# Interpreting Statistical Analysis

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he main objective of agricultural research is to explore improved methods for producing crops and/or livestock to optimize economic return to the farm. Research involves the comparison of two or more treatments. The treatments may consist of varieties, amounts of fertilizer, pesticide products and/or application strategies, tillage practices, or other factors of interest.  This comparison is done to determine differences due to the respective treatments. However, soil type, fertility, moisture, and other characteristics usually vary across a field, sometimes in a very short distance. Replicates (reps) are used to quantify how much natural variability occurs within a trial. Use of an appropriate experimental design greatly reduces the effect of this natural variability in comparing treatments. Agricultural researchers use statistics as a tool to help determine if differences between variables are real, so meaningful conclusions can be drawn. The statistical analysis compares the natural variability among reps to the variability among treatments. The result is the probability that a difference between treatments is due to a treatment effect and not just natural variability in the field.

A common indicator of the natural variability in an experiment is the C.V. (coefficient of variation), expressed as a percentage. The higher the C.V., the more variable the data within a study. With higher variability, a greater difference between treatments is needed to achieve a statistically significant difference. Unfortunately, the use of statistics does not allow us to draw conclusions with 100% certainty. Typically in crop-based studies a Least Significant Difference (LSD) is used to indicate when data values represent treatment differences with 95% certainty. A difference in treatments exists when the the difference between values for treatments is equal to or greater than the LSD.  For example, refer to the 2004 wheat yields in the table on page 38.  The LSD value is 6.8 bu/A.  Thus, when the yields for two varieties differ by 6.8 or more, the yields are significantly different.  The yields of Steele-ND and Briggs were significantly higher than all other varieties except Knudson.  When NS is listed for the LSD, the differences between values in that column are considered statistically non-significant. In the cases of an NS, the numeric differences shown may be due to some other factor(s) other than the treatments being evaluated. More locations or years of data may show these treatments to be significantly different.