# Experimental design Jenifer Udhaya P Basic Principles of

Experimental design Jenifer Udhaya. P

Basic Principles of Experimental Designs (1) Randomization. (2) Replication. (3) Local Control. Randomization. The random process implies that every possible allotment of treatments has the same probability. An experimental unit is the smallest division of the experimental material and a treatment means an experimental condition whose effect is to be measured and compared. The purpose of randomization is to remove bias and other sources of extraneous variation, which are not controllable.

Replication • The second principle of an experimental design is replication; which is a repetition of the basic experiment. • It is a complete run for all the treatments to be tested in the experiment. In all experiments, some variation is introduced because of the fact that the experimental units such as individuals or plots of land in agricultural experiments cannot be physically identical. • This type of variation can be removed by using a number of experimental units.

Local Control Choose a design in such a manner that all extraneous sources of variation are brought under control. “local control” a term referring to the amount of balancing, blocking and grouping of the experimental units. Balancing means that the treatments should he assigned to the experimental units in such a way that the result is a balanced arrangement of the treatments. Blocking means that like experimental units should be collected together to form a relatively homogeneous group.

Completely Randomized Design The design is completely flexible, i. e. , any number of treatments and any number of units per treatment may be used. Moreover, the number of units per treatment need not be equal. A completely randomized design is considered to be mo useful in situations where (i) the experimental units are homogeneous, (ii) the experiments are small such as laboratory experiments,

. An example of the experimental layout for a completely randomized design (CR) using four treatments and each repeated 3 times, is given below:

Suppose we have 4 different diets which we want to compare. The diets are labeled Diet A, Diet B, Diet C, and Diet D. We are interested in how the diets affect the coagulation rates of rabbits. The coagulation rate is the time in seconds that it takes for a cut to stop bleeding. We have 16 rabbits available for the experiment, so we will use 4 on each diet. How should we use randomization to assign the rabbits to the four treatment groups?

• Label the cages 1 -16. In a bowl put 16 strips of paper each with one of the • integers 1 -16 written on it. • In a second bowl put 16 strips of paper, four each labeled A, • B, C, and D. • Catch a rabbit. • Select a number and a letter from each bowl. • Place the rabbit in the location indicated by the number and feed it the diet assigned by the letter. • Repeat without replacement until all rabbits have been assigned a diet and cage.

If, for example, the first number selected was 7 and the first letter B, then the first rabbit would be placed in location 7 and fed diet B. An example of the completed cage selection is shown below.

Randomized Block Designs • They require that the researcher divide the sample into relatively homogeneous subgroups or blocks. • Then, the experimental design you want to implement is implemented within each block or homogeneous subgroup. • The key idea is that the variability within each block is less than the variability of the entire sample. • Thus each estimate of the treatment effect within a block is more efficient than estimates across the entire sample. And, when we pool these more efficient estimates across blocks

LATIN SQUARE DESIGN (LS) The Latin square design is used where the researcher desires to control the variation in an experiment that is related to rows and columns in the field. • Treatments are assigned at random within rows and columns, with each treatment once per row and once per column. • There are equal numbers of rows, columns, and treatments. • Useful where the experimenter desires to control variation in two different directions

Suppose that we want to test five drugs A; B; C; D; E for their effect in alleviating the symptoms of a chronic disease. • Five patients are available for a trial, and each will be available for five weeks. • Testing a single drug requires a week. • Thus an experimental unit is a ‘patient-week’. The structure of the experimental units is a rectangular grid

We can use the Latin square to allocate treatments. Now each patient receives all five drugs, and in each week all five drugs are tested.

Factorial Designs • A factorial design is often used by scientists wishing to understand the effect of two or more independent variable upon a single dependent variable. • These are helpful in economic and social research. • In factorial designs, a factor is a major independent variable. In this example we have two factors: time in instruction and setting. A level is a subdivision of a factor. • The number of different treatment groups that we have in any factorial design can easily be determined by multiplying through the number notation. For instance, in our example we have 2 x 2 = 4 groups. In our notational example, we would need 3 x 4 = 12 groups.

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