Slide 1:DESIGNS OF EXPERIMENTS IN AQUACULTURE RESEARCH   A.K. Roy and Ravi Saxena* Social Science Section Central Institute of Freshwater Aquaculture Kausalyaganga, Bhubaneswar – 751 002 *Associate Professor, Dept. of Statistics & Mathametic, IGAU, Raipur


Slide 2:Meaning of Research: Research in common parlance refers to a Search for knowledge. One can also define research as a scientific and systematic search for pertinent information on a specific topic. Research is an art of scientific investigation. ‘Research’ refers to the systematic method consisting of enunciating the problem, formulating a hypothesis, collecting the facts or data, analyzing the facts and reaching certain conclusions.


Slide 3:Objective of Research: The purpose of research is to discover answers to questions through the application of scientific procedures. The main aim of research is to find out the truth which is hidden and which has not been discovered as yet.


Slide 4:Types of Research: Descriptive vs. Analytical: Descriptive research includes surveys and fact-finding enquiries of different kinds. The major purpose of descriptive research is description of the state of affairs as it exists at present. In analytical research, on the other hand, the researcher has to use facts or information already available, and analyze these to make a critical evaluation of the material. Applied vs. Fundamental: Research can either be applied (or action) research or fundamental (or basic or pure) research. Applied research aims at finding a solution for an immediate problem facing a society fundamental research is mainly concerned with generalizations and with the formulation of a theory. “Gathering knowledge for knowledge’s sake is termed ‘pure’ or ‘basic’ research”.


Slide 5:Quantitative vs. Qualitative: Quantitative research is based on the measurement of quantity or amount. Qualitative research, on the other hand, is concerned with qualitative phenomenon, i.e., phenomena relating to or involving quality or kind.


Slide 6:Conceptual vs. Empirical: Conceptual research is that related to some abstract ideas or theory. It is generally used by philosophers and thinkers to develop new concepts or to reinterpret existing ones. Empirical research relies on experience or observation alone, often without due regard for system and theory. It is data-based research, coming up with conclusions which are capable of being verified by observation or experiment.


Slide 7:Research Process (Steps necessary to effectively carry out) formulating the research problem extensive literature survey developing the hypotheses preparing the research design, determining sample design collecting the data execution of the project analysis of data hypothesis testing generalizations and interpretation preparation of the report or presentation of the results i.e, formal write-up of conclusions reached.


Slide 8:Box-1: Stages of “Research Process”: Define Research Problem ? Review Literature (Last finding/theories/concepts) ? Formulate Hypothesis ? Design the Research (Experimental/ Sampling designs) ? Collection of data ? Analysis of data (Hypothesis testing etc.) ? Interpretation & Final report.


Slide 9:Preparing the Research Design: The research problem having been formulated in clear cut terms. The researcher will be required to prepare a research design, that can give maximum information. The research purposes may be grouped into four categories, viz., (i) Exploration, (ii) Description, (iii) Diagnosis and (iv) Experimentation.


Slide 10:Requirements for a good experiment (Cox, 1958) (i) Absence of systematic Error (ii) Precesion (iii) Range of validity (iv) Simplicity (v) Calculation of uncertainity


Slide 11:Statistical Hypothesis Every research problem evolves around a few hypotheses. Researchers are concerned with two types of hypotheses: research hypotheses and statistical hypotheses. Research hypotheses lead directly to statistical hypotheses. Statistical hypotheses are stated in such a way that they may be evaluated by appropriate statistical techniques. Hypothesis is generally defined as a declaratory statement, that is testable. It is a statement about the population that we wish to verify on the basis of available sample information.


Slide 12:Many Hypothesis can exist for the same Problem We may find many possible provisional answers (each one to be called an alternative Hypothesis) to the same problem. Only one of them is tested at a time for its validity against another. The hypothesis that is tested, is generally called Null Hypothesis (Ho) and the other, which usually gives a reverse statement, is called its Alternative Hypothesis (H1­). Neither hypothesis testing, nor statistical inference, in general, leads to the proof of a hypothesis. It merely indicates whether the hypothesis is supported or is not supported by the available data.


Slide 13:Box – 2: Classification of hypothesis testing


Slide 14:Test Criterion In every test, we generally compute the value of (the ratio of the deviation of the statistic from its expected value, with its standard error, SE): Where t is the statistic, which is computed from sample values


Slide 15:i) Test of proportions (single sample case): ii) Test of equality of proportions of two samples:


Slide 16:Small Sample Tests t - Test: We use t-test, when: (i) Sample Size is 30 or less, (ii) Population variance or standard deviation is unknown. While testing hypothesis following assumptions are usually made: (a) The population is normal (or approximately normal), (b) Observations are independently drawn for the random sample, (c) In case of 2 samples, population variances are assumed to be equal (for the test of equality of Means).


Slide 17:Areas of application (i) Test of dependence or association between 2 attributes, (ii) Test of goodness of fit, (iii) Test of homogeneity (of distributions, correlation coefficients and population variances). Test statistic formula is given by: This follows a ?2 distribution, with (n-1) degrees of freedom.


Slide 18:Some important definitions related to design of experiments Experiment: An experiment is a device or a means of getting an answer to the problem under consideration e.g. comparison of different doses of feed, etc. Experimental Unit : The smallest division of the experimental material to which we apply the e.g may be experimental unit pond. Treatment: Various object of comparison in an experiment is called as treatments e.g. species ratio, stocking density, feed and fertilizer, management practices. Experimental Error: Pond to pond variation under identical condition, which is due to random or chance factors beyond human control is known as experimental error.


Slide 19:Basic Principles of an Experimental Design: There are three important principles inherent in all experimental design like replication, randomization and local control. Replication: Replication of some experiment under identical conditions or Replication means that a treatment is repeated two or more times, its function is to provide an estimate of experimental error. Randomisation: Randomisation is a process of assigning the treatments to various experimental unit in a purely chance manner. Its function is to assure unbiased estimates of treatment means and experimental error. Local control: The process of reducing the experimental error by dividing the relatively heterogeneous experimental area into homogeneous groups is known as local control. By reducing the experimental error, we can increase the efficiency of the design.


Slide 20:Completely Randomised Designs (C.R.D.)   The application of the two principles of replication and randomization without the use of the third principle of local control of error results in the simplest of experimental designs known as completely randomized design (C.R.D.). Each treatment is assigned to a few units at random. It is not necessary that the number of replications for each treatment is the same but, if we are interested equally in all the treatment effects, it is simpler and more efficient to have each treatment replicated equally (Amble, 1975).


Slide 21:Characteristics of CRD: Simplest of all the designs, based on the principles of randomisation and replication   Treatments are assigned completely at random to each experimental unit. CRD is only appropriate for experiments with homogeneous experimental units, such as laboratory experiments: where environmental effects are relatively easy to control. Analysis of variance : A major advantage of the CRD is the simplicity in the computation of its analysis of variance, especially when the number of replication is not uniform for all treatments.


Slide 22:CRD FOR EQUAL REPLICATION


Slide 23:Step 8. Enter all the computed values in the ANOVA table Table of means : Significant difference between means : CD/LSD


Slide 24:RANDOMISED COMPLETE BLOCK DESIGN (RCBD) In the completely randomized design no attempt is made to reduce error through local control of error. In many situations the knowledge of the experimenter regarding the experimental material enables him to arrange the units in relatively homogeneous groups or blocks, each in size equal to the number of treatments, before allotting the treatments, one each to the units in a block at random. The resulting design, which is the simplest one employing all the three basic principles of planning experiments, is called the randomized block design. It is perhaps the most commonly used design in agricultural and biological investigations (Amble, 1975).


Slide 25:Characteristics of RCBD : Most widely used experimental design in aquaculture research where size of ponds/ tanks/cannals/ cisterns/glass jars are heterogenous. Especially suited for experiments where the number of treatment is not large. Important feature of the RCB design is the presence of blocks of equal size, each of which contains all the treatments.


Slide 26:Randomisation & layout: Randomisation process is applied separately and independently to each of the blocks. If there are six treatments T1, T2, T3, T4, T5 and T6 and three replications, we illustrate the procedure in the following steps. Block 1. Block 2. Block 3.


Slide 27:Table 2. Yield of different species of fishes.


Slide 28:Step 10. Enter all values computed in above steps in the analysis of variance outline. The Final result of our Example: is shown below.


Slide 29:Assumptions of Analysis of Variance (ANOVA) The error terms are randomly, independently and normally distributed. The variances of different samples are homogeneous. Variances and means of different samples are not correlated. The main effects are additive.


Slide 30:Procedure for detecting the presence and type of variance heterogeneity Compute the variance and the mean across replications for each treatment (the rang can be used in place of the variance) Plot a scatter diagram between the mean value and the variance Examine visually the scatter diagram to identify the pattern of relationship between mean and variance.


Slide 31:Transformation of data for stabilization of variances Logarithmic transformation Most appropriate for data where the standard deviation is proportional to the mean. Data that are whole numbers and cover a wide range of values e.g. number of insects per plot or the number of egg masses in per unit area etc.


Slide 32:Square-root transformation Appropriate for data consisting of small whole numbers.


Slide 33:Arc Sine Transformation Appropriate for data on proportions, data obtained from a count, and data expressed as decimal fractions or percentage. It is not applicable to percentage data which are not derived from count data such as percentage of protein in rice, percentage of carbohydrates, infection index etc.


Slide 34:Latin square design The randomized block design is intended to reduce error in respect of one factor by forming homogeneous groups. Often there is variation among test animal in respect of more than one factor. Variation in respect of two factors can sometimes be controlled simultaneously by an ingenious arrangement known as the latin square. In this design the number of replications must be equal to the number of treatments (Amble, 1975).


Slide 35:FACTORIAL EXPERIMENTS : In field experimentation, many situation arise when we want to test the variation in two or more factors at the same time simultaneously in the same experiment. For instance, we may be interested in growth performance of fish species stocked under different stocking densities and the best rates of fertilization. In order achieve this objective through the traditional approach, we have to perform two separate experiments - one for the variation amongst the stocking densities and the other for the variation amongst the different rates of fertilization, to select the best density and the best rate of fertilization, respectively. But, the conclusions drawn through this approach are valid only when the effect exterted by any one of the two factors is independent of the other. In most of the cases, the response of the first factor varies according to levels of the second factors i.e., the two factors interact each other and they are no longer independent. Another main drawback of this scheme is that the precision of two or more experiments thus conducted are different and hence, their results are not comparable.


Slide 36:Terminologies Factors The term factor refers to a set of related treatments, we may apply to different dosages of fertilizer. Here, ‘fertilizer’ irrespective of the doses is a factor, similarly stocking density, different types of feed etc., are also known as factor. Levels of factor The different states or components making up a factor are known as the levels of that factor. The levels may be quantitative or qualitative. The rates of fertilizer application, seed rate, stocking density, concentrations of chemicals etc., are examples for quantitative levels. The species composition of fish, species ratio, sources of fertilizer etc are some examples of qualitative levels.


Slide 37:Types of Factorial Experiments A factorial experiment is named based on the number of factors and the levels of each factor. For example, Ex1 : If there are four factors each at two levels, the experiment is known as 2x2x2x2 or 24 factorial experiment. Ex2 : If there are two factors each with three levels, the experiment is known as 3x3 or 32 factorial experiment. Ex3 : In general, if there are n factors each with p levels, then it is known as pn factorial experiments.


Slide 38:Simple, Main Effects and Interaction Simple Effect: The simple effect of a factor is the difference between its response for fixed level of other factors Main Effect : Mean of the simple effects of a factor is called the main effect of that factor. Interaction : The interaction of two factor is the failure of the levels of one factor, say A to retain the same order and magnitude of performance throughout all levels of the second factor, say B.


Slide 39:Example :In order to follow these terms consider an experiment with factors, each at two levels, generally known as a 22 factorial experiment. Let us suppose, we have to compare two species of fish and to study the response to the application of fertilizer. There are four treatment combinations. Species Fertilizer Mean Response N1-n0 n0 n1 S1 30 38 34 +8 (Simple Effect) S2 35 45 40 +10 (simple Effect) Mean 32.5 41.5 37 9 (Main Effect of fertilizer) S2-s1 +5 +7 +6 +2 (Simple (Simple (Main Effect Effect) Effect) of Species)


Slide 40:Analysis of variance (ANOVA) table for 22- Experiment


Slide 41:Switchover Designs In animal experiments the largest source of error variation is usually the variation from animal to animal. One way of overcoming this variation is to test different treatments on the same animal. This involves changing or switching the treatment from time to time. Hence the names : changeover design, crossover design, switchover design, etc., assigned to the design.