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Agricultural Experimentation
Procedure for Agricultural Experimentation Introduction Objective: This lesson is to help you to understand a few principles in statistical procedures and the fundamentals of experimental designs. Note: This lesson is very basic and is meant for technicians in agriculture to learn statistical concepts and methods for use field-level research. For a comprehensive study, you should refer to textbooks on statistical methods and experimental designs. You can also visit available on-line statistical tutorials such as:http://statpages.org/javasta4.html Procedure for Agricultural Experimentation In agriculture research a scientist identifies solutions to problems through experimentation. Research can be broadly defined as a systematic inquiry into a subject to discover new facts or principles.
Research involves the following steps:
The procedure for experimentation involves:
The experiment is an important tool of research. Some important characteristics of a well-planned experiment are:
Variability is a characteristic of biological material. Hence we need to decide whether differences between experimental units result from unaccounted variability or real treatment effects. An experimental unit refers to the unit of material to which a treatment is applied. It can be a single leaf, a whole plant, an area of ground containing many plants, a pot, or in the green house. The term plot is synonymous with experimental unit. A treatment may be an amount of material or a method that is to be tested and compared with other treatments in the experiment; e.g., cultivar fertilizer doses, etc. Variable: A measurable characteristic of an experimental unit is a variable; plant height, days to flowering, panicle length, or grain yield etc.Individual measurements of a variable are data; 150 cm plant height, 45 days to 50% flowering, 12 cm panicle length, or 3240 kg/ha of grain etc. Data: A set of observations or measurements of a particular variable in an experiment; 105 cm, 95 cm, 120 cm, 75 cm, 100 cm, ...., represent data about the variable (plant height). Population: In a statistical sense, a population is a set of measurements or counts of a single variable on all the units in the specified population. Sample: A sample is a set of measurements (observations) obtained from part of the specified population.For example: All 150 plants in a plot form the population. Ten plants used for recording the plant height from this population form the sample. We obtain information from the sample. Mean: Mean is the simple arithmetic average (of the sample or population). Standard Deviation (SD): The measure of dispersion of the data around their mean is the Standard Deviation. SD tells us how scattered the sample observations are around the mean. Variance: Square of the Standard Deviation.Standard Error (SE): The SD of the population of means is its standard error. SE tells us how scattered the treatment means (for example) will be. Degrees of freedom (df): Represents the freedom with which the variability in a data set could be accounted for. Usually, but not necessarily, df is one less than the number of observations(n-1). For example, with 24 observations on plant height, the degree of freedom to account for the variability in plant height is 23 (24 observations - 1). Probability level: We use a probability level to tell us whether an observed result is likely to have happened by mere chance.For example, a probability of 5% (0.05) tells us that a particular result observed may not happen in 5 trials out of 100 trials purely by chance. In other words, the result would normally be true in 95 cases out of 100 trials. In agricultural experimentation, it is customary to describe the results that would be expected by chance 5% or less as SIGNIFICANT and those expected by 1% or less as HIGHLY SIGNIFICANT. However it is up to the scientist to select the odds at which it is believed there are real effects.
Data on a variable may commonly follow one of the following distributions.
This type of distribution is expected in data, which describes the proportion of occurrences in which each occurrence can only be one of two possible outcomes. For example in data representing percent survival of insects, one can expect either dead or live insects. Poisson Distribution This is a distribution, which represents occurrences of rare events. For example, count data such as the number of infested plants, the number of lesions per leaf, or number of weeds per unit area. Normal Distribution These data represent a continuous distribution. Most biological data, when plotted in a frequency curve, represent a bell shaped and symmetrical curve. Such data are said to be normally distributed. For example, grain yield, plant height, etc.
Variability is a characteristic feature of nature. Two plants growing side by side are not alike even under similar conditions. We also know that data on plant growth characters reveal this variability. For example, from data on five samples plant height such as 115 cm, 95 cm, 82 cm, 108 cm, and 72 cm, ....., can we say the growth was good (115 cm plant height) or the growth was poor (72 cm plant height)? What is the truth? A statistical procedure to estimate the probability of a result happening by chance is called a test of significance. 't' test, 'F' test, and Chi-square test are commonly used statistical procedures for testing significance of observed results. 't' test of significance: The single-sample 't' is a statistics computed from a sample, which expresses the difference between the sample mean and a hypothetical population mean in standard error units. Thus: 't' = (sample mean - population mean) / standard error The theoretical 't' values for the degrees of freedom for different sample sizes at different probability levels are provided in a 't' Table. Comparing the calculated 't' value with that of the theoretical 't' value from the 't' table, one could test the significance of the sample mean being different from the hypothetical population mean. If the calculated 't' is > 't' table value, then the two mean values that are being tested are significantly different. 'F' test of significance: The 'F' test is a ratio between two variances and is used to determine whether two independent estimates of variance can be assumed to be estimates of the same variance. In the analysis of variance, the 'F' test is used to test equality of means of two or more treatments; that is, to answer the question, can it reasonably be assumed that the treatment means resulted from populations with equal means? Like the theoretical 't' values, theoretical 'F' ratios are also computed for different sample sizes at a given probability level in the form of a 'F' Table. Comparing a calculated 'F' ratio with that of the theoretical 'F' ratio from the 'F' Table, the significance among a group of treatments could be tested. If the 'F' calculated is > 'F' Table values, then the treatments are significantly different at that probability level. If the 'F' calculated is < 'F' Table value, then the treatments are not significantly different at that probability level.
A partitioning of the total variability in the data arising from various sources is presented in the form of a Table. This Table is called the Analysis of Variance Table and consists of:
The usage of an analysis of variance could be better understood if you review the lessons on experimental designs. We hope that this tutorial helped you to understand some of the basic principles in the statistical procedures used in agricultural experimentation. You may also refer to the following books:
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