# Plant Trials: statistical applications in the nursery industry

**Story by Chris O'Connor**

Most growers would be familiar with the need to conduct trials within their production nursery in order to optimise plant growth performance or business outcomes. Some examples of trials being used include evaluating;

· plant varieties for performance

· changed potting media formulations

· the performance of new fertilisers or other agrochemicals

· irrigation application

But for these trials to have merit and validity, they need to have good experimental design and data collection followed up with sound analysis. For example a visual assessment of crops may be unreliable especially where the differences are in small but still important magnitudes or where there is variation or overlap of the results of treated and untreated crops.

This is where the use of statistical analysis comes into play. Statistics helps us to organise, analyse and interpret data. This assists growers in determining probabilities and helps build confidence in decision making through increased sensitivity to differences between treatments and through overcoming our own biases and preconceptions.

A useful reference for growers who are looking at conducting trials and applying statistical analysis is the DOOR (Do Our Own Research) Manual for Plant Nurseries. First published in 1996, this text was designed specifically for the nursery industry and aims to empower growers to undertake their own statistically sound on -farm research. For those of you who do not own a copy, the text is now available for free from the Queensland Department of Primary Industries & Fisheries website http://era.daf.qld.gov.au/3054/

To whet your appetite on statistical analysis we’ll take a look at a basic tool which is standard deviation.

In statistics, the standard deviation is a measure that is used to measure the amount of *variation* or *dispersion* of a data set. For instance a low standard deviation indicates that the data points tend to be close to the mean or average of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.

This is well illustrated in the graph below (figure 1) where both examples have an average or mean of 100; however the standard deviation is very different; low standard deviation (10) indicates a reduced spread of values, whilst a higher standard deviation (50) indicates a wider spread of values.

So what you might ask, but imagine if these figures represented the height of a new batch of a trial crop. The average height is the same, but which one performs more consistently? Obviously in this example it is the red crop. Having an understanding of this information could influence your choice to incorporate the red variety into your cropping cycle given its more consistent performance.

*Figure 1 - Example 2 data sets with mean of 100 and differing standard deviation. Source https://en.wikipedia.org/wiki/Standard_deviation*

Another useful tool is that in a ** normal distribution** the following will occur

• Approximately **68%** of the observations fall within ±1 standard deviation of the mean

• Approximately **95%** of the observations fall within ± 2 standard deviations of the mean

• Approximately **99.7%** of the observations fall within ± 3 standard deviations of the mean

This is known as the 68, 95 99.7 rule and it can be seen on the distribution curve in figure 2. Normal distributions are common and occur in many natural populations however populations may not always fit a normal distribution.

*Figure 2 - Normal distribution curve with standard deviations illustrated Source - https://en.wikipedia.org/wiki/Standard_deviation*

Although these functions would normally be calculated using a spreadsheet or statistical analysis tool knowing how to calculate by hand is important to help understand how the calculation works. A good step by step worked example of how to calculate a standard deviation by hand is found on the following website. https://www.khanacademy.org/math/probability/data-distributions-a1/summarizing-spread-distributions/a/calculating-standard-deviation-step-by-step

Standard deviation is just one example of a basic statistical tool. To develop and increase your understanding of how to conduct statistical analysis, there are a vast number of resources such as courses, texts, websites and videos available. It can seem daunting at first; however if you are planning on conducting trials, it is well worth the effort to become more familiar and adept at using some basic statistical analysis and seek expert advice if you are not sure.

For some inspiration to as to why you should develop your statistical knowledge the following videos are well useful.

A good talk on the importance of statistics is “Why you should love statistics” by Alan Smithwhich. In this talk Alan highlights the need for statistics because of our disjoint between perception and reality and that we can be blind to the numbers and we can also be blind to our blindness https://youtu.be/ogeGJS0GEF4

Statistician’s Hans and Ola Rosling demonstrate through statistic’s how we perceive the world and how we can overcome our shortcomings. https://youtu.be/Sm5xF-UYgdg