VARIABILITY IN TRIALS Adapted fr M Gunther

Types of variability Normal random variability Controllable variability e.g. soil fertility gradients Uncontrollable variability e.g. theft of produce Unexpected variability e.g. digging a drain without thinking of the consequences

How to deal with variability Random variability can be a problem if there are limited plots – increase replication may help Trial design e.g. blocking may help overcome Controllable variability Uncontrollable variability may need data manipulation at analysis – missing plots, extrapolation from remaining portions Uncontrollable variability may be eased by careful site inspection, early planning, regular visits to the trial etc

Some experiences I have had The following set of slides represents a hypothetical variety trial It has nine treatments with five replications – this would often be considered to be over replicated

Basic yield of the varieties, randomised in each block II III IV V 22 24 21 23 27 25 26 28 29

Add a random variation component of up to 10% II III IV V 0.10 1.52 2.18 1.92 1.21 1.90 2.44 1.36 0.18 1.71 1.96 0.55 2.41 2.20 2.94 1.45 2.50 1.67 0.86 1.13 0.47 0.04 2.64 0.73 2.87 2.79 0.95 1.28 0.82 1.55 2.04 1.70 0.43 2.97 2.10 0.32 0.75 0.77 2.84 2.96

Next add on the effect of a soil fertility gradient II III IV V 1 2 3 4

What follows are things we may not have thought of!! Effects so far are what we could call normal and controllable variability What follows are things we may not have thought of!!

One corner of our trial extended onto an area of poor red soil II III IV V   -2 -4 -6

Some years ago, somebody had cleared a house site in the middle of our trial area II III IV V   -5

We had neglected to plan for adequate planting material and had to get what we could find II III IV V -4.86 -0.48 -4.54 -2.17 -3.05 -1.58 -4.36 -0.66 -1.84 -5.69 -0.89 -1.01 -5.28 -1.69 -1.39 -1.67 -1.95 -7.25 -0.80 -0.86 -0.01 -5.39 -1.92 -0.56 -5.89 -3.80 -2.22 -4.19 -2.95 -1.16 -4.12 -1.21 -3.76 -0.10 -5.34 -0.71 -5.23 -3.04 -1.24 -2.42 -1.17 -4.30

Weather got too wet and we had to dig drains quickly to avoid water logging 5.00  

Final yield results of the trial 22.24 31.04 23.64 26.75 28.16 25.31 22.08 29.23 21.52 19.49 33.82 32.94 29.28 33.73 30.81 27.26 22.50 26.16 38.70 38.81 24.86 16.74 23.56 29.56 26.15 31.97 30.93 30.65 28.60 28.00 28.11 23.70 32.34 35.18 34.94 25.36 27.63 25.58 31.40 25.09 29.71 34.97 29.35 33.67 29.66

Analysis of results with all the unexpected results Randomized Complete Block Source DF SS MS F P BLOCK 4 87.485 21.8714 TREAT 8 273.328 34.1660 1.65 0.1504 Error 32 663.645 20.7389 Total 44 Grand Mean 28.592 CV 15.93 Result is not significant- ie we cannot find any differences between any of the cultivars, even with five replicates. Note the CV is quite reasonable at 16 %.

Had we managed to avoid the drains Randomized Complete Block Source DF SS MS F P BLOCK 4 87.308 21.8271 TREAT 8 303.666 37.9582 3.49 0.0053 Error 32 348.307 10.8846 Total 44 Grand Mean 25.268 CV 13.06 LSD All-Pairwise Comparisons TREAT Mean Homogeneous Groups 9 28.800 A 6 27.758 AB 4 27.329 AB 8 26.928 AB 7 26.236 AB 3 23.680 BC 5 23.522 BC 2 21.716 C 1 21.444 C

Had we also managed to have prepared good planting material Randomized Complete Block Source DF SS MS F P BLOCK 4 76.968 19.2419 TREAT 8 265.157 33.1446 6.43 0.0001 Error 32 164.954 5.1548 Total 44 Grand Mean 27.804 CV 8.17 LSD All-Pairwise Comparisons TREAT Mean Homogeneous Groups 9 31.898 A 8 30.170 AB 6 29.584 AB 7 28.808 BC 4 27.802 BCD 5 26.632 CDE 3 25.938 CDE 2 25.056 DE 1 24.345 E

And avoided the old house site Randomized Complete Block Source DF SS MS F P BLOCK 4 57.938 14.4845 TREAT 8 309.554 38.6942 15.28 0.0000 Error 32 81.024 2.5320 Total 44 Grand Mean 28.255 CV 5.63 LSD All-Pairwise Comparisons TREAT Mean Homogeneous Groups 9 32.898 A 8 31.170 AB 6 29.584 BC 7 28.808 C 4 27.975 CD 5 27.632 CD 2 26.056 DE 3 25.938 DE 1 24.230 E

And the area of red soil !!! Randomized Complete Block Source DF SS MS F P BLOCK 4 103.901 25.9751 TREAT 8 264.631 33.0789 43.52 0.0000 Error 32 24.320 0.7600 Total 44 Grand Mean 28.681 CV 3.04 LSD All-Pairwise Comparisons TREAT Mean Homogeneous Groups 9 32.898 A 8 31.170 B 7 30.008 C 6 29.584 C 5 28.432 D 4 27.902 DE 3 27.138 EF 2 26.056 F 1 24.945 G

This may be an unreal result But, we can overcome some of these issues with good forward planning, careful site selection, close supervision of trials and …