RCBD
EXPEREMENTAL DESIGNS
The Randomized Complete Block Design (RCBD)
The RCBD is the standard design for agricultural experiments where similar experimental units are grouped into blocks or replicates. It is used to control variation in an experiment by accounting for spatial effects in field or greenhouse. e.g. variation in fertility or drainage differences in a field
Treatments are then assigned at random to the subjects in the blocks-once in each block. The defining feature of the Randomized Complete Block Design is that each block sees each treatment exactly once.
With RCBD the experimental field is divided into blocks which should be perpendicular to the direction of the gradient and such that there is uniformity with blocs and not necessarily between blocks. Blocking helps to remove any variation among blocks thereby reducing experimental error.
Advantages of the RCBD
Generally, more precise than the completely randomized design (CRD). No restriction on the number of treatments or replicates. Some treatments may be replicated more times than others. Missing plots are easily estimated. A large number of treatments and replications can be handled more than CRD.
Disadvantages of the RCBD
Error degrees of freedom is smaller than that for the CRD (problem with a small number of treatments). Large variation between experimental units within a block may result in a large error term. If there are missing data, a RCBD experiment may be less efficient than a CRD. The analysis of data in the case of missing data is complex. It is not able to eliminate the effect of soil heterogeneity that runs in two directions of the experimental field.
NOTE: The most important item to consider when choosing a design is the uniformity of the experimental units.
The Layout of the Experiment
• Choose the number of blocks (minimum 2) – e.g. 4 • Choose treatments (assign numbers or letters for each) – e.g. 6 trt – A, B, C, D, E, F. The number of blocks is the number of replications.
Experimental design showing randomized blocks and treatments.
Block2 Block 1 Bloc 4 Block 3
Treatment A A F B C
Treatment B B E C D
Treatment C C D A E
Treatment D D C E F
Treatment E E B F A
Treatment E F A D B
Some terms
Experimental plot (unit): it is the smallest unit of an experimental field to which a single dose of treatment is assigned to. Just as a farm is often sub divided into fields so is an experimental field divided into experimental plot (unit).
Experimental field: it is the entire field that accommodates experimental plots (units) and treatments.
Treatment: it is a variable that is to be tested or investigated by an experimenter. E.g. cassava, rice, soya, mongo, maize variety e.t.c.
Replication: it is the repetition of treatment on two or more experimental plots (units). The greater the number of replications, the better the results.
Experimental error: it is the measure of the variation which exist among treatments or experimental material that have received equal treatment.
Randomization: it means an unbiased or indiscriminate assignment of treatments to experimental plots (units) such that all the treatments have equal chance of occupying any experimental plot (unit).
ANOVA: Analysis of variance is the most common method used for analyzing data gathered during field experimentation. It is capable of testing the differences between two or more means.
Ho: the null hypothesis is rejected if the F – calculated value is greater than the F- table value, which means significant difference exist among the treatment means.
Ho: the null hypothesis is accepted if the F- calculated value is less than or equal to the F- table value, which means No significant difference exist among the treatment means.
CALCULATIONS ON RANDOMIZED COMPLETE BLOCK DESIGN (RCBD)
CHARACTERISITICS OF A RANDOMIZED COMPLETE BLOCK DESIGN (RCBD)
Treatments are assigned at random to plots within a block (replication)
There are as many blocks as replications. That is number of blocks and replications are equal.
Any treatment can be adjacent to any other treatment but not to the same treatment within the same block.
The experimental filed has a fertility gradient running in one direction.
Blocking is carried out such that all blocks runs perpendicular to the fertility gradient.
There is homogeneity among experimental units (plots) of the same block.
Question = the effects of 4 types of graphite coater on light box readings are to be studied. Since readings will differ from day to day, observations are taken on each of the 4 types every day. The results are as follows; NB: Tot. SS = 2.27766667 AND Grand Total = 57.4
Create the ANOVA Table for this data and at 5 % level, test the claim that all of the graphite coaters produce the same average light-box readings.
SOLUTION
Compute the correction factor (CF)
Question= in an experiment to find the effect of time of application of fertilizer on the yield of millet varieties. Six (6) growth stages were identified. The fertilizer was therefore applied at the following stages:- A = soil preparation stage
B = germination stage
C = knee high stage
D = tasseling stage
E = two weeks after tasseling
F = milk dough stage
Non-significant difference exist among treatment means therefore the null hypothesis is accepted. Since non-significant difference exist among the blocks, the CRD should have been used because of soil homogeneity of the experimental plots.
NOTE: We stand to be corrected.
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