ABSTRACT

It is true that on many important aspects of experimentation, the statistician has no expert knowledge. Nevertheless, in recent years, researchers have turned increasingly to statisticians for help: In planning and designing of their experiments and  In drawing valid conclusions from the results. Thus, this project work is geared towards analyzing factorial experiments. The factorial experiment used, involved two factors: fertilizer and cropping system. Each of which is in three levels with three replicates. The data used for analysis were secondary data collected f'im Mr. V.E. Osodeke in the college of crop and soil sciences, Michael Okpara University of Agriculture, Umudike. The ultimate objective is to present methods of analyzing factorial experiments. Whereas, the specific objectives are to show the advantages of factorial experiments over CRD and RCBD and to highlight basic requirements in designing factorial experiments. Data were analyzed by the general (conventional) method of factorial, CRD, RCBD and Yates' algorithm for 2'< and 3k series. Based on the analysis, fertilizer has significant effect on yield of maize. Whereas, cropping system and its irtevaction with fertilizer hive no significant effect on yield of maize. The orthogonal contrast method lor decomposition of degrees of freedom and sums of squares showed that there is no significant difference between 30kg and 60kg levels of fertilizer. Consequently, we recommend 30kg level of fertilizer since it minimizes cost more than 60kg level and it is as good as 60kg level.

TABLE OF CONTENTS

PAGE

TITLE PAGE

CERTIFICATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

TABLE OF CONTENTS v-vi

ABSTRACT vii-viii

CHAPTER ONE

1.0 INTRODUCTION 1

1.1 BACKGROUNbOFSTUDY 1

1,2 STATEMENTOF PROBLEM 2

1.3 MOTIVATION 2

1.4 OBJECTIVE OF THE STUDY 3

1.5 SCOPE OFTHE STUDY 3

1.6 DATA SOURCE 3

1.7 METHOD OF ANALYSIS 4

1.8 ASSUMPTIONS 4

CHAPTER TWO

2.0 LITERATURE REVIEW 6

2.1 ANALYSIS OF VARIANCE (ANOVA). 6

2.2 FACTORIAL EXPERIMENTS 7

2.3 STEPS IN FACTORIAL EXPERIMENTION 8

2.4 MEANS SEPARATION 11

2.4.1 LEAST SIGNIFICANCE DIFFERENCE (LSD) 12

2.4.2 TUKEY'S SIGNIFICANT DIFFERENCE (TSD) 13

2.4.3 ORTHOGONAL CONTRASTS FOR COMPARISON 14

2.5 IMPROVING PRECISION 15

2.5.1 INCREASING REPLICATION 15

2.5.2 SELECTION OF TREATMENT 16

CHAPTER THREE

3.0 BASIC STATISTICAL TECHNIQUES 17

3.1 CHI-SQUARES (72 ).TESTS 17

3.2 GOODNESS OF FIT TEST 18

3.3 TEST FOR INDEPENDENCE 23

3.4 TEST FOR HOMOGENEITY OF VARIANCES 26

3.5 ONE-SAMPLE RUNS TEST FOR RANDOMNESS 30

CHAPTER FOUR

4.0 ANALYSIS 35

4.1 SINGLE-FACTOR (ONE-WAY) ANOVA. 35

4.2 SINGLE-FACTOR (TWO-WAYS) ANOVA. 40

4.3 GENERAL FACTORIAL EXPERIMENT 44

4.4 YATES' ALGORITHM FOR 2'<SERIES 54

4.5 YATES' ALGORITHM FOR 3'<SERIES 63

CHAPTER FIVE

5.0 SUMMARY, CONCLUSION AND RECOMMEDATION 69

5.1 SUMMARY 69

5.2 CONCLUSION AND RECOMMENDATION 71

APPENDICES 72

REFERENCES