ANALYSIS OF VARIANCE OF THE YIELD OF SOME SELECTED MILLET VARIETIES(A CASE STUDY OF KADUNA STATE AGRICULTURAL DEVELOPMENT PROJECT, KADUNA)

ANALYSIS OF VARIANCE OF THE YIELD OF SOME SELECTED MILLET VARIETIES(A CASE STUDY OF KADUNA STATE AGRICULTURAL DEVELOPMENT PROJECT, KADUNA)  



DECLARATION


CERTIFICATION


DEDICATION













ACKNOWLEDGEMENT

           In the name of Allah, the most beneficent, the most merciful. I wish to express my profound gratitude to Almighty Allah for sparing my life and granting me the opportunity for attaining to this level of education. To him I say ALHAMDULILLAH!

          With due respect and honor, I wish to appreciate and express my profound gratitude to my humble supervisor, Professor S.U. Gulumbe for his purposeful guidance, valuable suggestion and corrections in all mistakes in this project, despite tight and occupied nature of his schedule once more I say thank you Sir, May Almighty Allah reward you abundantly. I will also like to express my sincere appreciation to Malam shamsudeen suleman who dedicated his time for making all necessary corrections and also his guidance for this work to be a reality, may Allah reward you and your family with his bounties in the world and hereafter Ameen. And i will also like to express my sincere appreciation to my other lecturers. My most sincere and loving heart goes to my dearest adored Father Alhaji Adamu Umaru Gadzama for his wonderful patience, financial, moral and intellectual support and to my beloved mother Hajiya Hauwa’u Buba Chul for her prayers. I owe a profound gratitude to my brother and sisters at home such as Salisu, Abdullahi, Umaru, Halima, Aisha, Amina, Bilkisu Wasila, Zainab and others, and also to   all my friends and course mates especially Usman Aliyu Sta, Mu’azu Muhammad, Muhammad Yahya, Faruq Umar Gwandu, Mudassir Lailaba, Salisu Suleiman, Zahradeen Magayaki. I will like to express my sincere appreciation to two persons Aliyu Buba and Yusuf Buba. My caring heart goes to Alhaji Musa Buba Chul, Alhaji Abdurrahman Buba Chul, Alhaji Yunusa Buba Chul and Ahaji Muhammad Adamu Gadzama for their support and my entire remaining course mate for their unfailing love and support.





LIST OF TABLES

Table3.1 data arrangement for a two-factor factorial design………………………………17

Table3.2 Treatment display………………………………………………………………...18

Table3.3 Fractional treatment combination………………………………………………..18

Table3.4 Analysis of variance table for the two factor two effect model…………………22

Table4.1 Presentation of data………………………………………………………………25

Table4.2 Data analysis……………………………………………………………………..27

Table4.3 Factorial fit………………………………………………………………………28

Table4.4 General linear model……………………………………………………………..30


LIST OF FIGURES

Figure4.1 Normal probability plot of the residual…………………………………………..29

Figure4.2 residual versus the fitted value…………………………………………………...29

Figure4.3 Residual versus the order of the data…………………………………………….30

Figure4.4 Normal probability plot the residual……………………………………………..32

Figure4.5 Residual versus the fitted values………………………………………………...32

Figure4.6 Residual versus the order of the data……………………………………………33










ABSTRACT

This project is aimed at conducting Analysis of variance for the yield of some selected millet varieties (a case study of Kaduna State Agricultural development project, Kaduna). The data is obtained from Kaduna state Agricultural development project (KADP). It covers a period of 5years, from 2007 to 2011 and constitutes only Kaduna north and Kaduna south. Analysis of variance was conducted for the selected millet varieties by the factorial fit and general linear model, some plots; were made using a statistical software called MINTAB. In factorial fit, the p-value (0.013) corresponding to the main effects is less than the level of significance (0.05) and the p-value (0.286) corresponding to the 2-way interaction is greater than the level of significance (0.05). This shows that the millets and fertilizers differs significantly and their interaction do not differ significantly. Thus, in the general linear model, the p-value (0.471) corresponding to the fertilizer level is greater than the level of significance (0.05) and the p-value (0.004) corresponding to the millet varieties is less than the level of significance (0.05), also the p-value (0.666) corresponding to the interaction of fertilizer level*millet varieties is greater than the level of significance (0.05). This shows that the fertilizer levels have no significance differences, and the millet varieties differs significantly in yield, while the interaction of the fertilizer and millet do not have any significant differences. The plots of factorial fit and general linear model have the same meaning. 





TABLE OF CONTENT

TITLE PAGE……………………………………………………………………………………...i

DECLARATION…………………………………………………………………………………ii

CERTIFICATION………………………………………………………………………………..iii

DEDICATION…………………………………………………………………………………...iv

ACKNOWLEDGEMENT……………………………………………………………………….v

LIST OF TABLES……………………………………………………………………………….vi

LIST OF FIGURES……………………………………………………………………………...vi

ABSTRACT…………………………………………………………………………………….vii

TABLE OF CONTENT…………………………………………………………………………viii

CHAPTER ONE………………………………………………………………………….1

Introduction……………………………………………………………………....1

1.1 Background of the study………………………………………………………….1

1.2 Statement of problems…………………………………………………………….3

1.3 Aim and Objectives……………………………………………………………….3

1.4 Significance of the study………………………………………………………….4

1.5 Scope and limitation of the study…………………………………………………4

1.6 Definition of terms………………………………………………………………..5

CHAPTER TWO …………………………………………………………………………6

Introduction…………..…………………………………………………………..6

2.1 Literature review………………………………………………………………….6

CHAPTER THREE……………………………………………………………………...14

3.0 Introduction……………………………………………………………………...14

3.1 Population to be study…………………………………………………………...14

3.2 Method of data collection………………………………………………………..14

3.3 Sampling procedure……………………………………………………………...15

3.4 Method of data analysis………………………………………………………….15

3.5 Analysis of variance……………………………………………………………...15

3.5.1 Statistical tool…………………………………………………………………….16

3.6 Hypothesis………………………………………………………………………..19

3.6.1 General procedure for hypothesis tests…………………………………………..20

3.7 Effect estimation…………………………………………………………………20

3.8 Software analysis………………………………………………………………...23

3.8.1 Validating Anova Analysis………………………………………………………24

CHAPTER FOUR……………………………………………………………………….25

Data presentation and analysis…………………………………………………..25

4.1 Data presentation………………………………………………………………...25

CHAPTER FIVE………………………………………………………………………..33

Introduction……………………………………………………………………..34

5.1 Discussion of findings………………………………………………………….. 34

5.2 Recommendation………………………………………………………………..35

5.3 Conclusion……………………………………………………………………….36

REFERENCES………………………………………………………………………….37















                                                   CHAPTER ONE

INTRODUCTION 

Although millet is most often associated as the main ingredient in bird seed, it is not just "for the birds." Creamy like mashed potatoes or fluffy like rice, millet is a delicious grain that can accompany many types of food. As with most grains, millet is available in markets throughout the year.

1.1        BACKGROUND OF THE STUDY 

                Millets are group of highly variable small-seeded grasses, widely grown around the world as cereal crops or grains for both human food and fodder. They do not form a taxonomic group, but rather a functional or agronomic one. Millet are important crops in the semi-arid tropics of Asia and Africa (especially in India, Nigeria and Niger), with 97% of millet production in developing countries. The crop is favoured due its productivity and short growing season under dry, high temperature conditions.

              The most widely grown millet is pearl millet, which is an important sized crop in India and parts of Africa. Finger millet, proso millet, foxtail millet are also important crops species. In the developed world, millets are less important. For example, in the United States the only significant crop is proso millet, which mostly grown for bird seed.

Pearl millet (pennsisetum glaucum (L) R. Br) is one of the four most important cereals (rice, maize, sorghum and millet) grown in the tropics (The Syngenta Foundation for Sustainable Agriculture, 2002). It is believed to have descended from a West Africa wild grass which was domesticated more than 40,000 year ago (National Research Council, 1996). It spread from there to East Africa and then to India. Today millet is a food staple for more 500 million people.     

Against this background, there is a need for promoting Agricultural productivity which can hardly be over emphasized. Over the years, agricultural research has received government attention. Consequently, various agricultural development projects have been established across the country. Such as Bauch state agricultural development project, Borno state agricultural development project, Kaduna state agricultural development project, Sokoto state agricultural development project, katsina state agricultural and rural development project, Abia state agricultural development project and Anambra state agricultural development project.

       Accordingly, the Kaduna state Agricultural Development Project (KADP) is the agricultural extension delivery arm of the state ministry of agriculture with sole aim of achieving agricultural development especially in all year round food and cash crops, livestock and fishery production.

The statistical approach to experimental design is necessary if we wish to draw meaningful conclusion from the data. When the problem involved data are subject to experimental error, statistical methodology is the only objective approach to analysis. Many of the early applications of experimental design methodology were in agricultural and, biological sciences. As a result, many of its terminology are of agricultural background. Modern day experimental designs are widely employed in all field of enquiry. Agricultural science, biology, engineering, the physical science, the social science and other discipline where the statistical approach to the design and analysis of experiment is an accepted practice. 

               To arrive at meaningful and result oriented experiment, appropriate experimental design and proper statistical analysis of data are two interlocking factors that determine the success of any experimentation.

               By the statistical design of experiment, we refers to the process of planning the experiment so that appropriate data that can be analyzed by statistical method will collected, resulting in valid and objective conclusion.

1.2       STATEMENT OF THE PROBLEMS

Despite Nigeria is one of the major millet production in the world after India, it rank 2nd out of 11 countries that produces millet in the world with the average of 4,884,890(tonnes) yearly. Also it the largest producer being in west Africa by 41%.

Millet are consumed as staple food, drinks & other uses for millions of people in Nigeria. Being high energy-nutritious grain make them useful component of dietary and nutritional balance in food. However, we shall see the continue and future importance of millet.        

1.3       AIM AND OBJECTIVES OF THE STUDY

               The aim of this project is to study factorial experiment involving two varieties of millet in Kaduna (north and south) in conjunction with twelve fertilizer rates with the following objectives.

To examine if there is significant differences in yield between the two varieties of millet and effective of using both organic and inorganic fertilizer.

To determine if there is significant difference among the twelve fertilizers rates and evaluate the yield of millet varieties to different fertilizer amendment.

To determine if there is significant interaction effect between the varieties of millet and fertilizer rate and study the differences in the yield of millet in northern and southern part of the state.

1.4 SINIFICANCE OF THE STUDY

               The research study can serve as a yardstick for stakeholders and investors to provide knowledge and insight by explaining and enlightening them on the features and characteristics between the varieties of millet produced by farmers in northern and southern Kaduna. 

The research study can also help agricultural institution on how to improve and innovate new methods of agro enhanced millet using the data and estimation analyzed from this research.

The study also examines and explains the numerations and proportions of how to combine the different levels of fertilizer used in farming.

Also, the study provides an understanding and conception of crop- fertilizer interaction between millets and fertilizers for the purpose of in sighting as to how different species of millet can fit for different types of fertilizer. 

1.5     SCOPE AND LIMITATION OF THE STUDY

               The relatively small size of the sample limits generalization of the research outcome. All samples are collected from Kaduna state Agricultural development project (KADP) which may or may not be enough to generalize the whole population. This also implies that its analysis and interpretation of result could not be conclusive in generalizing the study.





1.6      DEFINITION OF TERMS

Millet: are group of highly variable –seeded grasses, widely grown around the World as cereal crops or grains for both human food and fodder.

Fertilizer: an organic or synthetic substance usually added or spread onto soil to Increase its ability to support plant growth.

Organic fertilizer: are fertilizer derived from animal or vegetable matter. (e.g. Compost, manure).

Inorganic manure: is comprised of synthetic, artificial ingredients manufactured ready to use on plant.

                        

                                                                  









CHAPTER TWO

2.0 INTRODUCTION

This chapter deals with the collection of other relevant research works that will provide basis for the present research work. So a number of research have been carried out on the analysis of variance of the yield of millet varieties, in this chapter a review of literature on these previous researches would be discussed. 

2.1 LITERATURE REVIEW

Several studies conducted in eastern (Machakos, Kitui) and western provinces of Kenya have shown that adoption of improved finger millet cultivars, suitable plant densities and use of nitrogen (N) and Phosphorus (P) fertilizers (20 kg N and P  to 60 kg N and P ) can increase millet yields significantly (Whiteman, et al.1981). Fertiliser of 25 kg P and 25 kg N is used in western, and compost in eastern Kenya, (M` Ragwa: personal communication). The recommended rate of fertilizers in sorghum and Finger millet by Kakamega Research Centre is 20 kg P 205  and 20 kg N , or 10t  FYM (KARI, 1994). During a transect walk of a PRA exercise in 1994 in Chobosta village, Soy Division of Uasin Gishu district, finger millet was observed to be retarded in growth with P and N deficiency symptoms (PRA Report, 1994). These deficiencies were also confirmed from soil analysis results of samples taken from the farmers fields in 1995 at Chobosta village (LH4) Agroecological zone of Uasin Gishu District North Rift Valley Province of Kenya.The objective of the study was to evaluate the effectiveness of low levels of Phosphorus (P), Nitrogen (N), compost/FYM and their combinations on finger millet performance.   

Some soils samples were taken from a few farms in 1995 before experimentation for laboratory chemical analysis. Fertiliser treatments were:- the control with no organic or inorganic fertiliser (), 25 kg P205 and 25 kg N  ( ) applied through a compound fertiliser 20:20:0, compost/FYM at 5 t  (), and 12.5 kg P205 plus 12.5 kg N plus compost /FYM at 2.5 t ha-1 (). All the treatments were applied at planting time and there was no topdressing. The selection of 25 kg P205  and compost/FYM at 5 t  was based on the assertion by farmers that finger millet does not require very fertile soils and normally farmers do not apply fertilizers nor chemicals during its production (PRA Report, 1994); instead new land is prepared every two or three years. However, due to land pressure rotation is not now possible (Kute, 1995). 

In previous years in Nigeria, DFID (2005) undertook a review of annual field surveys which showed a decline in yield of maize in 26 states, cassava in 10 states, millet in 8 states, and rice in 13 states from 1996-2004. Cereals yields have declined between 1980 and 2003, yet this has been accompanied by a decline in fertilizer consumption and erratic fluctuation in accessibility among small-holder rural farmers (Yusuf, 2007) which make them to employ some sustainable agricultural practices.


The level of inorganic fertilizer use is very low due to cost, availability, lack of credit, and low grain prices resulting from limited market options (Kadi et al., 1990). Efficient use of both organic and inorganic fertilizer is required to optimize crop yield to meet the food needs of a growing population and minimize soil degradation (Bationo, et al., 2001; Palm et al., 1997; Pieri 1989).

 Maman et al. (2000) reported that pearl millet grain and stover yields were increased with application of a combination of cattle manure and chemical fertilizer.

Farmers have broadcast applied this poultry manure to fields as a fertilizer source in the past, but have reported crop damage and now apply small amounts near the crop plants, sometimes with a side dress application of inorganic fertilizer when the crops reach the tillering growth stage. However, research on use of this poultry manure resource had not been conducted. Most of the reported studies on poultry manure use as a nutrient source and to improve soil properties have been conducted in developed countries, but environmental problems have arisen (Mahimairaja et al., 1995; Robinson and Sharpley, 1995; Sharpley, 1996).

 During a Participatory Rural Approach (PRA) exercise conducted in 1994 in Chobosta village, Soy Division of Uasin Gishu District, it was observed that finger millet was retarded in growth and plants had P and N deficiency symptoms. These deficiencies were also confirmed from soil analysis results of samples taken from the farmer’s fields. A study was conducted in Chobosta in the lower highland (LH4) to evaluate the effectiveness of low levels of P, N and compost and/ or farm yard manure (FYM) and their combinations on finger millet performance. Five farmers planted the trial in a randomized complete block design (RCBD) and each farm acted as replicate. The effect of fertilizer rates (12.5 kg P + 12.5 kg N + 2.5 t compost/FYM ; 25kg P + 25kg N ha-1, 5 t compost/FYM  and zero or no application as farmer treatment) on millet grain yields were evaluated. A compound inorganic fertilizer of 20:20:0 was used in the trial. Results of the two year study indicate that the use of inorganic fertilizers and combinations of inorganic and organic fertilizers application increased finger millet grain yields to more than a tone per hectare and reduced P and N deficiency. The farmer evaluations indicated that the combinations of fertilizers and manures were preferred to zero treatment in finger millet production (kute, et al., 1994).

Fertilizer treatments were:- the control with no organic or inorganic fertilizer ((),), 25 kg P205 and 25 kg N  ( ) applied through a compound fertilizer 20:20:0, compost/FYM at 5 t  (), and 12.5 kg P205 plus 12.5 kg N plus compost /FYM at 2.5 t ha-1 (). All the treatments were applied at planting time and there was no topdressing. The selection of 25 kg P205  and compost/FYM at 5 t ha-1 was based on the assertion by farmers that finger millet does not require very fertile soils and normally farmers do not apply fertilizers nor chemicals during its production (PRA Report, 1994); instead new land is prepared every two or three years. However, due to land pressure rotation is not now possible (Kute, 1995).

Okalebo et al., (1990), found that finger millet in the semi-arid zones of Eastern Province responded to fertilizer at rates of 135 kg P205 and 135 kg N . These rates are very high for small scale resource poor farmers who may not afford to buy fertilizers. Not much research has been done in the country on finger millet. It is therefore necessary to determine low rates of fertilizers and organic manures for use on this crop.

The effect of planting date and variety on the growth and yield components of Millet in the Southern Guinea Savanna Zone of Nigeria was evaluated in the research farm of the School of Agriculture and Agricultural Technology, Federal University of Technology, Minna during the 2006 cropping season. Minna lies within the Southern Guinea Savanna Zone of Nigeria, latitude 90411 N and logititude 60311 E Treatment consisted of three planting dates (10th, 17th and 24th of June) and three varieties (Maiwa, Ex-bronu and Sosaat-c88). The experiment was a 3x3 factorial experiment in a randomized complete block design (RCBD) and data collected were: Plant height, leaf area, Flag leaf length, grain, panicle and husk weights respectively. Results obtained showed that Sosaat-C88 recorded a grain weight of 2,246 kg 

while Ex-bronu gave 2,324 kg . The lowest was 2,083 kg  recorded by local variety Maiwa. Results also revealed that 17th June was the suitable planting date irrespective of varieties followed by 24th June. Sosaat –c88 which had the best growth and yield components irrespective of planting date should therefore be recommended for further studies (uzoma, et al., 2010).

The combined analysis of variance of 1997 and 1998, showed that combinations of fertilizers and organic manures at half rates  gave yields of 3.3 t ha-1. This showed that finger millet responded to inorganic fertilizers and organic fertilizer applications at all rates. The yields of 1998 were lower than those of 1997 due to the El nino rains that may have caused leaching and there was blast on the fingers, therefore poor seed set. Okalebo et al., (1990).

There is a great deal of evidence on the ability of organic matter to increase yields when used alone or in combination with inorganic fertilizers. In the Sahel, plowing under crop residues and using chemical fertilizers increased yields 50 to 150% more than using either technique alone (Bationo, et al., 1993). On millet fields where crop residues had been returned to the soil during a 4-year period, yields were comparable to those having been treated with inorganic fertilizers. When both fertilizer and crop residues were combined, millet grain yields were 15 times greater than the control (Bationo, et al., 1991). Four-year trials in three different agro ecological units of Kenya found that maize yields increased substantially when Manure was combined with fertilizer; however, the most profitable treatments were those using only chemical fertilizers, which were subsidized at the time of the analyses (Smaling et al. 1992).

In an experiment (Tavasoli et al, 2010), the effects of chemical and organic fertilizers on red bean and pearl millet's quantitative and qualitative features in mixed cultivation were studied. Based on their research, for both crops, the highest yield was obtained from dry forage grass, seed, and the index of harvest from treatment of the recommended half manure+ the suggested half chemical fertilizer. However, the manure treatments had no significant effect on the weight of thousand seeds from these two species. 

The purpose of this study was to assess the effect of soil amendments on the growth and yields of pearl millet using; saw dust with cow, saw dust with poultry droppings, cow dung, and poultry droppings. Soil sampling was done in 20 small scale millet farms in Njimtilo in Konduga Local Government Area of Borno State at 0-20 cm depth in addition to soil profile description. Results of a structured questionnaire showed that 51% of the farmers used inorganic fertilizers predominately (NPK and Urea), 17% used only farmyard manure, 26% used both organic and inorganic fertilizer, while 7% did not use any soil amendments. Most of the farms had a pH of less than 5.2 within the 20cm depth but increased to 7.02 at the AB horizon. Organic carbon (C) ranged linearly from 2.4 at lower horizon to 6.8gkg-1 at the surface with a mean value of 4.04. Most of the farms were phosphorus (P) deficient. All farms had sufficient amounts of extractable potassium (K). Total nitrogen (N) ranged from 0.07 to at the lower horizon to 0.2gkg-1 at the surface with a mean value of 0.15. Cow dung incorporated with saw dust (CS) showed significant effect on the number of panicle, panicle length, chaff weight, grain weight and stover weight indicating that saw dust improves the soil and thereby increases yield of pearl millet. Poultry droppings incorporated (PS) with saw dust and Poultry droppings without the saw dust (PD) have statistically similar yields but (PS) has higher yields. K.A sadiq., et al (2012)

In the same study, combined application of crop residue and mineral fertilizer also improved soil physical properties, but the improvement by mineral fertilizer alone was limited. Ayoolaand Makinde (2009) reported that after two years of application and cropping, enriched poultry manure increases soil N, P and K contents by 42, 2 and 21%, respectively. While, fortified cow dung increases the nutrients by 25, 0.3 and 3%, respectively in the degraded tropical rain forest zone in Nigeria. Similarly, Mucheru-Muna et al. (2007) reported improved total soil carbon and nitrogen contents with the application of organic residues and manure in particular improved soil calcium content after 2 years in Eastern Kenya. Use of gliricidia prunings for 11 years resulted in a 24% increase in organic C in surface soils (0-20 cm) (Makumba et al., 2006).

A field experiment was carried out during kharif 2001 and 2002 at field unit of All India Co-ordinated Research Project on Weed control, University of Agricultural sciences, Hebbal, Bangalore, under irrigated conditions. The treatment consisted of four weed management practices and two fertility levels. The hand weeding twice resulted in higher grain (3450 kg ha-1), followed by butachlor and 2, 4-D Na salt 0.75 kg ha-1. The higher yield was reflected in terms of yield parameters such as ear length, 1000 grain weight, number of fingers per ear head, ear weight per plant and grain weight per plant. Unweeded control treatment caused significant reduction in these traits and consequently lowered the yield by 43 per cent owing to weed competition. Application of butachlor and 2, 4 - D Na salt 0.75 kg  was resulted in higher net returns and benefit cost ratio as compared to hand weeding twice and unweeded control, owing to less cost. Integrated use of recommended NPK and FYM treatment recorded significantly higher grain (3086 kg) as compared to recommended NPK alone (2946 kg). This higher yield in integrated use of recommended NPK + FYM applied plot was reflected in terms of better yield parameter like ear length, ear weight per plant, 1000 grain weight, number of fingers / ear head and grain weight per plant and growth parameter like leaf area, total dry matter production and better distribution of dry matter to graim. O.kamara., et al (2006).

In detreminning the effect of sowing dates and integrated use of organic and in organic fertilizer of growth of forage yield of pearl millet (pennisetum glaucum (L) R.Br) in newly cultivated land. The experiment was conducted at experimental farm faculty of agriculture, Egypt, during the year 2009 and 2010.their sowing date were assigned to main plot. Five combination of organic and inorganic fertilizer were assigned to sub plot. Result revealed that growth parameters and forage yield were significantly affected by sowing date and fertilizer treatments. E.A Abd EL. Lattief, (2011).  











CHAPTER THREE

RESEARCH METHODOLOGY

3.0 INTRODUCTION

This section discusses on how the data were collected to achieve the selected objective, therefore. In the pursuance of this task, the method of data collection employed  for the purpose of this study will be discussed.

3.1 POPULATION TO BE STUDY

This study concern itself solely with the yield of millet in Kaduna State Agricultural Development Program (KADP).

3.2 METHOD OF DATA COLLECTION

This is the process of obtaining statistical data, which are being analyzed in orders to draw a valid and reasonable conclusion of decision making. Basically, there are two main categories of data collection; these are primary and secondary data.

Primary Data: These are data collected specifically for the analysis desire. It is a statistical data which is collected by the investigated originated for the purpose of inquiry in hand. These data can be collected through observation, interviewing, questionnaire, telephone, e.t.c. It is more reliable since it is collected for the first time by the investigator.



Secondary Data: These are data that have been already compiled and made available by an authorized agent or body for statistical analysis. The data is not originated by the investigator for inquiry at hand but have been used for particular purposes by someone else. It has advantage of serving time and cost when collecting.

3.3 SAMPLING PROCEDURE

It is very difficult to study all the yield of millet in Kaduna State, this is because of insufficient of time. As a result of this, a few were chosen as sample for the purpose of this project.   

3.4 METHOD OF DATA ANALYSIS

3.5 ANALYSIS OF VARIANCE

Analysis of variance (ANOVA) is a statistical analysis tool that separate the total variability found within a data set into two components: random and systematic factors. The random factors do not have any statistical influence on the data set. While the systematic factors do. The ANOVA test is used to determine the impact independent variables have on the dependent variables in a regression analysis.

By speed 1987, the idea of partitioning variation, counting degree of freedom and identifying the error of terms are fundamental to any data analysis.

                    The main purpose of Analysis of variance (ANOVA):

-The reason for doing ANOVA is to test if there is significant difference between the mean groups on some variables.

For example, you might have data on student performance in non-assessed tutorial exercise as well as their final grading. You interested in seeing if tutorial performance is related to final grade. ANOVA allows you to break up the group according to the grade and see if the performance is difference across the grades. 

-ANOVA is available for the both parametric (scores data) and non-parametric (ranking/ordering) data.

3.5.1 STATISTICAL TOOL

Factorial experiment: factorial experiment provide more information for an experimenter which makes it useful for agricultural research. It involves simultaneous investigation of two or more factor effects; we mean that each complete trial or replicate of the experiment, all possible combination of the level of factors are investigated. Consider a simple case of factorial experiment where the yield of crop depends on a particular variety of the crop being used and also from the particular manure applied. We may have two sample experiments, one for the variety and the other for the manure. They introduce the idea of two factors (A and B) experiment with a and b levels respectively. And if several blocks were run, it is possible to analyze the data as two way classification and test for significant differences among the various treatment means. In this instance, however, the experimenter is interested in all the possible factorial effect.  

The simplest type of factorial experiment involves only two factors, say, A and B. There are a levels of factor A and b levels of factor B. This two-factor factorial is shown in Table below. The experiment has n replicates, and each replicate contains all ab treatment combinations.

Table 3.1 Data Arrangement for a Two-Factor Factorial Design.

                                                                               Factor B                 

                                 

                                1                    2                       . . .                          b                    Total           Average


               

                1




Factor A 2

               


                 

                


                 a   

          

        

          Total               





      

         


       







      

        



       

















        


       












        Average


















Table3.2 Treatment display

                                                   Factor B



Kaduna/ north                                              

Kaduna/south


Factor A


2007


2008


2009


2010


2011


2007


2008


2009


2010


2011


1

1.6

2.3

2.5

2.1

2.3

2.3

1.2

2.3

2.1

1.4


2

2.2

2.1

2.7

2.3

2.8

1.8

1.7

2.0

2.4

2.2


3

1.5

2.7

1.1

1.4

2.2

2.7

1.3

1.7

2.0

2.3


4

2.9

1.3

2.4

2.5

2.0

1.9

2.0

1.4

2.7

2.2


5

1.7

2.9

1.7

1.7

1.8

1.9

2.3

1.5

2.8

1.7


6

2.6

2.1

1.8

2.7

1.4

2.3

1.5

1.9

2.2

1.6


7

2.3

2.3

1.5

2.0

2.3

2.9

2.4

1.2

1.7

1.0


8

1.1

1.6

2.2

2.8

1.8

1.8

1.8

2.3

1.9

2.0


9

2.8

2.2

1.9

2.1

2.0

2.1

1.7

2.2

2.0

1.9


10

2.7

2.6

1.8

2.3

1.5

1.9

1.2

2.0

1.2

1.0


11

2.2

2.5

1.7

2.8

2.3

1.5

2.3

1.2

1.7

2.4


12

2.3

1.9

2.3

2.5

2.6

2.1

1.7

2.8

1.3

2.4




Table3.3 Factorial treatment combination

Fertilizer level

Kaduna north

Kaduna south


1

 1()

1()


2

2()

2()


3

3()

3()


4

4()

4()


5

5()

5()


6

6()

6()


7

7()

7()


8

8()

8()


9

9()

9()


10

10()

10()


11

11()

11()


12

12()

12()





The coding 1 through 12 of fertilizer level represent the following:

1.5t/ha organic manure + 0-0-0 NPK

1.5t/ha organic manure + 15-15-15 NPK

1.5t/ha organic manure + 40-15-15 NPK

1.5t/ha organic manure + 30-15-15 NPK

3.ot/ha organic manure + 0-0-0 NPK

4.5t/ha organic manure + 0-0-0 NPK

3.0t/ha organic manure + 15-15-15 NPK

3.0t/ha organic manure + 30-15-15 NPK

3.0t/ha organic manure + 40-15-15 NPK

4.5t/ha organic manure + 30-15-15 NPK

4.5t/ha organic manure + 30-15-15 NPK

4.5t/ha organic manure + 45-15-15 NPK


3.6 HYPOTHESIS

Hypothesis: hypothesis is a statement made about the population parameter that decide whether to accept or reject.

Hypothesis testing: is the decision making procedure about a hypothesis.




3.6.1 General Procedure for Hypothesis Tests

1. From the problem context, identify the parameter of interest.

2. State the null hypothesis, .

3. Specify an appropriate alternative hypothesis, 

4. Choose a significant level α.

5. Determine an appropriate test statistic.

6. State the rejection region for the statistic.

7. Compute any necessary sample quantities, substitute these into the equation for the test statistic, and compute that value.

8. Decide whether or not  should be rejected and report that in the problem context 

3.7 EFFECTS ESTIMATION

Main effect: The effect of a factor is defined change in response produced produce by change in the level of the factor.

Interaction effect: It refers to the effect due to joint action of the factor involved in the experiment.

The linear statistical model is   



Where                i=1,2,…a        j=1,2,…b        k=1,2,…

 And   µ is the overall mean effect

  is the effect of the  level of factor A

   is the effect of the  level of factor B

 is the effect of interaction between factor A and B

    is a random error component having a normal distribution with                                                                            zero Mean and variance     

The hypothesis that we will test are as follows:

The null hypotheses want to test are: 

: =0 for i=1,2,… (no main effect for factor A)

: =0   for j=1,2,…,12 (no main effect for factor B)

: =0    for i=1,2 and j=1,2,…,12 (no interaction)

The alternative hypotheses are respectively:

: ≠0  for atleast one value of i

: ≠0  for atleast one value of j

: ≠0   for atleast one value of i and j



Computing formulas for main effect



Computing formulas for sum of squares in a two factor analysis of variance:

 



Table3.4 Analysis of variance table for the two-factor fixed effect model.

Source of variation

Sum of squares

Degree of freedom


Mean Squares                


           


 treatments          

   

      

        

       


 treatments         

   

                                

    

      


 interaction      

      

   


    


Error        

    

   

       



Total    

                         






3.8 SOFTWARE ANALYSIS

We use minitab for the main and residual of the research. Its software design to carter for statistical analysis and also has good graphical facilities.

Steps involve in MINITAB data arrangement.

Collect the data appropriately

Arrange the data in MINITAB worksheet

Click stat button in the menu

Click on DOE

Click on factorial

Click on analyze factorial design

Enter the factors in the dialogue box provided

Click on the general full factorial

Click ok

Enter the response in the box provided

Click on terms

Put the two terms in the model 

Click ok to view the result

3.8.1 Validating ANOVA Assumptions

              There are three assumptions in ANOVA analysis: normality, constant variance, and independence. The normality plot of the residuals is used to check the normality of the treatment data. If the distribution of residuals is normal, the plot will resemble a straight line. The constant variance assumption is checked by the plot of residuals versus fitted values. If the plot of residual vs. fitted values (treatment) does not show any pattern, the constant variance assumption is satisfied. If the plot of residual vs. run order (time order of data collection) does not reveal any pattern, the independence assumption is satisfied. 










CHAPTER FOUR

4.0 DATA PRESENTATION AND ANALYSIS

This chapter deals with data presentation and analysis.

4.1 DATA PRESENTATION

The data used in this study is yield of millet in conjunction with fertilizer applied from the year 2007 to 2011. The data was classified under secondary data source obtained from Kaduna State Agricultural Project (KADP), Kaduna. 

An experiment was performed in other to study the effect of two varieties of millet and twelve fertilizer rate coded from 1 to 12 and five replicate of a two factor factorial experiment were run. The observed data are shown in the table below.

TABLE 4.1 Presentation of Data

                                            Varieties of millet                                      



Kaduna north                                              

Kaduna  south


Fertilizer

Level


2007


2008


2009


2010


2011


2007


2008


2009


2010


2011


1

1.6

2.3

2.5

2.1

2.3

2.3

1.2

2.3

2.1

1.4


2

2.2

2.1

2.7

2.3

2.8

1.8

1.7

2.0

2.4

2.2


3

1.5

2.7

1.1

1.4

2.2

2.7

1.3

1.7

2.0

2.3


4

2.9

1.3

2.4

2.5

2.0

1.9

2.0

1.4

2.7

2.2


5

1.7

2.9

1.7

1.7

1.8

1.9

2.3

1.5

2.8

1.7


6

2.6

2.1

1.8

2.7

1.4

2.3

1.5

1.9

2.2

1.6


7

2.3

2.3

1.5

2.0

2.3

2.9

2.4

1.2

1.7

1.0


8

1.1

1.6

2.2

2.8

1.8

1.8

1.8

2.3

1.9

2.0


9

2.8

2.2

1.9

2.1

2.0

2.1

1.7

2.2

2.0

1.9


10

2.7

2.6

1.8

2.3

1.5

1.9

1.2

2.0

1.2

1.0


11

2.2

2.5

1.7

2.8

2.3

1.5

2.3

1.2

1.7

2.4


12

2.3

1.9

2.3

2.5

2.6

2.1

1.7

2.8

1.3

2.4



TABLE4.2 DATA ANALYSIS

Yield

Fert

level

Millet

varieties

Yield

Fert

level

Millet

Varieties

Yield

Fert

level

Millet

varieties


1.6

1

1

2.4

4

1

2.3

7

1


2.3

1

1

2.5

4

1

2.0

7

2


2.5

1

1

2.9

4

1

2.4

7

2


2.1

1

1

1.9

4

2

1.2

7

2


2.3

1

1

2.0

4

2

1.7

7

2


2.3

1

2

1.4

4

2

1.0

7

2


1.2

1

2

2.7

4

2

1.1

8

1


2.3

1

2

2.2

4

2

1.6

8

1


2.1

1

2

1.7

5

1

2.2

8

1


1.4

1

2

2.9

5

1

2.8

8

1


2.2

2

1

1.7

5

1

1.8

8

1


2.1

2

1

1.7

5

1

1.8

8

2


2.7

2

1

1.8

5

1

1.8

8

2


2.3

2

1

1.9

5

2

2.3

8

2


2.8

2

1

2.3

5

2

1.9

8

2


1.8

2

2

1.5

5

2

2.0

8

2


1.7

2

2

2.8

5

2

2.8

9

1


2.8

2

2

1.7

5

2

2.2

9

1


2.4

2

2

2.6

6

1

1.9

9

1


2.2

2

2

2.1

6

1

2.1

9

1


1.5

3

1

2.8

6

1

2.0

9

1


2.7

3

1

2.7

6

1

2.1

9

2


1.1

3

1

1.4

6

1

1.7

9

2


1.4

3

1

2.3

6

2

2.2

9

2


2.2

3

1

1.5

6

2

2.0

9

2


2.7

3

2

1.9

6

2

1.9

9

2


1.3

3

2

2.2

6

2

2.7

10

1


1.7

3

2

1.6

6

2

2.6

10

1


2.0

3

2

2.3

7

1

1.8

10

1


2.3

3

2

2.3

7

1

2.3

10

1


2.9

4

1

1.5

7

1

1.5

10

1


1.3

4

1

2.0

7

1

1.9

10

2







DATA SOURCE: Kaduna State Agricultural Development Program, Kaduna.

TABLE4.2 DATA ANALYSIS

Yield

fert

level

Millet

Varieties


1.2

10

2


2.0

10

2


1.2

10

2


1.0

10

2


2.2

11

1


2.5

11

1


1.7

11

1


2.8

11

1


2.3

11

1


1.5

11

2


2.3

11

2


1.2

11

2


1.7

11

2


2.4

11

2


2.3

12

1


1.9

12

1


2.3

12

1


2.5

12

1


2.6

12

1


2.1

12

2


1.7

12

2


2.8

12

2


1.3

12

2


2.4

12

2



Data on yield of millet per tone in conjunction with fertilizer levels.









DATA SOURCE: Kaduna State Agricultural Development Program, Kaduna.

TABLE4.3 Factorial Fit: yield versus fertelizer/level, millet/varieties

Source  

DF   

Seq SS   

Adj SS  

Adj MS     

F

P


Main Effects          

2   

2.0055   

2.0055  

1.0028  

4.49  

0.013


2-Way Interactions    

1

0.2564   

0.2564  

0.2564  

1.15  

0.286


Residual Error      

116  

25.8879  

25.8879  

0.2232




Lack of Fit        

20   

4.0679   

4.0679  

0.2034  

0.89  

0.594


Pure Error         

96  

21.8200  

21.8200  

0.2273




Total  

119

28.1499










Interpretation of result

Main effects: from the above analysis, the last column shows the p-value for each F-ratio. The p-value (0.013) corresponding to the main effects is less than the level of significance (0.05). Therefore, we reject the null hypothesis and conclude that there is significance difference between the two millet varieties and levels of fertilizer used. 

Interaction effect: also from the analysis above, the p-value (0.286) corresponding to the 2-way interactions is greater than the level of significance (0.05). Therefore, we do not reject the null hypothesis and conclude that there is no interaction difference between the millet varieties and fertilizer levels. 

 





 

Figure 4.1 Normal Probability Plot of the Residual

From the figure above, since the residual lie approximately along a straight line, we do not suspect any problem with normality in the data. 




 Figure 4.2 Residual Versus the Fitted Values


From the above figure, the residual are spread within graph, and the constant variance assumption is satisfied.




 

Figure 4.3 Residual Versus the Order of the Data

  

From the figure above, the plot of residual versus the order of the data does not reveal any pattern. Therefore, the independence assumption is satisfied. 








TABLE4.4 General Linear Model: yield versus fertilizer/level, millet/varieties

Source

DF   

Seq SS   

Adj SS  

Adj MS     

F      

P


fert/level                    

11

2.4469   

2.4469  

0.2224  

0.98  

0.471


millet/varieties               

1

1.9508   

1.9508  

1.9508  

8.58  

0.004


fert/level*millet/varieties   

11

1.9323   

1.9323  

0.1757  

0.77  

0.666


Error

96

21.8200  

21.8200  

0.2273




Total

119  

28.1499












Interpretation of result:

Fertilizer level: from the Analysis above, the P-value (0.471) corresponding to the fertilizer level is greater than the level of significant (0.05). Therefore, we do not reject the null hypothesis and we conclude that there is no significant difference among the fertilizer levels.

Millet Varieties: Also from the above analysis, since P-value (0.004) corresponding to the millet varieties is less than the level of significance (0.05). Therefore, we reject the null hypothesis and we conclude that there is a significance difference between the two varieties of millet. This implies that two varieties of millet differ significantly in yield.

Interaction effect (millet varieties and fertilizer rate): from the above analysis, since the P-value (0.666) corresponding to the millet varieties & fertilizer level is greater than the level of significance (0.05). Therefore, we do not reject the null hypothesis and conclude that there is no interaction difference between the millet varieties and fertilizer levels.        














 Figure 4.4 Normal Probability Plot of the Residual


From the figure above, since the residual lie approximately along a straight line, we do not suspect any problem with normality in the data. 




 Figure 4.5 Residual Versus the Fitted Values


From the above figure, the residual are spread within graph, and the constant variance assumption is satisfied.


 Figure 4.6 Residual Versus the Order of the Data


From the figure above, the plot of residual versus the order of the data does not reveal any pattern. Therefore, the independence assumption is satisfied. 












CHAPTER FIVE

5.0 INTRODUCTION

This chapter presents the discussion of findings, conclusion and recommendation.

5.1 DISCUSSION OF FINDINGS

This study has critically examine factorial experiment or analysis of variance involving two factors; factor (A) rate of fertilizer coded from 1 through 12 and factor (B) two millet varieties (Kaduna north and Kaduna south). In a complete randomize block design.

The data were obtained from Kaduna state Agricultural development project (KADP). It covers a period of 5years, from 2007 to 2011.

The analysis of variance of the yield of some selected millet varieties was analyze by the factorial fit and general linear model, also some plot were made using a statistical software called MINTAB. 

In factorial fit, the p-value (0.013) corresponding to the main effects is less than the level of significance (0.05) and the p-value (0.286) corresponding to the 2-way interaction is greater than the level of significance (0.05). This shows that main effects differs significantly and the 2-way interaction do not differ significantly. 

 Thus, in the general linear model, the p-value (0.471) corresponding to the fertilizer level is greater than the level of significance (0.05) and the p-value (0.004) corresponding to the millet varieties is less than the level of significance (0.05), also the p-value (0.666) corresponding to the interaction of fertilizer level*millet varieties is greater than the level of significance (0.05).

 This shows that the fertilizer levels have no significance differences, and the millet varieties differs significantly in yield, while the interaction of the fertilizer and millet do not have any significant differences.  

The plot of factorial fit and general linear model have the same meaning. More importantly, the statistical analysis of the data formed integral part of the overall study. The statistical gave rise to meaningful and valid conclusion concerning the aims and objectives of the study.

5.2 RECOMENDATION

Millet which is being cultivated in northern Nigeria has continued to serve both economic and consumption purpose of the nation. Therefore, the need to enhance its productivity cannot be over emphasized.

The following are recommended for further studies

More varieties of millet should be evaluated under a similar study to assess the yield in different fertilizer amendments.

An integrated nutrient management combination of organic and inorganic fertilizer could also be studied to support general fertilizer application.

The experiment should be carried out in other agro ecological zone to evaluate the yield of millet varieties to different fertilizer amendments.






5.3 CONCLUSION

From this study, it is clear that the data did not provide sufficient evidence to reject the null hypothesis at 5% level of significance for the fertilizer factor (A). This implies that there is no significance variation or difference among the twelve fertilizer levels. However, the data provide evidence to reject the null hypothesis for the variety of millet factor (B).

There is also no sufficient evidence to reject the null hypothesis at 5% level of significance for possible interaction effect between fertilizer level and millet varieties. Therefore the combination of the two have no interaction differences.   

  


  













REFERENCES

Douglas C. Montgomery and Geoge C. Runger (2003) “ Applied statistics and probability for engineers” 510-518.

E.A Abd El Lattief (2011) “ growth and fodder yield of forage pearl millet in newly cultivated land as affected by date of planting and integrated use of mineral and organic fertilizers” Asian jounal of crop science, 3: 35-42.

K.A Sadiq (2012) “ The effect of incorporation of saw dust into two types of organic manure on the growth and yield of pearl millet at njimitilo village in the sud- humid region of borno state of  Nigerian” 60-65

Kute C.A.O and P.Chirchir (1994) “ effect of low levels of organic manure on yields of finger millet in chobosta, northern Kenya.” 48-51

O. kamara (2006) “ effect of weed management practices and fertilizers levels on growth and yield parametres in finger millet” Karnataka j. Agric. Sci 20(2): (230-233) 2007.

O.T. Mustapha and Y. Mustapha () “ Growth and yield of pearl millet (pennesetum glaucum L.R. Br) As influence by downey mildew and snut diseases in kabuga area of kano state, Nigeria “ 1-5    

Nouri Maman and Stephen Mason (2013) “poultry manure and organic fertilizer to improve millet yield in Nigeria” African jounal of plant science, 7(5) 162-169.

Uzoma (2010) “the effect and planting date on the growth and yield of pearl millet in the southern guinea savanna zone of Nigeria” journal of agriculture and veterinary sciences, 2: 122-127.

Yusuf R.O (2007) “organic fertilizer: the under estimated component in agricultural transformation initiatives for sustainable small holder farming in Nigeria” Ethiopian journal of  environmental studies and management. Vol.6


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