Statistics for Agricultural sciences /

Includes bibliographical references and index.

Contents
Preface to Second Edition ....................................................... (vii)
Preface to First Edition ............................................................. (ix)
Acknowledgements ..................................................................... (xi)
PART I
STATISTICAL METHODS
Introduction ................................................................... 3
2 Collection, Classficiation and Tabulation of Data .......... 5
2.1 Collection of Data .................................................. 5
2.2 Classification of Data ............................................. 6
2.3 Tabulation of Data ................................................. 7
3 Frequency Distribution ................................................. 10
3.1 Frequency Distribution ........................................ to
3.2 Diagrammatic Representation ......... ...... ....... .... .... 12
3.3 Graphic Representation ....................................... 17
4 Measures of Location .................................................. 26
4.1 Arithmetic Mean .................................................. 26
4.2 Median ................................................................. 29
4.3 Mode .................................................................... 31
4.4 Geometric Mean .................................................. 32
4.5 Harmonic Mean ................................................... 33
5 Measures of Dispersion ............................................... 38
5.1 Range ................................................................... 38
5.2 Quartile Deviation ................................................ 38
5.3 Mean Deviation .................................................... 40
5.4 Standards Deviation ............................................. 42
5.5 Coefficient ofYariation ........................................ 44
(xiv) Contents
5.6 Statistical Population ............................................ 44
5.7 Sample .................................................................. 45
6. Moments, SKewness and Kurtosis .............................. 49
6.1 Moments ............................................................... 49
6.2 Skewness ............................................................. 49
6.3 Kurtosis ................................................................ 52
7. Elementary Probability .................................................. 57
7.1 Definition of Probability ....................................... 57
7.2 Mutually Exclusive Events ................................... 58
7.3 Mutually Independent Events ............................... 59
7.4 Dependent Events ................................................ 60
7.5 Sub-populations ................................................... 62
7.6 Probability Based on Binomial Distribution .......... 62
8. Binomial and Poisson Distributions .............................. 67
8.1 Binomial Distribution ............................................ 67
8.2 Properties of Binomial Distribution ...................... 68
8.3 Fitting of the Binomial Distribution ...................... 69
8.4 Poisson Distribution ............................................. 70
8.5 Properties of Poisson Distribution ....................... 71
8.6 Fitting of the Poisson Distribution ....................... 71
9. Normal Distribution ...................................................... 75
9.1 Standard Normal Distribution .............................. 76
9.2 Frequency Function ............................................. 77
9.3 Properties of Normal Distribution ....................... 78
9.4 Distribution Function ........................................... 78
9.5 Fitting of the Normal Distribution ....................... 80
10. Tests of Hypotesis ........................................................ 85
10.1 Introduction ......................................................... 85
10.2 One Sample Test .................................................. 87
10.3 Two Sample Test ................................................. 90
(xv) Contents
10.4 Student's t-distribution ......................................... 90
10.5 One sample t-test ................................................. 93
10.6 Two Sample t-test ................................................ 94
10.7 Paired t-test .......................................................... 95
10.8 S.N.D. Test for Proportions ................................ 97
10.9 One-tailed Tests ................................................. 100
II. Chi-Square Distribution .............................................. 107
11.1 Chi-Square Distribution ...................................... 107
11.2 Properties ............... ................... ........ ......... ........ 108
11.3 Ch-square Test of Goodness of Fit ................... 108
11.4 2 x 2 Contingency Table .................................... 109
11.5 r 'X s Contigency Table ........................................ 113
I \.6 Chi-square Test for Genetic Problems ............... 114
11.7 Chi-square Test for Linkage Problems ............... 117
12. Correlation and Regression ........................................ 123
12. I Correlation .......................................................... 123
12.2 Test of Significance of
Simple Correlation Coefficient ........................... 125
J 2.3 Fisher's Z-transformation .................................. 127
J 2.4 Rank Correlation ................................................ 129
12.5 Coefficient of Contigency .................................. 131
12.6 Correlation of Attributes ..................................... 131
12.7 Regression .......................................................... 131
12.8 Regression VS. Correlation ................................. 136
13. Multiple Regression and Correlation ........................... 142
13.1 Introduction ....................................................... 142
13.2 Multiple Linear Regression Based on
Two Independent Variables ................................ 142
13.3 Partial Correlation ............................................... 147
13.4 Multiple Linear Regression with
more than Two Independent Variables ............... 148
(xvi) Contents
14. D2--Statistics and Discriminant Functions ................. 155
14.1 D2-Statistics ....................................................... 155
14.2 Discriminant Functions ...................................... 159
15. Introduction to Probit Analysis ................................... 163
15.1 Introduction ....................................................... 163
15.2 Analysis of Biological Data ................................ 164
15.3 Maximum Likelihood Method ............................ 169
15.4 Application to Economic Data ........................... 173
PART II
EXPERIMENTAL DESIGNS
16. Experimental Designs ................................................. 179
16.1 Introduction ....................................................... 179
16.2 Uniformity Trial ................................................. 180
16.3 Analysis ofYariance ........................................... 181
16.4 Completely Randomized Design ........................ 182
16.5 Duncan's Multiple Range Test.. ......................... 186
16.6 Transformations ................................................. 187
16.7 Randomized Block Design ................................. 189
16.8 Latin Square Design ........................................... 193
16.9 Cross Over Design ............................................. 199
16.10 Factorial Experiments ........................................ 20 I
16.11 Spl it-plot Design ................................................. 228
16.12 Split-split Plot Design ......................................... 238
16.13 Strip Plot Design ................................................ 239
16.14 Analysis of Covariance ...................................... 241
16.15 Tukey's Test of Additivity,,, .. , ............................ 247
16.16 Random Effects Models .................................... 248
16.17 Mixed Models ..................................................... 251
16.18 Hederson Methods ............................................. 252
16.19 Compact Family Block Design .......................... 260
(xvii) Contents
16.20 Simple Lattice Design ........................................ 262
16.21 Combined Analysis of Experiments ................... 267
16.22 Response Surface .............................................. 270
16.23 Path Coefficients Analysis .................................. 276
16.24 Least Squares Procedure-
Two way Analysis of Variance .......................... 280
PART III
SAMPLE SURVEYS, ECONOMIC
AND NON-PARAMETRIC STATISTICS
17. Sampling Methods ...................................................... 293
17.1 Introduction ....................................................... 293
17.2 Simple Random Sampling .................................. 293
17.3 Stratified Random Sampling .............................. 298
17.4 Cluster Sampling ................................................ 303
17.5 Two-stage Sampling .......................................... 310
17.6 Systematic Sampling .......................................... 314
17.7 Non-Sampling Errors ......................................... 315
17.8 Tolerances in the Testing of Seeds .................... 316
18. Economic Statistics .................................................... 321
18.1 Introduction ....................................................... 321
18.2 Analysis of Time-Series Data ............................ 321
18.3 Index Numbers .................................................. 338
18.4 Interpolation ....................................................... 347
19. Non-parametric Statistics ........................................... 353
19.1 Introduction ....................................................... 353
19.2 Parametric vs Non-parametric Tests ................. 355
19.3 One-samples Tests ............................................ 355
19.4 Two Related Sample Tests ................................. 363
19.5 Tests for Two Independent Samples ................. 369
(xviii) Contents
19.6 Tests Based on p Related Samples ..................... 374
19.7 Tests based on p Independent Samples ............. 378
19.8 Coefficient of Concordance ............................... 380
PART IV MULTIVARIATE
STATISTCAL METHODS
20. Multivariate Statistical Methods ................................. 389
20.1 Multivariate Normal Distribution ....................... 389
20.2 Classification by Linear Discriminant Function 402
~0.3 Principal Component Analysis ........................... 407
20.4 Factor Analysis ................................................... 412
20.5 Canonical Correlatons ........................................ 421
References and Bibliography... ................ .. ...................... 427
Appendices ......................................... , ..................... , 431
Index .. . ............................................................. 463