Simple Experimental design-Analysis of Variance, Biology tutorial

Introduction:

Over the years, a huge range of experimental patterns has been build up and designs are available to suit a broad variety of conditions. Experimental design might be considered beneath two main headings. The primary is the real pattern of the experiment in which a right design based partially on knowledge of the experimental material and partially on the type of question wish for to ask. Second is the analysis of the data. As a rule, the outcomes of the type of experimental can be sum up in an analysis of variance (Anova) table. The design and analysis of an experiment evidently affect one other very strongly.  That is for a specific design, there really one satisfactory manner of examining the data.

Experimental Design:

Experimental design basically deals with the techniques of constructing and examining comparative experiments like comparing the effect of various factors or treatments. Planning experiments is made much more efficient if you comprehend the merits and demerits of various experimental designs and how they influence the 'experimental error' against which we test our differences between treatments. There is the requirement to comprehend how experimental design plus treatment and replicate numbers impact on the 'residual degrees of freedom' and whether you must be looking at one-tailed or two-tailed statistical tables.

 Experimental design makes sure that highest precision is accomplished for the amount of effort expended in the experiment. In each and every design, it is significant that the roles of the treatments must be well stated and the objectives of the experiment correctly understood. 

An experiment is a systematic method for making observations beneath controlled conditions in such a manner that they can be employed for arriving at general conclusions regarding the population beneath study. The experimental unit is a plant or animal or group of plants or animals making up a single duplicate of a single treatment. It is as well termed as a plot.

Principles comprised in experimentation:

1) Randomization: This comprises the assigning of treatments to the available material at arbitrary.

2) Replication or Reproducibility: It is the requirement for an experiment to be planned in such a manner that it can be replicated or reproduced. Replication is significant in diminishing error and improving accuracy.

3) Homogeneity or Sensitivity: A homogenous experimental established is one that consists of uniformity of materials and thus doesn't need the control of local variation. Whereas sensitivity is to be capable to approximate the effects of the treatments so that convincing conclusion can be drawn.

Types of Experimental Design:

1) Completely Randomized Design (CRD):  It is the simplest kind of experimental design in which treatments are allocated at random to a set of plots. It is applicable if homogenous (that is similar) experimental material is employed on heterogeneous (that is, different) experimental units or treatments, that is replicated more than once. CRD makes sure that treatments allotment is fully random thus avoiding biasness and minimizing inherent differences in experimental units or treatment.

Merits of CRD:

i) The design is extremely flexible and can be employed for any number of treatments.

ii) The statistical analysis is somewhat simple and straight-forward.

iii) It is unchanged by missing observations for any treatment for some purely arbitrary accidental reason.

Demerits of CRD:

i) The design is inherently less informative than the other more complicated layouts.

2) Randomized Block Design (RBD): It is an experimental design in which the net area is splitted into blocks and all of the treatments are arranged in each block in a random manner. It is perhaps the most broadly employed experimental design. 

Merits and Demerits of RBD:

i) With heterogeneous material, the residual variance can be decreased by selecting blocks of plots in such a way that the plots in the blocks are fairly identical, that is, the design decreases the effect of heterogeneous material.

ii) There is no limit on the number of blocks or treatments, however in each block there should be the similar number of plots, one to each treatment.

iii) If some yields are by chance lost, the analysis is again without due complications, however special modifications are needed.

Method of a randomized block experiment:

Phase I:

a) Total rows and columns, and make sure grand total by adding both row and column totals.

b) Compute correction factor for experiment = (Grand total 2)/(number plots)

c) Compute total sum of squares (added squares - correction factor!).

Phase II:

a) Create the analysis of variance table having the headings: Source of variation, d.f., Sum of squares, Mean square, F and P.

b) Place the sources of variation as Treatments, Blocks, Residual and Total.

c) Assign degrees of freedom as (n - 1) for number of Treatments and Replicates, and the product of such two d.f. for the Residual. Verify that the three d.f.'s add up to (n - 1) for the Total (that is, one less than the number of data in the experiment).

c) Square and add the TREATMENT totals to get the Treatments sum of squares of the deviations.

d) Square and add the REPLICATE totals to get the Replicates sum of squares of deviations.

e) The 'Residual' sum of squares of deviations is the remainder of the 'total' sum of squares of the deviations.

End Phase:

Compute the mean square for 'treatments', 'replicates' and 'residual' by dividing each sum of squares of deviations by its own degrees of freedom.

3) Latin square:  Is an experimental design in which the number of rows, columns and treatments are equivalent and each treatment takes place just once in each row and column. As the name entails, a Latin square is a square design in that it comprises of the similar number of plots (though such don't encompass to be square) in two dimensions, i.e. 4 × 4, 5 × 5, 6 × 6 and so on. The 'dimension' of the square is the number of treatments in the experiment.

Simple Factorial Experiment:

A factorial experiment is one where the treatments assigned to the experimental plots are combinations of two or more factors (therefore the word 'factorial').

Analysis of Variance (ANOVA):

The Analysis of variance (that is, ANOVA) is a systematic method for getting two or more estimate of variance and comparing them. Anova as a method allows the comparison of means and variances in an experiment which comprises more than two treatments. This approximates the value of the true variance of the population (σ2) from which the sample is drawn.

Anova allows us to conclude whether or not all means of the population beneath study are equivalent base on the degree of variability in the sample data. Thus, it is much proficient and powerful method for investigating relationships among various groups of data.

Assumptions in ANOVA:

In Anova, the given suppositions should be made or else its suitability becomes questionable.

1) Samples are drawn arbitrarily and each and every sample is independent of the other samples.

2) The populations in study include distribution that is around the normal curve.

3) The populations from which the sample values are obtained all encompass the similar population variance (σ2). That is (σ12 = σ22 = σ32 = .............σk2), the variances of all the populations are equivalent.

Hypotheses in ANOVA:

1) The null hypothesis (that is, Ho) in Anova is that the independent samples are drawn from populations having the similar means: Ho: µ1 = µ2 = µ3 = ................µk.

Where, k, is the number of populations in study.

2) The alternative hypothesis (H1) in Anova is that, not all population means are equivalent. That is, at least one mean is dissimilar from the others. 

H1: µ1 ≠ µ2 ≠ µ3 ≠ .........µk.

The Conclusions:

Conclusions regarding Ho in Anova test are mainly based on computed variance ratio, at times termed as the F-ratio.

1) Accept the null hypothesis, Ho, when the F-ratio value is less than the table value. That is, it is not important.

2) Refuse the null hypothesis, Ho, and accept the alternative hypothesis, H1, when the F-ratio value is more than the table value.

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