Data trending

• This section provides a step-by-step explanation of how to use microbiological indicator test results to identify historical trends and improve environmental hygiene management. It introduces several statistical methods including arithmetic mean, geometric mean, rolling geometric mean, cumulative sums (cusums).

Monitoring trends in microbiological test data allows for early detection of issues and more informed decision-making. However, interpreting this data can be complex due to variations in microbial counts. This section outlines common challenges and presents recommended techniques for meaningful data interpretation.

Also known as a simple average or log arithmetic mean, this method involves adding together all counts and dividing by the number of samples.

Example:

If you collected 5 samples and the test results (cfu/100 ml) were:

• 30
• 1,000
• 2,650
• 150,000
• 25

To calculate the arithmetic mean:

Add 230 + 1,000 + 2,650 + 150,000 + 25 = 153,905

Average = 153,905 ÷ 5 = 30,781 cfu/100 ml

The arithmetic mean of test results over time can be plotted as shown in figure 1.

This method gives disproportionate weight to extreme values. In this case, one very high result (150,000) distorts the average, which otherwise would be below 3,000. This can give a misleading impression of overall hygiene levels.

Taking the log of the arithmetic mean (log₁₀ 30,781 = 4.49) is optional and can make plotting trends easier. This approach is also called a log arithmetic mean, which is less influenced by extreme values.

This is also known as the mean log. You calculate a geometric mean by taking logs before you take any averages.

To calculate the geometric or mean log of the same five samples:

Calculation:

Add logs = 2.36 + 3.00 + 3.42 + 5.18 + 1.40 = 15.36

Average = 15.36 ÷ 5 = 3.08

Again, mean log values can be plotted over time to show a trend. 

How to interpret the graph: Note the zero line in the centre of the graph on the y-axis. If an upward trend is present, the results are worse than the baseline, conversely if a downward trend is observed, results are better than the baseline. A flat line indicates that results are consistent with the baseline. In the above graph the samples for October 2008 get progressively worse over the course of the month (above the baseline determined for that business), but then improve over the course of November. There is a temporary increase for the 28th November testing, but then a steady decrease until early January. If, in this example, a new measure was introduced at the end of October, then this graph would demonstrate that this new measure was working well to improve the microbial cleanliness in the business.

Insight: Cusums amplify small changes in performance, making them valuable when indicator counts usually fall within a narrow range.

The rolling geometric mean is calculated in a similar way to the geometric mean. As with the geometric mean you start off by taking the logs of your indicator counts, add them together and divide by the number of samples taken. The main difference between a geometric mean and a rolling geometric mean is that all of the results from several weeks of testing are used to calculate a rolling geometric mean, i.e. this method averages test results over a rolling period, updating weekly to create a smoothed long-term trend. In microbiology it is common to use the results of six weeks of testing for the rolling geometric mean. It is important to note that the six weeks do not have to be consecutive.

How it works: Calculate the geometric mean for weeks 1–6 by taking the log of each result, add them all up and divide the sum by the total number of samples (6 in this case). For week 7, drop week 1 and include week 7 (i.e. weeks 2-7). Continue this pattern for each subsequent week.

Cusum charts track whether test results are improving or deteriorating over time by comparing weekly geometric means to a baseline average which is generated from your own data. So, essentially, you are comparing how your current samples are comparing against their historical selves. Cusums tend to exaggerate trends in data so are particularly useful in data sets with a narrow range of values. 

Step-by-step calculation:

Choose a baseline period (often13 weeks which is three months’ worth of data) during which you would consider your sampling to be representative of your business. Calculate the baseline geometric mean from those weeks, i.e. take the log of each result, add them up, and divide the sum by the total number of results, 13 in this case – this is your baseline. For each new week calculate the week’s geometric mean then subtract it from the baseline and add this difference to a running tally. An example of the running tally can be seen below. The explanation may seem a bit complicated, but if you have a look at the table below, and then re-read the above paragraph, it will (hopefully) all become a bit clearer.