WARC Annual Reports

Statistics

Statistics are very important for agricultural research.  They allow a person to understand how different treatments relate to one another.  Statistical analysis is a mathematical way to determine if the differences between treatments are a real effect or a random effect.  For agricultural research a significance level of α=0.05 is generally used.  This means that if there is a significant difference, the difference is expected to occur 95 percent of the time.  The following are some common statistical terms and their corresponding definition.

Experimental unit - the smallest unit that is measured in an experiment

Experimental design - is the way a researcher designs an experiment to reduce the amount of error in a project.  There are many different types with randomized complete block and split plot being the most common in WARC research.

Location - where the experiment takes place, as the number of locations increase the number of different environments increase allowing for better results because the treatments were exposed to more environments (also called sites).

Mean - average of the sample being measured.

Median - the exact middle when comparing a range of numbers.

Plot - in WARC related research it is the same as experimental unit

Replication - the amount of times that an experiment is repeated at each site (also called blocks).  Four is a common number of replication.

Standard error - a measure of the statistical accuracy of an estimate (often mean).  The smaller the standard error the more accurate the estimate.

Treatment - what is being applied to the experimental unit.  The treatments are being tested in an experiment (also called entry).

Trial - another term for experiment.  It encompasses all of the plots, or treatments and blocks in a test.

For example if the yield of variety A is larger and statistically different from variety B, variety A is higher yielding 95% of the time under the environmental conditions of the experiment.  Least significant difference (LSD) will be used in the WARC annual report to show differences among treatments like varieties and herbicides.  To compare treatment averages you subtract one treatment average from another.  If the difference is greater than the LSD the treatments are statistically different.  Table 1 shows an example of three different treatments.

Table 1  A statistical example of using LSD to determine significant differences between treatments.

treatment A (10) – treatment B (8) = difference (2)

2 is less than LSD of 2.5 so treatment A is not statistically different than treatment B

treatment A (10) – treatment C (5) = difference (5)

5 is greater than LSD of 2.5 so treatment A is statistically higher than treatment C

treatment B (8) – treatment C (5) = difference (3)

3 is greater than LSD of 2.5 so treatment B is statistically higher than treatment C

Statistical differences can also be presented by letters next to the average.  Treatment averages with the same letter are not different but treatment averages with different letters are significantly different (Table 2).  Treatments A and B are not significantly different but they are both significantly different from treatment C.

Table 2 A statistical example using letters on treatment averages to denote significant differences.

Statistical significance is usually shown as error bars on graphs.  If the error bar reaches as high as another average the treatments are not statistically different.  If the error bar does not reach as high as another average they are significantly different.  Treatment A and B are not significantly different but both are different from treatment C.

Figure 1  A statistical example using error bars on treatment averages to denote significant differences.

If treatment averages are not significantly different under the conditions of the experiment it is assumed that the environment of the experiment explains more of the treatment differences than do the treatments themselves.  When there is no significant difference it is difficult to predict which treatment will perform better.  The environment is the years and locations that the experiment takes place.

Two important factors that influence how precise an experiment is are the number of locations used and the number of years the experiment occurred in.  The more site years (multiply number of sites by the number of years) an experiment occurs in the more precise the results.  Experiments with few sites and few years do not have many different environments to compare.  More conclusive results are obtained by experiments with more site years of data.