 Hypothesis test of a proportion......Page 293
18.5 Comparing two proportions......Page 295
18.6 The chi-square goodness of fit test......Page 296
18.7 r x c contingency tables......Page 300
18.8 2 x c contingency tables: comparison of several proportions......Page 302
18.9 2 x 2 contingency tables: comparison of two proportions......Page 303
18.10 Association of plant species......Page 305
18.11 Heterogeneity chi-square......Page 306
19.1 Introduction......Page 309
19.2 The Sign test......Page 310
19.3 The Wilcoxon single-sample test......Page 312
19.4 The Wilcoxon matched pairs test......Page 313
19.5 The Mann-Whitney U test......Page 315
19.6 The Kruskal-Wallis test......Page 318
19.7 Friedman's test......Page 320
Appendix 1: The normal distribution function......Page 323
Appendix 2: Percentage points of the normal distribution......Page 324
Appendix 3: Percentage points of the t-distribution......Page 325
Appendix 4a: 5 per cent points of the F-distribution......Page 326
Appendix 4b: 2.5 per cent points of the F-distribution......Page 328
Appendix 4c: 1 per cent points of the F-distribution......Page 330
Appendix 4d: 0.1 per cent points of the F-distribution......Page 332
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......Page 334
Appendix 6: 5 per cent points of the Studentised range, for use in Tukey and SNK tests......Page 335
Appendix 7: Percentage points of the chi-square distribution......Page 337
Appendix 8: Probabilities of S or fewer successes in the binomial distribution with n 'trials' and p = 0.5......Page 338
Appendix 9: Critical values of Tin the Wilcoxon signed rank or matched pairs test......Page 339
Appendix 10: Critical values of U in the Mann-Whitney test......Page 340
References......Page 343
Further reading......Page 344
Index......Page 345