Abstract
The goal is to determine the variability of yields in Type II and III agricultural experiments involving improved yields in Murangiri, Kenya, while determining an appropriate model that ex- plains this variability. In this study, we investigated the effects of different treatments ranging from organic, inorganic and mixture of the two on the maize yields in Murangiri, Tharaka Nithi constituency in Kenya. We applied three statistical models to the data obtained from Type II and Type III experiments namely; FIXED EFFECTS MODEL, GENERALIZED LINEAR MODEL (GLM) and MIXED EFFECTS MODEL. We focused on interpretations and computation of model parameters and also investigated which model best fits the two datasets from the two experiments. Our study found that the treatments in general had the effects on the Maize yields in the two experiments as shown by all models fitted since the p-values of both mixed and fixed effect model are less than level of significance 0.05 while for GLM by using the deviance we showed that the fitted model with treatments were significant on both cases. On the best model, we used the model comparisons Akaike’s Information Criterion (AIC) to determine model that best fit the two datasets from the Type II and Type III experiments respectively. The study found that the mixed model was the best among the three models considered under this study as it was having the smallest values of AIC 169.071 and 280.01 for Type II and Type III experiments as indicated in tables 5 and 9 respectively. Despite the mixed model showing the smallest AIC value among the three models, the differences among these values were not very significant, implying that all three models could be used to explain the variability of yields in Type II and III agricultural experiments.
Table of Contents
Abstract ii
Declaration and Approval iv
Dedication vi
List of Figures ix
List of Tables x
Acknowledgments xi
CHAPTER ONE
1 INTRODUCTION 1
1.1 RATIONALE 1
1.2 BACKGROUND 2
1.3 PROBLEM STATEMENT 3
1.4 RESEARCH OBJECTIVES 4
1.4.1 OVERALL OBJECTIVES 4
1.4.2 SPECIFIC OBJECTIVES 4
1.5 SIGNIFICANCE OF THE STUDY 5
CHAPTER TWO
2 LITERATURE REVIEW 6
CHAPTER THREE
3 RESEARCH METHODOLOGY 9
3.1 RESEARCH DESIGN 9
3.1.1 Data source and its description 9
3.1.2 Study variables 9
3.1.3 Exploratory data analysis 9
3.2 STATISTICAL MODELS 10
3.2.1 Fixed effects model 10
3.2.2 Generalized Linear Model 10
3.2.3 Mixed Effect Model 11
3.3 MODEL COMPARISON TECHNIQUES 13
3.4 MODEL CHECKING TECHNIQUES FOR MIXED EFFECT MODEL 13
3.5 DIAGNOSTIC TESTS 14
3.5.1 Shapiro-Wilk Test 14
3.5.2 Normality plots. 14
3.5.3 Ethical Considerations. 14
CHAPTER FOUR
4 DATA ANALYSIS AND RESULTS 15
4.1 Introduction 15
4.2 Exploratory Data Analysis 15
4.2.1 Descriptive statistics of field data 15
4.3 Diagnostics test of Normality 16
4.3.1 SHAPIRO –WILK NORMALITY TEST 17
4.4 Inferential Statistics 17
4.4.1 Fixed effect model 17
4.4.2 Generalized Linear model (GLM) 19
4.4.3 Mixed Model 20
4.4.4 Model comparisons 21
4.5 Statistical models fitted Type III experiment data 21
4.5.1 Fixed effect model 21
4.5.2 Generalized Linear model (GLM) 23
4.5.3 Mixed Model 24
4.5.4 Model comparisons 25
CHAPTER FIVE
5 CONCLUSIONS AND RECOMMENDATION 26
5.1 Introduction 26
5.1.1 Interpretations of results 26
5.1.2 Recommendations 27
References 28
APPENDIX A 30
List of Figures
Figure 1. Strip chart for Type II and Type III data. 15
Figure 2. Box Plot for Type II and Type III data. 16
Figure 3. Normality plot. 16
Figure 4. Plot of residuals & fitted values and QQ norm for the fixed effect model 18
Figure 5. Plot of residuals & fitted values and QQ norm for the fixed effect model 22
List of Tables
Table 1. Shapirowilk normality test 17
Table 2. Fixed effect model 17
Table 3. Results for GLM Type II experiment 19
Table 4. Results for Mixed model 20
Table 5. Model Comparison Results 21
Table 6. Fixed effect model – Type III 21
Table 7. Results from generalized linear model (GLM) assuming the Gaussian family 23
Table 8. Results for Mixed model 24
Table 9. Model Comparison Results 25
CHAPTER ONE
INTRODUCTION
1.1 RATIONALE
In agricultural research, there are three types of experiments Type I, II, and III that can be con- ducted to improve the yield production while minimizing costs. A Type I experiment is one that is designed and managed by the researcher. A Type II experiment is designed by the researcher and managed by the farmer. The researcher looks for the farmer contribution in the designed experiments. The farmer provides the land, and the researcher monitors the treatments that were successful at the on-station level on the farmer’s field. The farmer is provided instructions and researcher monitors farmer contribution. This provides some aspect of variation that is not explained by the treatment effect. A Type III experiment is designed and managed by the farmer.
The farmers go to the on-station and learn various methodologies of interest. They then utilize their knowledge to replicate some of the experiments that they found useful. It is expected that the Type III experiment will have the most variability when a comparison is done with the other experimental units of Type I and II. This is because there is no design structure on the farms under Type III when compared to those on Type I and II that are designed by the researcher. The on- station designs would likely have less variability due to the environment, treatments used and effective monitoring systems. The purpose of this study is to determine the variability in Type II and III experiments of improved yields.
1.2 BACKGROUND
The study was conducted in Tharaka Nithi county, Tharaka constituency. The primary economic activities of this county are subsistence dairy farming, rearing of goats and sheep, tea farming, and coffee planting. Farmers from this study used different treatments on their maize crops. The treatments were organic, inorganic, or a mixture of both. Organic farming entails the cultivating plants or the rearing of animals using natural methods. It involves using cover crops, manure (plant and animal), crop rotation, and other techniques to control weeds, pests, and diseases. Inorganic farming entails the use of synthetic fertilizers and pesticides to improve yield production (Kakar et al., 2020 [13]).
The organic treatments used on the farms were Mucuna pruriens, Tithonia diversifolia, Calliandra haematocephala, Crotalaria retusa, Leucaena leucocephala and Manure. Mucuna pruriens is used as a green manure because it introduces nitrogen to the soil making it more fertile. Tithonia diversifolia decomposes rapidly as releases nitrogen, phosphorous and potassium into the soil improving its fertility and increasing yield production (Ajao & Moteetee, 2017 [3]). Calliandra haematocephala is an important cover crop as it provides nitrogen to the soil. Crotalaria retusa also introduces nitrogen into the soil as has been shown to improve soil fertility.
Leucaena leucocephala is a good cover crop and also adds nitrogen into the soil. The manure used by most farmers came from cows, goats and sheep. According to Moyin-Jesu, 2012 [16], Liquid Cattle Manure (LCM) is very useful as a treatment as it contains nitrogen that can be used to enhance plant growth and improve yield production. LCM can also improve the soil salinity as well as increasing micro nutrients in it. The inorganic treatment used was NPK (nitrogen, phosphorous, and potassium) based fertilizer. Nitrogen improves the leaf structure enabling the plants to produce better yield. Phosphorous assists in seed germination and root development, while potassium is vital for maintaining growth while enabling the plant become disease resistant.
1.3 PROBLEM STATEMENT
A lot has been done on organic and inorganic fertilizers and their effect in improving yields. More has been done on different agricultural experimental designs, and discussions generated about the integrated soil fertility management (Dafallah, 2017 [9] & Bailey-Serres et.al., 2019 [4]). Some of these studies focus on treatments used in the on-farm and on-station experiments and their effect on yield production, but do not discuss about the variability of these experiments (Acer et.al, 2004; [1]; MoyinJesu, 2012 [16]). Not much has been done on determining the variability between the Type II and Type III experiments.
In controlled experiments such as the on-station researcher designed and managed, it is possible to have experimental plots receiving the same treatment but exhibiting different outcomes showing the existence of variability. It is also expected that experiments that are farmer designed and man- aged at the on-farm level will show more variability than those at the on-station level managed by the researcher. The variability may be attributed to environmental factors such as weather, climate, pests, soils and topography. Gupta et.al (2015) [11] posited that variability in agricultural designs may be wanted and desirable, or unwanted and undesirable implying the diversity of these experiments and the need to conduct more research. Proper experimentation designs ensure the identification and isolation of natural variation so that true effects due to treatments can be measured with some degree of accuracy.
To minimize field variability, blocking is done on the fields so that the slope and soil characteristics of the land are taken into consideration. There are several methods that are used to measure the variability in agricultural designs. In this study we will discuss the variability using Analysis of Variance (ANOVA), Generalized Linear Models (GLM) and Mixed Modelling methods and determine which best model to use for Type II and III experiments.
1.4 RESEARCH OBJECTIVES
1.4.1 OVERALL OBJECTIVES
To determine the variability in type II and III experiments involving improved yields in Murangiri, Kenya.
1.4.2 SPECIFIC OBJECTIVES
1. To determine the best model that explains the variability of yields in type II and III experiments involving improved yields in Murangiri, Kenya.
2. To determine the variability of yields in type II and III experiments involving improved yields in Murangiri, Kenya.
1.5 SIGNIFICANCE OF THE STUDY
Our study reveals the relevance of statistics to answer specific questions in the can be controlled as the researcher can design the on-station farms, observe the environment and control the treatments used According to Bailey-Serres et.al (2019) [4], future food security will heavily rely on trans-formative methods used to improve yield production, due to environmental factors caused by climate change. As the world population increases, it is imperative that we utilize our resources accordingly, while ensuring that there will not be any shortage of food at any time. Heat waves, the continual increase in droughts, torrential rainfall and other extreme weather patterns that are seen across the world have a dismal effect on agricultural production, and are predicted to continue doing so in future BaileySerres et.al (2019) [4]. This sensitizes our need to look at ways of improving food production and yields for a sustainable future.
One of the sustainable development goals created through the United Nations Development Pro- gram (UNDP) focuses to end hunger, achieve food security and improved nutrition, and promote sustainable agriculture (The 2030 Agenda and the Sustainable Development Goals: An Opportunity for Latin America and the Caribbean, 2018). While not all variability such as the experimental error can be explained, the study will explain some of the variability found in the Type II and III experimental methods and possibly look for patterns on the improved yields to be used for recommendations to future researchers and farmers.
Poverty is the leading cause of death in many developing countries due to fluctuations in the availability of food (Bationo et al., 2011 [19]). To slow down this food insecurity problems in the developing countries while empowering their communities to be self-sufficient, agricultural researchers need to step up their continual efforts to improve food security by developing sustainable programs that can work for those communities. Poverty can be decreased by ensuring agricultural production is high so that majority of these countries facing food security issues can be self-sustained.
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