two way classification design (CRD).pptx

This is used for expiremental reseach. RCBD Randomized Completed Block Design

1. TWO-WAY CLASSIFICATION DESIGNS

2. TWO CLASSIFICATION DESIGNS Experimental units are markedly heterogenous with respect to some criteria of classification, and usually the differences among the eu’s is the major source of experimental error. The design must account for the heterogeneity. These design is the RCBD and Latin Square.

3. THE RANDOMIZED COMPLETE BLOCK DESIGN One way of increasing precision of an experiment is by proper grouping or blocking of the experimental units. T he eu’s are grouped into blocks in such a way that the differences between the units among different blocks are greater than the differences between the units within each block. Likewise the blocking should be done in such a way that the blocks cut across or are perpendicular to the direction of the eu’s gradient. This way, if there are differences among the blocks ,the variability is removed from the experimental error thereby improving the precision of the experiment.

4. RCBD 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 The field or space is divided into uniform units to account for any variation so that observed differences are largely due to true differences between treat- ments . Treatments are then assigned at random to the subjects in the blocks-once in each block

5. RCBD 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.

6. RCBD 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.

7. RCBD Randomization and Layout Suppose there are four treatments which are replicated three times thus the total eu’s is 12. The randomization procedure uses draw lots. T = T 1, T 2 , T 3, , T 4 R = 3 Steps: Eu = 12 1. Group the eu’s into r = 3 blocks Block I Block II Block III

8. RCBD 2. Group the eu’s into r = 3 Block I Block II Block III 3. For each block, allocate the treatments into the eu’s at random and independently of other blocks as follows: a. Label the eu’s consecutively from 1 to t = 4 Block I 1 2 3 4 Block II 1 2 3 4 Block III 1 2 3 4

9. RCBD b. Obtain a sequence of t = 4 numbers using draw lots Block I 1 T 3 2 T 1 3 T 4 4 T 2 Block II 1 T 2 2 T 4 3 T 3 4 T 1 Block III 1 T 2 2 T 3 3 T 1 4 T 4 c . Using the sequence of draws as the treatment numbers as the eu numbers assign the treatments to the respective eu’s . Draw 1= T 3 Draw 2= T 1 Draw 3= T 4 Draw 4= T 2 Draw 5= T 2 Draw 6= T 4 Draw 7= T 3 Draw 8= T 1 Draw 9= T 2 Draw 10= T 3 Draw 11= T 1 Draw 12= T 4

10. RCBD Sample Problem 1. An experiment was conducted to study the effects of four varieties of mongo. The experiment was laid out in five farms . In each farm, four uniform plots were chosen on which the four varieties were randomly assigned. Make a lay out using the RCBD. 2. A hardness testing machine operates by pressing a tip into a metal test “coupon.” The hardness of the coupon can be determined from the depth of the resulting depression. Four tip types are being tested to see if they produce significantly different readings . The coupons might differ slightly in their hardness (for example , if they are taken from ingots produced in different heats). Thus coupon is a nuisance factor, which can be treated as a blocking factor. Since coupons are large enough to test four tips on, a RCBD can be used, with one coupon as a block. Four blocks were used.

11. R = 5 farms T = 4 varieties of Mongo EU = 20 V1 V3 V4 V2 V3 V1 V3 V1 V3 V1 V1 V3 F1 F 2 F3 F4 F5

12. LATIN SQUARE DESIGN If the eu’s exhibit heterogeneity in two direction of classification heterogeneity the two dimensional blocking method is to be used- LSD. Also known as C omplete B lock Design, it is a two way classification design. This is used when the experimental unit can be grouped into two categories (double blocking) such that the variations due to each category are eliminated from the experimental error.

13. LATIN SQUARE DESIGN One grouping or blocking is denoted as the column classification and the other is row classification. The grouping of the eu’s should be done so that the differences among rows and columns represent major sources of variation. The effect of the double grouping is to eliminate from the experimental error the variations due to the differences among the rows and the columns. The rows and the columns are general terms referring to criteria of classification. They may be kinds of treatment or factors. Thus the LSD design may be used to study three factors simultaneously assuming that the factors have no interactions among themselves.

14. LSD Blocking of LSD In the LSD design, the whole experimental materials are divided into as many rows and as many columns as there are many treatments. The treatments are then arranged in blocks in two ways: by rows and by columns, such that each treatment occurs once in each row and column. Each row is a complete block, each column is likewise a complete block. Randomization Steps: Obtain a basic Latin (T x T) square plan Example T = 4 r = 4

15. LSD 3 x 3 plot 4 x 4 plot 5 x 5 plot

16. LSD 6 x 6 plot

17. LSD Col 1 Col 2 Col 3 Col 4 Row 1 Row 2 Row 3 Row 4 A A A A B B B B C C C C D D D D

18. LSD R 1 – R 2 – R 3 – R 4 – 2. Randomize the assignment of the row classification to the rows on the plan. Draw sequence: 1 2 3 4 variable a ( location) Draw numbers: 3 1 4 2 plan rows L 2 L 4 L 1 L 3

19. LSD 3 . Randomize the assignment of the column classification to the columns on the plan. Draw sequence: 1 2 3 4 variable b ( type of plant) Draw numbers: 4 2 1 3 plan columns Col 1- Col 2- Col 3 - Col 4 - P 1 P 2 P 3 P 4

20. LSD A B C D B C D A C D A B D A B C 4. Randomize the assignment of treatments on the plan Draw sequence: 1 2 3 4 Treatment (kind of fertilizer) Draw numbers: A B C D plan for treatment L 2 L 4 L 1 L 3 P 3 P 2 P 4 P 1 T 1 T 1 T 1 T 1 T 2 T 2 T 2 T 2 T 3 T 3 T 3 T 3 T 4 T 4 T 4 T 4

21. B D C A D B A C C A D B A C B D L 1 L 2 L 3 L 4 P 1 P 2 P 3 P 4 T 2 T 4 4. Rearrange the rows and columns in sequence T 3 T 1 T 4 T 2 T 1 T 3 T 3 T 1 T 4 T 2 T 1 T 3 T 2 T 4

22. LSD 1. An agricultural experiment considered the effects of K 2 O ( potash) on the breaking strength of cotton fibers. Five K 2 O levels were used (36, 54, 72, 108, 144 lbs /acre). A sample of cotton was taken from each plot, and a strength measurement was taken. The experiment was arranged in 3 blocks of 5 plots each. Sample Problem

23. LSD 2. A plant biologist conducted an experiment to compare the yields of 4 varieties of peanuts (A, B, C, D). A plot of land was divided into 16 subplots (4 rows and 4 columns ). Sample Problem