By Robert Battel
Michigan State University Extension offers farmers data to consider from field research trials. Here’s some background on understanding the statistical analysis or treatment response side of the data.
Field research results are often shared by researchers, consultants, salespersons and Michigan State University Extension educators to assist farmers in determining if a particular practice or product is worth adopting. Statistical analysis provides a tool to determine the value and reliability of the data provided. Two common statistical values used in presenting research data are LSD (0.05 or sometimes 0.10) and CV. In addition to the use of these values, data can be presented in manner that allows the viewer a quick statistical evaluation.
LSD is the Least Significant Difference. The LSD represents minimum difference between treatments in the study (whether it’s a fungicide treatment, difference in population, difference in fertilizer rate or hybrid/variety) for the difference to be attributed to the treatment rather than some external factor like soil variability, difference in drainage, insect feeding or simply chance.
An LSD at the 0.05 level means that 95 percent of the time, given similar circumstances, researchers should get similar or repeated results. Less frequently, researchers will report the LSD 0.10, or that 90 percent of the time, given similar circumstances, they should get similar or repeated results.
CV stands for Coefficient of Variation. The CV is a measure of the variability of the data that cannot be explained by the statistics. Again, there are factors other than the treatment that can influence the data, like number of replications, drainage, soil variability and rainfall. The lower the CV, the more confident you can be that the study contains quality results. In field-based research, a CV of less than 10 percent is usually considered good data, and a CV of less than 5 percent is usually considered very good data. Researchers aim to find sites with uniform soils, keep weed pressure minimized, replicate treatments at least three times, and do other things to minimize variation. Some variation cannot be controlled and is inherent to field research, thus the use in reporting CV.
Presentation of data
When showing that one or more treatments were statistically different from other treatments, researchers usually choose one of two presentation formats. The first is to use letters to show significant differences. See Table 1.
|Table 1. Corn response to sidedressed nitrogen.|
|Sidedress N (lbs./A)||Moisture (%)||Yield (bu./A)|
|LSD @ 0.05||—||15|
In this trial, we are 95 percent certain that the two treatments with the lowest sidedressed N (0 and 40 pounds) yielded significantly lower than any treatment that yielded greater than 123 bushels [108 + 15 (15 is the LSD) = 123]. They are designated with a “c”, or they are the lowest yielding treatments.
The 0 and 40 pound treatments also yielded statistically similarly to the 80 pound treatment, because they were within 15 bushels of the 80 pound treatment. The 80 pound treatment also yielded within 15 bushels of the 160 pound treatment. But the 160 pound treatment yielded more than 15 bushels compared to 0 and 40 pound treatments, so the 80 pound treatment is designated with a “bc”, showing that it was within 15 bushels of both the lowest yielding and second lowest yielding treatments.
The 160 pound treatment yielded within 15 bushels of the 80 pound treatment and the 120, 200 and 240 pound treatments, so it is designated with an “ab”. The 120, 200 and 240 pound treatments, yielded more than 15 bushels greater than anything designated with a “c” or “b”, so they are designated with only an “a”, or they are the highest yielding treatments.
A second way researchers present data is to mark the treatments that yielded statistically greater than other treatments with a symbol such as an asterisk (*) or sometimes a bold font. See Table 2.
Table 2. Soybean Liberty link variety trial.
DF 9171 N LL
DF 9232 N LL
Great Lakes 2264NLL
Great Lakes 1769NLL
DF 9221 N LL
DF 9127 N LL
* Yield not statistically different than highest yield variety.
** Highest yield variety.
In this case, the researchers wanted to show statistically significant differences from the top yielding variety. The top yielding variety yielded 70.8 bushels per acre. The LSD at the 0.05 level was 8.1 bushels per acre. Therefore, any variety that yielded within 8.1 bushels of 7.08, or 62.7 bushels per acre or greater, yielded statistically the same as the top yielding variety.
The top seven yielding varieties all yielded the same as the top yielding variety, from a statistical standpoint. The yielding variety is reported with a double asterisk, and each variety that yielded statistically the same is designated with one asterisk. The bottom yielding three varieties all yielded statistically less than the top yielding variety.
Statistical difference does not imply economic difference. Two treatments may be statistically different in yield but neither economically viable from a cost standpoint.