TY - BOOK AU - Rao, G. N. TI - Statistics for Agricultural sciences SN - 978-81-7800-141-8 U1 - e-book (NRM) PY - 2012/// CY - Hyderabad PB - BS Publications N1 - Includes bibliographical references and index N2 - 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 ER -