What's In A Number

Numbers are everywhere, but what do they mean? 

Everyone talks about averages - average rainfall, average temperature, average yield! Webster's dictionary defines "average" as "the result of dividing the sum of two or more quantities by the number of quantities summed". In other words, an average is essentially meaningless if the data used to calculate it is extreme. 

Let's look at an example. Consider three situations which have the same average bu/ac yields:

Although the best yield was recorded as 200 bu/ac in example C, which example do you think is more likely to give you more reliable average yield in the future? Example A is, because the variation between the individual numbers making up the average is "tighter". There is more likelihood that these differences are real and repeatable. By understanding the concept of variation, you are in a better position to interpret data and make the correct choices for your business. 

When you are faced with averages of data from which you are trying to make decisions, insist on a measure of the variation that is present. This could include the raw data that makes up the averages, so you can see the amount of variation present. It could include the Coefficient of Variation (CV) for the test or the Least Significant Difference (LSD). 

Coefficient of Variation (CV)

The CV describes the amount of variation in the data. The lower the CV value, the lower the underlying variation impacts the data. Values of less than 10% are best, but numbers up to 20 - 30% are likely acceptable, depending on the type of test.

Least Significant Difference (LSD)

The LSD is the amount of difference that has to occur between treatments for them to be assumed to be "statistically" different. The LSD determines if the differences between the average response of different treatments (ie hybrids, seeding rates, fertilizer rates) is due to the treatment or due to random chance that results from soil, climate, management or other variations across the trial site.

In the corn hybrid performance report, an LSD value is presented for each table. If the averages of two treatments differ by a value greater than the LSD, then they are considered significantly different from each other. LSD is a probability statistic measuring the potential for "chance" to occur. The LSD value is calculated in reference to some measure of chance, for example 0.05 (5%). This means that if the treatment means vary by more that the LSD value, then the difference can be considered significant with 95% confidence. In other words, if the two treatments differ by more than the LSD value, there is only a 1 in 20 chance that this difference is mearly random, and not "real".

Consider % Differences, Not Necessarily Bushels

Another mistake we commonly make with numbers is comparing "apple to oranges", or in this case corn to soybean yield differences. We tend to get excited about a new management technique that yields a 10 bu/ac increase in corn, but scoff at a 2 bu/ac increase in soybeans.

Consider two extreme years, 2001 and 2006, for average corn and soybean yields (Table 1). In 2001, a 10% increase in provincial yield would have resulted in a 12.2 bu/ac increase. The same percentage increase in soybean yield would have been 2.1 bu/ac. If we consider the same 10% increase in productivity for both crops in 2006, the results would be 16.5 bu/ac for corn and 4.7 bu/ac for soybeans. This is because the starting points are so different between the crops.

When we compare the advancements in yield between crops we have to be sure we are considering the percentage increase occurring and not the number of bushels. Two bushels of increased soybean yield can be as significant as more than 10 bushels of corn. Keep things in perspective! Of course the economics of each new practice must always be considered as well.

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