# Stats for the Rest of Us…How to Read Your Annual Report

02/13/17

Difficult though it may seem to many of us, statistical analysis is a fundamental tool that researchers at the CREC use on data to develop conclusions which helps identify whether treatments affect yield, gain, etc., or not.  Data usually comes from experiments where scientific approaches test variables (fertilizer, variety, herbicides, soil tillage, feedstuff, diets, components in a diet, etc.) and measure crop (yield, protein content, height, etc.) or livestock (daily weight gain, carcass weight, marbling, etc.) response to those variables (called treatments). Among them is a control (or check), to which the others are compared. Treatments are applied to experimental units (plots). For livestock experiments, a plot could be a pen with 10 steers in it, or each individual steer in the pen. For crop trials, we usually use field plots, which can vary in size from a few square feet to a few acres.

Experimentation has two basic principles: replication and randomization. Replication means that treatments within our trials are typically exist three to six times within a trial (i.e. treatments are replicated 3-6 times). This helps determine a true average for a treatment. Randomization means that plots are placed randomly throughout a trial area to avoid instances where some treatments experience better conditions than others due to location variability.

Table 1 is from a trial completed at the CREC in 2016.  The first column lists the treatments (rates of nitrogen) and “Check.” The remaining columns are variables potentially affected by the treatments. Table 1 summarizes the data from the study by using the mean (of four replicates) for each treatment.

These statistical terms are crucial to interpreting the results of any trial.

• Mean - is the same as average. The values presented for each treatment are the mean of 4 replications of that treatment within the trial.
• Standard deviation (SD) - a measure of the variation within a set of data values. A low SD indicates that values cluster close to the mean, while a high SD results from values spread over a wide range from the mean.
• Coefficient of Variation(CV) – the CV represents the SD of a data set as a percentage of the mean (CV= [SD/Mean]*100). A higher CV means there is more variability within the data set whereas a low CV means the data is more consistent. The green box in the table demonstrates that “Yield” and “Grain N-uptake” show the largest CV values and thus more variability in the data.
• P-value - if the p-value is less than or equal to the chosen significance level (typically 5%), it means that you are at least 95% confident that two treatment means are different, but it does not tell which treatment is better or worse. For that we use other statistical tests, such as the least significant difference.
• Least Significant Difference (LSD) – takes into account variability within a trial to calculate whether means are truly different by identifying the smallest (statically) significant value that is used to compare means. Any difference larger than the LSD value is considered significant (see LSD values (blue box) for “Flag leaf nitrogen” and “Grain protein” in Table 1). Notice that the means for those variables are followed by lower case letters. The way to read this is if two means are followed by the same letter they are not significantly different (purple box). When the difference between two means is smaller than the LSD value, the difference is called not significant and the LSD is usually represented by the letters “NS” (see LSD values for “Yield”, “Test Weight”, “250 kernel weight”, and “Grain N-uptake” in Table 1, gold box), and no letters are written behind the mean values since they will all be identical.

Actual table from the 2016 CREC Annual Report page 13:

Our hope is that this helps clarify things when you’re reading the Annual Report or listening to one of us present during a meeting. If you have questions about how to read something or what we’re trying to convey, don’t hesitate to contact us. You can request a printed copy of the CREC 2016 Annual Report by contacting us. We’re all available at 701-652-2951.

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