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Analysis of Data from Designed Experiments |
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Incomplete Block Design |
Example : An experiment was conducted at Jorhat under the aegis of Project Directorate of Cropping Systems Research, Modipuram using a balance incomplete block (BIB) design with parameters v = b = 7, r = k = 4, λ = 2. The treatment details are as given below:
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Treatments (Crop Sequences) |
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| Season | T1 | T2 | T3 | T4 | T5 | T6 | T7 |
| Kharif | Rice | Rice | Rice | Rice | Rice | Rice | Rice |
| Rabi | - | Boro Rice | Mustard | Brinjal | Tomato | French Bean | Potato |
| Summer | Rice | - | Rice | Rice | Rice | Rice | Rice |
The yields from each of the crop sequence were converted into calories/ hectare. The block structure and the calories of the output per hectare obtained are given as
| Block 1 | T2 (3325060) | T4 (2606200) | T5 (3279420) | T6 (2330180) |
| Block 2 | T1 (2992900) | T2 (3228180) | T5 (3348780) | T7 (2982000) |
| Block 3 | T1 (3639920) | T4 (2467800) | T6 (2196580) | T7 (2730780) |
| Block 4 | T3 (2602410) | T5 (3696340) | T6 (2388060) | T7 (2921790) |
| Block 5 | T1 (3055180) | T3 (2653680) | T4 (2501060) | T5 (3594320) |
| Block 6 | T2 (3380420) | T3 (2760690) | T4 (2522100) | T7 (2961270) |
| Block 7 | T1 (2921420) | T2 (3380420) | T3 (2677400) | T6 (2594420) |
| T# denotes the treatment number and the figures in brackets are the Kilo calories/hectare. | ||||
1. Perform the analysis of variance of the data to test whether there is any difference between treatments.
2. Perform the analysis of variance of the data to test whether there is any difference between blocks.
3. Obtain adjusted treatment means and perform all possible pair wise treatment comparisons.
4. The experimenter is interested in ascertaining that the average effect of 1st two treatments is same as the average effect of the remaining 5 treatments.
5. Also compare the treatment 3,4,5,6,7 among themselves.
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For
exposure on SAS, SPSS, MINITAB, SYSTAT and
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data from designed experiments:
Please see Module I of Electronic Book II: Advances in Data Analytical Techniques
available at Design Resources Server(www.iasri.res.in/design)