Split Plot Design(ppt).ppt
- 1. Split Plot Design In factorial experiments certain factors may require larger plots than for others. For e.g., experiments on irrigation, tillage etc require larger areas. On the other hand experiments on fertilizers, weedicides etc., may not require larger area. To accommodate factors which require different sizes of experimental plots in the same experiment split-plot design has been evolved.
- 2. In this design larger plots are taken for the factor which requires larger plots. Each of the larger plots is split into smaller plots. To accommodate the other factors. The different treatments are allotted at random to their respective plots. Such arrangement is called split-plot design. Factor – A – larger area – 3 levels Factor – B – smaller area – 3 levels
- 3. Example 1: a1 a0 a2 a1b1 a0b0 a2b1 a1b2 a0b1 a2b0 a1b0 a0b2 a2b2 a1b1 a2b0 a0b0 a1b0 a2b1 a0b1
- 4. In split plot design the larger plots are called Main plots. Smaller plots with in each of this larger plot are called as sub plots. The factor levels allotted to the Main plots or main plot treatments and the factor levels allotted to the subplots are called as sub plot treatments. Advantages: This design provides increased precision in the estimates of subplot treatments and interaction effect compared to FRBD with 2 factors. This design helps in saving in experimental material. In many cases it would be enough to have wider borders between main plots only. This results in the saving of experimental area and resources devoted to the provision of border rows.
- 5. Disadvantages The major disadvantage of split plot design is that the effects of main plot treatments are estimated with less precision than they are in factorial RBD. The analysis becomes more complex when missing data occurs. The difference in the precision of the estimates of main plot treatment & subplot treatment is due to the sizes of main plots & subplots. Since the main plots are larger in size than the subplot, the heterogeneity will be more within main plot than within subplot.
- 6. Hence the experimental error for main plot will be more than that for subplot treatments. Split plot should therefore we used only after careful consideration of the relative importance of the factors to be examine. It should not be used when all the factors are to be compared with equal precision. Layout and analysis: First, the main plot treatment and subplot treatment are decided based on the required precision. The factor for which greater precision is required is assigned to subplots. The replication is then divided into number of main plots equal to main plot treatments.
- 7. Each main plot is divided into subplot depending on the number of subplot treatments. The main plot treatments are allotted at random to the main plots as in the case of RBD. Within each main plot the subplot treatments are allocated at random as in the case of RBD. The same procedure is followed for all the replications. Rep I Rep II Rep III a3 a1 a2 b2 b3 b1 b3 b2 b1 b1 b2 b3
- 8. ANOVA Model: Yij = µ +ri + tj +eij ----------RBD Yijk = µ +ri + Aj + bk + ABjk + eijk ---------FRBD (two factors) Split plot design Yijk = µ +ri + Mj + e(a) ij + Sk + MSjk + e(b)ijk
- 9. Sources df SS Mss F Rep r-1 Rss Rms Rms/ E(a)ms Main plot m-1 Mss Mms Mms/ E(a) ms Error (a) (r-1) (m-1) E(a)ss E(a)ms Subplot s-1 Sss Sms Sms/ E(b)ms Main X Sub (m-1) (s-1) M x Sss M x Sms M x Sms/ E (b) ms Error (b) m(r-1) (s-1) E(b)ss E(b)ms Total rms-1 Tss Note: Error (b) df = Total df - all df