completely randomized design for experiments

1. Completely Randomized
Design
By: Jan Dave E. Deocampo and Riza Joy Palomar

2. A completely randomized design (CRD) is one assigned completely at random so that
each experimental unit has the same chance of receiving any one treatment. For the
CRD, any difference among experimental units receiving the same treatment is
considered as experimental error. Hence, the CRD is only appropriate for experiments
with homogeneous experimental units, such as laboratory experiments, where
environmental effects are relatively easy to control. For field experiments, where there
is generally large variation among experimental plots, in such environmental factors as
soil, the CRD is rarely used.

3. In experiments, a treatment is something that researchers administer to
experimental units. For example, a corn field is divided into four, each part is
'treated' with a different fertiliser to see which produces the most corn; a
teacher practices different teaching methods on different groups in her class to
see which yields the best results; a doctor treats a patient with a skin condition
with different creams to see which is most effective. Treatments are
administered to experimental units by 'level', where level implies amount or
magnitude. For example, if the experimental units were given 5mg, 10mg,
15mg of a medication, those amounts would be three levels of the treatment.

4. Randomization Procedure
-Treatments are assigned to experimental units
completely at random.
-Every experimental unit has the same probability of
receiving any treatment.
-Any difference among experimental units receiving
the same treatment is considered experimental
ERROR
-Randomization is performed using a random number
table, computer, program, etc.

5. Advantages of a CRD
-Its layout is very easy.
-There is complete flexibility in this design i.e. any number of
treatments and replications for each treatment can be tried.
-Whole experimental material can be utilized in this design.
-This design yields maximum degrees of freedom for
experimental error.
-The analysis of data is simplest as compared to any other design.
Even if some values are missing the analysis can be done.

6. Disadvantages of a CRD
-It is difficult to find homogeneous experimental units
in all respects and hence CRD is seldom suitable for
field experiments as compared to other experimental
designs.
-It is less accurate than other designs.

7. SOURCES OF VARIATION
TREATMENTS-source of variation of interest
EXPERIMENTAL ERROR- factors beyond control

9. Analysis of variance (ANOVA)
 Analysis of variance (ANOVA) can be used to test hypothesis if
there are more than two treatment groups to determine if there
are any significant differences between any of the groups.
 The samples must be of equal size, regularly distributed,
randomly chosen, and independent in order for ANOVA to be
reliable. Each population's variances are assumed to be the same
in this example.

10. TEST FOR HOMOGENEITY OF VARIANCE

15. ANOVA for Any Number of Treatments
with Equal Replication

21. (TSS/Tdf)
(ESS/Edf) TMS/EMS)

35. THANK YOU!