Variance

     Had some time to spend with a young vet this week.  I was picking his brain about variation and its cost in pig production.  He related to me a story about a client who, while doing seemingly everything pretty well thought he was “missing one pig” (psy) and wanted this vet to “find the pig” for him. 

     He followed everyone around, observed everything from insemination techniques to farrowing and processing procedures and examined all the other practices as well as doing the prerequisite health checks etc. and didn’t find much out of order. 

     Here is an interesting result which illustrates the impact of variation on the optimal selling weight of finisher pigs.  The optimal weight of a single pig can be readily calculated if you know the approximate feed efficiency and adg for the last couple of weeks of finishing as well as an expected market price.  In general you want to add the next lb as long as the value received for that lb is in excess of the cost.

     As you add lbs each day in late finishing, adg tends to stablize around 2 lbs per day but feed efficiency begins to deteriorate.  Therefore, each additional lb will cost a little more to put on.  As you add weight, at some point you will begin to incur a discount to the base price and lean percent will begin to deteriorate.  If you know how these things change, you can estimate the optimal selling weight of a single pig.

You can get an idea about some of the principles of variation by taking a look at everyone's favorite topic, corn prices. If you examine the average national corn price for the last ten years you will find that it was $2.28/bu with a standard deviation of about $0.43. Just by looking at those two numbers you can get an idea that there is some considerable variation going on in the historical pattern of corn prices.

Calculating the coefficient of variation (CV) yields 0.189, which you will recall is the standard deviation divided by the mean. Now if I were to ask you if the volatility in the corn market had increased since October 2006 what would your gut reaction be? I suspect you would be suckered in to saying "yes".

     There arises an issue though when comparing two distributions which requires some additional insight.  For instance, if you examine the average corn price and its associated standard deviation over two different time periods, you may want to judge which period had the greatest variability.  Simply comparing the standard deviations would be the first thought, however, that would describe the absolute difference in variation. When comparing two different distributions we are usually interested in knowing their relative variability.

     One way is to compare the ratio of the standard deviations to the means.  This is a form of indexing and can reveal which variability is more significant (when compared to the average value).   Why is this important?  When I was a lot younger, I was a carpenter's assistant which meant that I would often have the job of cutting 2x4's to stated lengths called out by my boss.  At first, I was not very good at this and would often be off a small amount.  One day the boss was angry at me over this and told me the board I just cut was 1/2 inch off.  At first blush that sounded trivial to me so I told him 1/2 inch was not very much, and asked why was he so mad?  His reply was "if your nose was 1/2 inch longer you would think it was a big deal."

     Variation in a group or population is usually described with reference to one or more basic statistical functions.  The mean or average of a group or distribution is the most common statistic used.  It is calculated simply by adding all of the observations and dividing by the number of observations.  The mean is sometimes referred to as the expected value since it is a measure of central tendenancy and in one single oberservation, represents all of the different observations in the population.  All of the observations, when taken together, will be closer to the mean than any other single number.

Technology is providing increasingly available ways to both assess variation and to respond to it. If you don’t hang around the crop guys very much you may not know that they now have at their disposal some remarkable ways to respond to variation in soil type, elevation and drainage issues when planting and harvesting fields.

GPS systems coupled with satellite photos, soil maps and elevation map layers are providing the modern cropping system with a means to deliver a more ideal seed density, fertilization rate and treatment distribution as well as capture yield monitoring data dynamically as fields are planted, tilled and harvested. These systems allow the producer to automatically distribute fertilizer for instance in an infinitely variable dose to fields based on the crop planted, the previous crop planted, the soil type and the elevation of the land being driven over. Delivery nozzles are calibrated on the fly in response to GPS location and layers of related maps.