Experimentation design of different Agricultural Research

Agricultural experimentation

1. Luigi Giussani Institute of Higher Education Department of Education AGR: 1203 May Session-2024 AGR: 1203 Agriculture Science Practicals and Laboratory I Lecture material Bonny Aloka -0779208745, [email protected]

2. Introduction The course aims at introducing the students to the concepts of Agricultural Experimentation and to experimental design and analysis By completing this course, the students are expected to have achieved the following skills & capabilities; Demonstrate an understanding of designing an experiment, collecting, analyzing, & interpreting data Being able to design & select the most appropriate methods for performing experiments Being able to analyze methods and models used in agricultural experimentation Demonstrate the ability of analyzing the real data using different models and methods

3. Introduction –Course Outline An introduction to agricultural experimentation: basic concepts and definitions The experimental plot: size and shape of experimental plots and blocks, heterogeneity of experimental field, examples Field experiments, greenhouse experiments, laboratory testing: randomization– replication - field testing Analysis of Variance (ANOVA), confidence intervals, Type I and II errors Single factor designs: Completely randomized design (CRD) : design, construction of an experiment, comparing means, analysis of data extracting results

4. Introduction –Course Outline Randomized Complete Block Design (RCBD) : design, construction of an experiment, comparing means, analysis of data Latin square design: design, construction of an experiment, comparing means, analysis of data Subsampling, anterior and posterior comparisons Factorial designs: pros and cons of factorial analysis. Test of assumptions. Examples. Correlation & linear regression analyses Split plot experiments : design, construction of an experiment, comparing means, analysis of data Data transformation

5. Introduction –Basic Concepts & Definitions Statistics is a branch of science dealing with collecting, organizing, summarizing, analyzing and making decisions from data Descriptive statistics deals with methods for collecting, organizing, and describing data by using tables, graphs, and summary measures Inferential statistics deals with methods that use sample results, to help in estimation or make decisions about the population A population is the set of all elements (observations), items, or objects that bring them a common recipe and at least one that will be studied their properties for a particular goal A sample is a subset of the population selected for study

6. Introduction –Basic Concepts & Definitions A variable is a characteristic under study that takes different values for different elements An observation is the value taken by a variate for a particular unit of investigation Quantitative data are observations that are measured on a numerical scale. Examples: number of leaves per plant, yield of cowpea, the heights (or weights) of students in a class May be continuous or discrete A qualitative variate or attribute is a variate whose values cannot be put in any numerical order i.e. are observations that are categorical rather than numerical & are not capable of being measured The central limit theorem states that as the size of the samples gets large, the distribution of the means becomes normally distributed

7. Introduction –Basic Concepts & Definitions These include calculation of measures of central tendency such as mean, median, and mode; dispersion measures such as standard deviation and range; association measures such as correlation and regression; frequency distribution tables; cross tabulation tables; and graphs and figures Normally, a combination of tables, graphs, charts, and a discussion is used to summarize and present a data set A major drawback of descriptive statistical analysis is that it limits generalization to the particular group of individuals only

8. Introduction –Basic Concepts & Definitions Measures of central tendency are used to describe the central position of a frequency distribution for a group of data For describing this central position, the mean, mode, and median are generally used Among these, the most commonly used measure of central tendency is the arithmetic mean If all the data fall in a ‘normal distribution’, the mean, the median, and the mode coincide

9. Introduction –Basic Concepts & Definitions Measures of spread or dispersion help us to have some idea about the variation of measured data around the mean A number of statistics are used to describe this spread including the range, percentiles, quartiles, mean deviation, variance, and standard deviation Among these, standard deviation is the most popular one Measures of association enable to see whether there is a relation between two sets of observed data through the use of correlation and regression techniques The relationship between two paired variables can be estimated using correlation.

10. Introduction –Basic Concepts & Definitions Tests of significance Chi-square (X2) test The chi-square test is a nonparametric test used for qualitative data (especially of the nominal types) to test hypotheses concerning the frequency distribution of one or more populations A Chi-square test for independence compares two variables in a contingency table to see if they are related

11. Introduction –Basic Concepts & Definitions Tests of significance The t- and Z-tests The Z-test and the t-test are popular tools to find whether an observed difference between the means of two groups can be considered significant Here, the word ‘significant’ has a specific meaning For example, we know that 10 and 12 are not equal, and the difference is 2. However, 10 and 12 may not be ‘significantly’ different, if the differences are due to chance Our concern is how to find out whether the differences are real (significant) and not due to chance (non-significant) The researcher should have some skepticism in this regard, especially when using statistics We assume that all results are chance results unless shown otherwise (remember how a null hypothesis is written)

12. Introduction –Basic Concepts & Definitions Tests of significance The t- and Z- testsThe z-test is generally used to ascertain the significance of difference between the mean of a large sample and the hypothesized mean of a population or to compare the difference between the means of two independent large samples (when n is greater than 30) The z-test is also utilized to compare the sample proportion value to a theoretical value of population proportion or to compare the difference in proportions of two independent samples when n is large For applying z-test accurately, the data should follow normal distribution and standard deviation must be known.

13. Introduction –Basic Concepts & Definitions Tests of significance

14. Scales of Measurement of Variables The nominal level of measurement classifies data into mutually exclusive (disjoint) categories in which no order or ranking can be imposed on the data e.g., Gender: Male, Female The ordinal level of measurement classifies data into categories that can be ordered, however precise differences between the ranks do not exist e.g., Rating scale (poor, good, excellent) The interval level of measurement orders data with precise differences between units of measure The ratio level of measurement is the interval level with additional property that there is also a natural zero starting point i.e., zero means nothingness

15. Measures of Center or Central Tendency The most important aspect of studying the distribution of a sample of measurements is the position of a central value, i.e., a representative value about which the measurements are distributed Any numerical measure intended to represent the center of a data set is called a measure of location or central tendency The two most commonly used measures of center are the mean & the median

16. Measures of Center or Central Tendency –Mean The sample mean or average of a set of n measurements x1, x2, · · · , xn is the sum of these measurements divided by n The mean is denoted by ¯ x and is expressed as: Examples: given the heights in inches of five men as 66, 73, 68, 69, and 74 Then the mean equals

17. Measures of Center or Central Tendency –Median The sample median of a set of n measurements x1, x2, · · · , xn is the middle value when the measurements are arranged in order of magnitude, e.g., from smallest to largest If n is an odd number, there is a unique middle value and it is the median If n is an even number, there are two middle values and the median is defined as their average Roughly speaking, the median is the value that divides the data into two equal halves In other words, 50 % of the data lie below the median and 50 % lie above it

18. Measures of Variation or Dispersion No two objects are exactly alike, even “identical twins” differ The universe is filled with objects & individuals which vary from one another by some characteristics more so in biological & medical data The averages (mean, median, and mode) or measures of location which we have treated measure the center of data The assumption is that all data in the observation takes a single value, in most cases does not hold Therefore, there is a need to measure the degree of spread or variation of our data from one another and (or around the average) This degree of spread is called variation or dispersion

19. Measures of Variation or Dispersion –The Range The range which is defined as highest data value - lowest data value, is a basic measure of variability or spread For example, in the two schools’ data above, we have for both the schools: School I: Range = 22 - 13 = 9 School II: Range = 19 - 17 = 2 The data in school II is said to be more homogeneous than those from school I

20. Measures of Variation or Dispersion –Variance & Standard Deviation Variance of a sample is always represented by S2 The standard deviation will be represented by the square root of S2, i.e., S = √S2 While the standard deviation is an absolute measure of dispersion, it is measured in units & coefficient of variation on the other hand is a relative measure of dispersion based on the standard deviation & dimensionless

21. Types of Hypotheses in Experiment A hypothesis is a tentative explanation or prediction that can be tested through empirical research It is a statement that posits a potential relationship between variables (dependent & independent), Categorised as Null and alternative hypothesis These have to either be accepted or rejected based on statistical results

22. Types of Hypotheses in Experiment The null hypothesis posits that there is no effect in the population being studied It assumes that the independent variable has no impact on the dependent variable When conducting statistical tests, we start by assuming the null hypothesis is true The alternative hypothesis states that there is an effect in the population or a difference Represents the researcher’s prediction or expectation regarding the relationship between variables When we find evidence supporting the alternative hypothesis, we reject the null hypothesis

23. Type I and Type II Errors in Research A type I error occurs when in research when we reject the null hypothesis & erroneously state that the study found significant differences when there indeed was no difference In other words, it is equivalent to saying that the groups or variables differ when, in fact, they do not or saying an intervention works yet it doesn’t; look for examples A type II error occurs when we declare no differences or associations between study groups or an intervention when, in fact, there was

24. Terms Related to Experimental Designs Replication is the repetition of experimental conditions so that the effects of interest can be estimated with greater precision and the associated variability can be estimated Additionally, it guarantees that the result was not accidental

25. Terms Related to Experimental Designs Blocking is a technique that can be used to control and adjust for some of the variations in experimental units In order to allow treatments assigned to experimental units in the same block to be compared under reasonably similar experimental conditions, blocking is used An experiment is called to be blocked when the experimental units are divided, or partitioned, into groups called blocks

26. Terms Related to Experimental Designs Randomization is a process that ensures that research participants/treatment units have an equal chance of being selected into any treatment group/intervention of the study This distributes the confounders/sources of errors by creating similar/comparable intervention groups The reason for the variation in study findings and observations is due to confounders They may be known or unknown, & because of the unknowable impacts of unmeasured factors, they may provide inaccurate results A control is employed to reduce the impact of known or unknown factors (apart from the variable under investigation) on the study conclusion, hence enhancing the reliability of the findings The inclusion of control in the study enables the researcher to determine that, for instance, if a new herbicide is demonstrated to be successful in reducing couch grass, was not the result of chance

27. Agricultural Experimental Designs Completely Randomized Designs (CRD) This layout works best in tightly controlled situations and very uniform conditions For this reason, CRD is not commonly used in field experiments It can be applied in a greenhouse or growth chamber, on a fairly homogeneous field, or in situations when you are unsure of the variability in your field The CRD functions well in very homogeneous and strictly regulated environments A farmer wants to study the effects of four different fertilizers (A, B, C, D) on maize productivity

28. Agricultural Experimental Designs Randomized Complete Block Designs (RCBD) The randomized complete block design is used to evaluate three or more treatments Similar to the paired comparison, plot orientation and blocking aid in addressing the issue of field variability The ideal solution is to utilize randomized complete block design when the field is not homogeneous , for example, in terms of slope, fertility level, soil texture, moisture gradient, etc. In this case, every block comprises a complete set of treatments, and inside each block, the treatments are assigned at random.

29. Agricultural Experimental Designs Split-plot designs The split-plot design is for experiments that look at how different sets of treatments interact with each other It is an experimental design in which researchers are interested in studying two factors in which one of the factors is “easy” to change or vary For instance, in research on cover crops, it could be more practical—due to mechanical limitations to plant the cover crops in the main plots, which are bigger areas, and then apply different treatments, such as different fertilizer rates, to the sub-plots In the illustration in the Figure, one treatment the main plot—fallow or pea is split further into another treatment (sub-plots) of interest Here, compost and fish fertilizer are compared to a control

30. Agricultural Experimental Designs Latin Square designs (Assignment) Design an experiment while using Latin square design, clearly defining dependent and indepent variables and how the data will be analysed . Send a pdf format through the e-mail: [email protected] within 2 weeks from today 06/07/2024

31. Analysis of Experimental Data Different methods can be used to analyse data depending on the scales of measurement of the data (data type) and the experimental design Analyses can be done at univariate, bivariate and multivariate levels Univariate level involves descriptive statistics like mean, standard deviation, median, frequency & percentage Bivariate level involves test of association depending on the scale of measurement of dependent variable Chi-square test (categorical) Pearson correlation teste (continuous) Multiva riate level involves test of magnitude of association mainly regression Other tests like t-test (means of two groups), ANOVA (means of more than 2 groups)