Application of multivariate analysis to agronomic trial

Project Abstract

<p> </p><p>Bivariate correlation was carried out on the growth and yield characters of cowpea<br>(Vigna unguiculata [L] Walp) and pod yield and number of pods were observed to<br>be positively and significantly correlated with all the components assessed<br>(Number of Branches, Weight of defoliated leaves, Number of Pods, Length of<br>Pods, Shoot Dry Weight, Plant Height, Number of Leaves, Leaf Area Plant, and<br>Crop Growth Rates) except leaf area index and weight of defoliated leaves. The<br>various parameters exhibited significant interrelationship with one another. Of the<br>10 growth characters considered in the study, the Principal component analysis<br>shows the reduction of the dimension of the variates to 3 components and these<br>three components explain about 95.57% of the variation. All variables considered<br>shows normality with a linear line indicating that the data observed multivariate<br>normal distribution.</p><p>&nbsp;</p><p><strong>&nbsp;</strong></p> <br><p></p>

Project Overview

<p> GENERAL INTRODUCTION<br>1.0 Introduction<br>Multivariate analysis refers to any statistical technique used to analyze data<br>that arises from more than one variable. This essentially models reality where each<br>situation, product, or decision involves more than a single variable. Multivariate<br>analysis can be used for both spectral and non-spectral type of data. Spectra data<br>are essentially data derived by the use of spectroscopic instrument. This data<br>specifies variable with its properties and undoubtedly provide a great deal of<br>useful information about organic molecules. Spectral data are used by scientists to:<br>(i). Discover the chemical composition of materials by looking at the high (and<br>other kinds of electromagnetic radiation) and (ii). Identify and monitor the<br>production of products in factories.<br>The advent of gas chromatograph (GC) machines with non-destructive<br>detectors has made research in flavor more interactive, and some GCs now<br>incorporate sniffing ports to enable trained assessors to smell individual flavor<br>compounds as they are separated by the GC.<br>A Non-spectral data is essentially data collected from sensory and<br>environment. Any data that is collected from other sources, than spectroscopic and<br>chromatographic instruments is non-spectral data.<br>2<br>The principal component analysis (PCA) and cluster analysis (CA) are the<br>most common multivariate statistical methods in environmental studies. Principal<br>component analysis is widely used to reduce data dimensionality (Salawu, 2008)<br>and to extract a small number of latent factors for analyzing relationships among<br>the observed variables. If large differences exist in the standard deviations of<br>variables, PCA result will vary considerably depending on whether the correlation<br>or covariance matrix is used (Farnham et al, 2003).<br>Factor analysis (FA) is a statistical approach that can be used to analyze<br>interrelationship among a large number of variables and to explain these variables<br>in terms of their common underlying dimension (factors). The statistical approach<br>involving finding a way of condensing the information contained in a number of<br>original variables into a smaller set of dimension (factors) with a minimum loss of<br>information (Everith and Dunn, 2001).<br>Agronomy is the study of soils and plants, relating to the scientific study of<br>soils management, land cultivation and crop production. It describes plants<br>characteristics that are important during growth and development of a crop e.g<br>height and stem strength. The data on cowpea was collected and used for the<br>analysis.<br>3<br>1.1 Statement of the Problem<br>Over the years the measurable dimensions of agricultural trial are<br>numerous. This leads to cumbersome and time consuming tasks in the gathering<br>and analysis of data from agricultural experiments.<br>Efforts were made in this thesis to reduce the dimensionality of the<br>measurement from m to p, (p &lt; m) such that maximum information will be<br>retained and large percent variation will be explained with the use of fewer<br>variables.<br>1.2 Objective of the Study<br>The specific objectives of the study include:-<br>ï‚· To test the multivariate normality assumption on agronomic trial.<br>ï‚· To study the relationship of the agronomic measured characteristics in<br>both the growth and yield parameter.<br>ï‚· To determine the percent contribution of both direct and indirect<br>correlation in path analysis.<br>ï‚· To reduce the dimensionality of the measured characteristics from m to<br>p; where p &lt; m.<br>4<br>1.3 Significance of the Study<br>The Significance of this study is that the model constructed will provide:<br>ï‚· The agriculturist with useful information on the most prominent<br>characteristics to use in the crop management.<br>ï‚· The agriculturist with information on direct and indirect contributions of<br>the crop characteristics<br>ï‚· Demonstration of the application of Path Analysis and Principal<br>Component Analysis in agricultural experiments to obtain useful<br>information.<br>1.4 Brief History of Cowpea<br>Cowpea (vigna Unguiculata (L) walp), common name for any of a genus of<br>leguminous herbs also knows as black-eyed pea. Cowpeas are sprawling or<br>twining herbs with triple leaves and pods 20 to 30 cm long enclosing several<br>kidney-shaped seeds. Cowpeas were cowpea originally native of Asia are now an<br>important forage and cover crops in Southern United State and Africa. Worldwide<br>Cowpea production has increased dramatically in the last 25 years (Adebayo and<br>Tukur, 1999).<br>Being a drought tolerant and warm weather crops, cowpea is well as<br>adapted to the drier regions of the tropics where other food legumes do not<br>perform well.<br>5<br>It also has the unique ability to fix atmospheric nitrogen through its nodules<br>and it grows well even in the soil with more than 85% sand and with less than<br>0.2% organic matter and low level of phosphorous, where soil PH is in the range<br>of 5.5 to 6.5 (Tuan and Philips, 1992).<br>Cowpea is consumed in many forms: young leaves, green pods, green seeds<br>are used as vegetables and dry seed are used in various food preparations. With<br>over 25% protein, in its seeds and tender leaves, cowpea is a major source of<br>protein, minerals and vitamins in the daily diets. Therefore Cowpea seed is valued<br>as a nutritional supplement to cereals and animals. Its seeds is a nutritious<br>component in the human diet as well as livestock feed with nutrient content as<br>follows: Protein, 24.8%, Fat, 1.9% Fiber, 6.3% Carbohydrate, 63.6%, Thiamine,<br>0.00074%, Riboflavin, 0.00042% and Niacin, 0.00281%, thus its positively<br>impacts on the health of women and children (Van and Gerike, 2000).<br>1.5 Definition of Terms and Concepts.<br>Variance (MS): The term MS (mean sum of square) is a short form of mean sum<br>of squares (MSS), which is calculated by dividing the sum of squares with its<br>degrees of freedom. One of the ‘S’was dropped in usage and its short form MS is<br>used. It is the most important measure of dispersion. In fact it has a very crucial<br>role in biostatistical analysis of experimental data and in the tests of significance.<br>The MS in the analysis of variance table is the same as variance. Mathematically,<br>it is square of standard deviation.<br>6<br>Coefficient of Variation (C.V): It is defined as the calculated standard deviation<br>expressed as a percentage of the mean.<br>Completely Randomized Design: The simplest experimental design used where<br>experimental material is uniform e.g. in the laboratory, green house, screen house,<br>growth chamber.<br>Continuous Variable: They are variables which can have any values between<br>certain limits e.g. yield, weight etc.<br>Number of Pods: The average number of pods in a stand of cowpea.<br>Length of Pods: The length of pods from the base to the tips of the pod. Shoot<br>Dry Weigh<br>Plant Height: It’s the measurement of cowpea stand from the ground to the<br>longest leaf tip or panicle.<br>Number of Leaves: This will be determined by counting the total number of fully<br>expanded leaves on the tagged plants and the average will be computed.<br>Leaf Area Plant: This will be determined by measuring the length and maximum<br>width of the leaves of five tagged plants and multiplied by a constant coefficient of<br>0.75 (Montgomery, 1911)<br>Leaf Area Index: This will be determined by measuring the length and breadth<br>from the widest portion of functional leaves of each leaf from the tagged plant<br>with a ruler. The product of length and breadth will then be multiplied by a factor,<br>7<br>0.75 from which area of individual leaves of the sampled plants will be obtained,<br>added and divided by the land area occupied by the tagged plants.<br>LAI =<br>P<br>A = leaf area per plant / Area subtended by plant<br>Where, A = Leaf area per plant (m2)<br>P = Ground area per plant (m2)<br>LAI = leaf area index.<br>Crop Growth Rates: Three plants will be randomly sampled from each sub-plot<br>for destructive sampling these will be oven dry at 700c for 24 hours using the<br>formula by Smith and Haddad, (2000). The unit of measurement is g cm -2 wk-1.<br>( ) 2 1<br>2 1<br>t t<br>CGR W W<br><br><br> 1.x<br>W1 = dry matter weight at a sampling period<br>W2 = dry matter weight at the next sampling period<br>t1 = time at which w1 was taken<br>t2 = time at which w2 was taken<br>Path Model: A path model is a diagram relating intermediary, and dependent<br>variables. Single arrows indicate causation between exogenous or intermediary<br>variables and the dependent(s). Arrows also connect the error terms with the<br>respective endogenous variables. Double arrows indicate correlation between pairs<br>of exogenous variables.<br>8<br>Endogenous Variables: These are variables which form an internal part of the<br>system. Endogenous variables are those which do have incoming arrows.<br>Endogenous variables include intervening casual arrows in the path diagram. The<br>dependent variable(s) have only incoming arrows.<br>Exogenous Variables: These are variables which form an external part of the<br>system. Exogenous variables are those with no explicit causes (no arrows going to<br>them, other than the measurement error term). If exogenous variables are<br>correlated, this is indicated by a double-headed arrow connecting them.<br>Causal Paths: To a given variable include (1) the direct paths from arrows<br>leading to it, and (2) correlated paths from endogenous variables with others have<br>arrows leading to the given variable.<br>Path Coefficient: A path coefficient is a standardized regression coefficient (beta)<br>showing the direct effect of an independent variable on a dependent variable in the<br>path model. Thus when the model has two or more causal variables, path<br>coefficients are partial regression coefficients which measure the extent of effect<br>of one variable on another in the path model controlling for other prior variables,<br>using standardized data or a correlation matrix as input.<br>Effect Decomposition: Path coefficients may be used to decompose correlations<br>in the model into direct and indirect effects. This is based on the rule that in a<br>linear system, the total causal effect of variable i on variable j is the sum of the<br>values of all the paths from i to j.<br>9<br>Disturbance Terms: The residual error terms, reflect unexplained variance (the<br>effect of unmeasured variables) plus measurement error.<br>1.6 Contribution to Knowledge<br>This research x-rays the application of Principal Component Analysis and<br>Path Analysis in the reduction and partitioning of agricultural data. <br></p>