Many of the articles that appear in The Poultry Professional and other publications rely on statistics to make their point. I felt that it would be a good idea to give a little background as to why we use statistics, what they do and what they do or do not mean to us in practice.

The science of statistics has evolved as a means of measuring and quantifying variability and probability. Variability, both between individual animals in an experiment and the pens or houses in which they are grown, leads to problems in interpreting experimental results. This variability comes as no surprise to poultry producers as they have to deal with it with every flock of layer pullets or broiler breeders that they rear. Variability between birds is represented by what is known as a Bell Curve, a good example of which appears in the Hy-Line Breeder guide (figure 1.) In a more uniform flock the "peak" will be higher and the two "tails" shorter.

An example of how variability may affect our interpretation of the results of an experiment is discussed here. Animals on treatment X may have higher average daily gains than those on treatment Y, but variability within treatments may indicate that the differences in production between X and Y were not the result of the treatment alone. Environmental factors, chick quality and/or bird health may all be implicated in cases like these. Statistical analysis allows us to calculate the probability that such differences are from treatment that was applied rather than from chance (environment).

In some of articles you will see the notation P<. 05. This means the probability of the differences resulting from chance is less than 5%. If two averages are said to be "significantly different," the probability is less than 5% that the difference is from chance or that the probability exceeds 95% that the difference resulted from the treatments applied. These differences are calculated using a methodology called Analysis of Variance (AOV). A value of P < 0.01 means that there is a 99% chance that the differences measured were as a result of the treatment applied and this is often referred to as a "Highly Significant Difference".

A common way of indicating these differences is by using alphabetical superscripts. In data published by Leeson and Summers (1997) this can be clearly seen.

Despite the differences in the protein level of the diet there were no significant differences in body weight or energy intake to 20 weeks of age. However, those birds on the 20% protein diet consumed significantly more protein than those birds on the 19% protein diet (superscripts ^a&b). Although the 18% protein treatment did not differ from the 17% protein treatment (superscript ^c&cd) it was significantly different to the 16% protein diet (superscripts ^c&d). There were no differences between the 15% and 16% diets (both superscript ^d).

Some papers report correlation or measures of the relationship between traits. The relationship may be positive (both traits tend to get larger or smaller together) or negative (as one trait gets larger, the other gets smaller). A perfect correlation is one (+1 or -1). If there is no relationship, the correlation is zero. This is mostly reported as an R squared value and may sometimes be expressed as a percentage. This form of statistics is most often used to illustrate significant trends in a data set and in my opinion is often not used enough or correctly.

This is well illustrated in the following example. A major influence on egg size has to do with the size of the point of lay pullet. In some work recently published by Harms and his co-workers in the Journal of Applied Poultry Research a flock of point of lay hens was split into Light, Medium and Heavy groups at 27 weeks of age. The effect that this had on egg size is clearly illustrated below.

From these data it is clear that the weight of the hens at 27 weeks were significantly different from each other. Whilst the egg weight of the Light birds was significantly lower than the remainder at 37 weeks of age, there was no significant difference between the Medium and Heavy groups egg weights.

The presentation of these results is a classic case of an incomplete statistical analysis having being carried out on a data set. I carried out a regression analysis between hen weight at 27 weeks of age, and egg size at 37 weeks of age. I was able to determine that there was a highly significant trend between these two parameters and that the correlation coefficient was .933. Remember that a perfect correlation is 1. This means that egg weight between treatments is indeed significantly and that "grading" point of lay pullets may be a viable option for the producers who wants to produce larger eggs, in the case of free range egg production for example.

In other papers, you may see an average given as 2.5 ± .1. The 2.5 is the average; .1 is the standard error (SE). The SE is calculated to be 68% certain that the real average (with unlimited number of animals) would fall within one standard error from the average, in this case between 2.4 and 2.6.

As its name would imply, the SE is also used as a measure of variability or uniformity depending on your point of view. By calculating a Coefficient of Variation (CV) it is possible to see how uniform a data set is. CV is calculated thus SE/Average * 100. The CV is a measure that is widely used as a management tool in pullet and broiler breeder rearing and is also a very useful way of analysing laboratory data.

In order to generate valid trial data an experiment needs to be properly designed. There are a number of basic rules that need to be followed in order to do this. An adequate number of animals per treatment are required. Using uniform individuals, such as broiler chicks hatched from a single parent flock, increases the probability of finding real differences when they exist. Each treatment should be replicated (in a pen or a house) several times. The number of replications required differs depending on the experimental layout but I do not like to see a trial with less than 4 replicates per treatment. The environment needs to be uniform as possible. This means that a single house or single farm should always be used for a trial. The replicates should ideally be randomised. For example, if one half of a farm is used for treatment X and the other half for treatment Y, the prevailing wind may play a role in the outcome of the trial.

Even the most perfectly designed trial can go badly wrong if the local control or management is missing. It is important that the correct diets be mixed, fed to the correct birds in the correct amounts. Data collection needs to be meticulous and accurate. Failure to attend to these details results in inconclusive trail results and are probably the key reason why many farm trials fail.

Once a valid data set has been generated, it should be submitted to statistical analysis. This will always lead to a more valid interpretation of the results, regardless of the experimental design. Scientific papers demand the use of correct experimental layout and statistical procedures in order to increase the confidence placed in the published results. Fortunately, most modern spreadsheet packages have a full range of statistical functionality built in to them so it is likely that most of us have the tools to carry out the correct analysis on our desktops already.

You may well ask why I have gone into this detail about something that would appear to be very scientific. The reality is that each one of us has to make decisions, which often have large financial implications, based on data derived from our own farms or by the suppliers of certain products.

We need to be sure that the differences that are claimed are "real" and not simply the result of chance. A simple comparison of two houses or sites tells us little as there is simply no way of knowing if any differences occurred as a result of chance or as a result of the treatment applied. In short, there is a 50% chance that the treatment applied will have a positive result.

A comparison of averages of large numbers of birds or animals under commercial conditions may or may not be meaningful. If this comparison is between birds kept in different geographic regions it is probably not valid. It is also questionable to compare results between two different time periods (cycles) because apart from the weather there may also have been a number of other management changes.

I am very wary, possibly even cynical, of the result of trials that have not been properly designed or submitted to proper (valid) statistical analysis. You should be too!