INTRODUCTION:

Nested and Split Plot experiments are multifactor experiments that have some important industrial applications although historically these come out of agricultural contexts. “Split plot” designs are originally divided into whole and split plots and then individual plots get assigned different treatments (Jitendra Ganju and J.M. Lucas, 1999). For instance, one whole plot might have different irrigation techniques or fertilization strategies applied or the soil might be prepared in a different way. The whole plot serves as the experimental unit for this particular treatment. Then one could divide each whole plot into sub plots and each subplot is the experimental unit for another treatment factor. Split plot designs focus on the experimental unit for a particular treatment factor. Nested and split-plot designs frequently involve one or more random factors. There are many variations of these designs and here are some of the more basic Nested and Split Plot experiments

The Two-Stage Nested Design:

When factor B is nested in levels of factor A, the levels of the nested factor don't have exactly the same meaning under each level of the main factor, in this case factor A. In a nested design, the levels of factor (B) are not identical to each other at different levels of factor (A), although they might have the same labels. For example, if A is school and B is teacher, teacher will differ between the schools. This has to be kept in mind when trying to determine if the design is crossed or nested. To be crossed, the same teacher needs to teach at all the schools.

When B is a random factor nested in A, researcher can think as it replicates for A. So whether factor A is a fixed or random factor the error term for testing the hypothesis about A is based on the mean squares due to B(A) which is read "B nested in A".

The General m-Stage Nested Design:

The results from the previous section can easily be generalized to the case of m completely nested factors. The text book gives an example of a 3-stage nested design in which the effect of two formulations on the alloy harness is of interest. To perform the experiment, three heats of each alloy formulation are prepared, two ingots are selected at random from each heat and two harness measurements are made on each ingot.

Split-Plot designs:

In the statistical analysis of split-plot designs, scientist must take into account the presence of two different sizes of experimental units used to test the effect of whole plot treatment and split-plot treatment. Factor A effects are estimated using the whole plots and factor B and the A*B interaction effects are estimated using the split plots. Since the size of whole plot and split plots are different, they have different precisions. Generally, there exist two main approaches to analyze the split- plot designs and their derivatives (P.A. Parker, C.M. Anderson-Cook, T.J. Robinson and Li Liang, 2007). First approaches the Expected Mean Squares of the terms in the model to build the test statistics. The major disadvantage to this approach is the fact that it does not consider the randomization restrictions which may exist in any experiment.

1. Second approach which might be of more interest to statisticians and the one which considers any restriction in randomization of the runs is considered as the tradition approach to the analysis of split-plot designs.

The Split-Split-Plot Design:

The restriction on randomization mentioned in the split-plot designs can be extended to more than one factor. For the case where the restriction is on two factors the resulting design is called a split-split-plot design. These designs usually have three different sizes or types of experimental units.

The Strip-Plot Designs:

These designs are also called Split-Block Designs. In the case where there are only two factors, Factor A is applied to whole plots like the usual split-plot designs but factor B is also applied to strips which are actually a new set of whole plots orthogonal to the original plots used for factor A.

Incomplete split plot designs:

Another proposal of an incomplete split plot design where levels of one factor (say A) are applied to the whole plots and levels of the other (say B) to subplots and where the number of subplots in each whole plot may be less than the number of levels of factor B. The t levels of factor A are arranged in a completely randomized design. The s levels of factor B are arranged in a connected and proper incomplete block design within each level of factor A, by considering the whole plots as blocks.

Split-Plot Factorial Design:

It is often inconvenient, costly, or even impossible to perform a factorial design in a completely randomized fashion. An alternative to a completely randomized design is a split-plot design. The use of split-plot designs started in agricultural experimentation, where experiments were carried out on different plots of land. Classical agricultural split-plot experimental designs were full factorial designs but run in a specific format. The key feature of split-plot designs is that levels of one or more factors are assigned to entire plots of land referred to as whole plots or main plots, whereas levels of other factors are assigned to parts of these whole or main plots. These parts are called subplots or split-plots. Split-plot designs thus have two types of experimental units, whole plots and subplots. The smaller experimental units, the subplots are nested within the larger ones, the whole plots (Soren Bisgaard, 2000).

CONCLUSION:

Experiments should adhere the protocol; Nested and Split Plot experiments can be considered in case of multifactor experiments. Nurse scientist can broaden the notion in research designs and conduct research patent to innovate designs on Nested and Split Plot experiments. Even though certain designs do not suit for nursing research, nurses must be familiar and well exposed at the time of research platform.

REFERENCES:

1. Jitendra Ganju and J.M. Lucas, “Detecting Randomization Restrictions Caused by Factors,” Journal of Statistical Planning and Inference, Vol. 81, 1999, pp. 129-140.

2. Li Liang, C.M. Anderson-Cook and T.J. Robinson, “Cost Penalized Estimation and Prediction Evaluation for Split-Plot Design,” Quality and Reliability Engineering International, Vol. 23, No. 5, 2007, pp. 577-596.

3. Peter Goos and Martina Vandebroek, “Outperforming Completely Randomized Designs,” Journal of Quality Technology, Vol. 36, No. 1, 2004 pp. 12-26.

4. Soren Bisgaard, “The Design and Analysis of 2k--px2 q--r Split-Plot Experiments,” Journal of Quality Technology, Vol. 32, No. 1, 2000, pp. 39-56.

5. Li Liang, C.M. Anderson-Cook and T.J. Robinson, “Cost Penalized Estimation and Prediction Evaluation for Split-Plot Design,” see reference 2.

6. P.A. Parker, C.M. Anderson-Cook, T.J. Robinson and Li Liang, “Robust Split-Plot Designs,” Quality and Reliability Engineering International, Vol. 23, 2007.

7. P.A. Parker, S.M. Kowalski and G.G. Vining, “Classes of Split-Plot Response Surface Designs for Equivalent Estimation,” Quality and Reliability Engineering International, Vol. 22, 2006, pp. 291-305.

Received on 14.05.2016 Modified on 21.05.2016

Int. J. Nur. Edu. and Research. 2016; 4(4): 497-498.

DOI: 10.5958/2454-2660.2016.00092.2