Do you really want to be 'average'?
A provider client once said to me, “I don't understand all this ‘statistical gobbledygook.' Tell me why I should care and how I can actually use this.”
It was a valid request. When we start talking about statistical significance, I can literally see eyes start to glaze over. But as the industry gravitates to data-driven decision-making and we increasingly track, trend and analyze our data, it's crucial to revisit some important statistical terms that significantly affect the interpretation of your data. So bear with me — because this is important to QAPI and many other requirements — (and I promise to make it as painless as possible).
It begins with the three M's: Mean, median, and mode. These are three examples of "Measures of Central Tendency” (MCT). There are many MCTs in statistics, but these are the most common. They're useful because they:
- Present a large amount of data in a single value, for example the facility's rate of pressure ulcers; and
- Indicate that there's variability around this single value within the original dataset. For example, if your multi-site corporation rate of infection is 8%, you know there may be instances where individual facility rates are higher or lower.
The mean is a good MCT to use when a dataset contains values that are relatively evenly spread with no exceptionally high or low values (outliers). The mean is the MCT that we refer to most often. In fact, when we say “average,” we literally add up all the values and then divide by the total number in the group — that's the mean. The mean is most used as a benchmark for comparison purposes; however, there are times when one may not want to be compared to the average. For example, if a relatively small dataset contains one or two very high or very low values, the mean will be less representative of the entire group as it will be more significantly influenced by the outlier values.
To put this into context, we can say that a group of five nursing homes has a mean of four deficiencies, but what happens if three facilities have deficiency-free surveys? The mean deficiency count suddenly drops to a much lower value when those three zeroes are added to the dataset. Additionally, the resultant mean is not representative of the entire group.
When outliers significantly impact the mean, it's better to use the median. The median refers to the middle value within a dataset, when the values are arranged in order of magnitude from smallest to largest or vice-versa. Since you can't always know what's going on in other survey districts the median number of citations for your state may be a better MCT.
The last type of MCT commonly used is the “mode.” Using this MCT allows you to determine which value occurs most frequently in the dataset. For the dataset below, the mode is “2.” This helps you to focus attention on the first few days of residency and what might be contributing to rehospitalization. onsider this dataset of the number of days prior to rehospitalization: [1, 2, 2, 2, 4, 5, 6, 100, 100]. The mean (or average) is 25 days; the median is 4 and the mode is 2. Which do you think best describes your facility's performance? And, which MCT provides greatest insight for quality improvement?
The median for this group is 4 days, indicating that you have many quick returns to the hospital and many stays of two days or less. The two 100-day outliers really distort the picture. The use of the mean in this instance obscures the issue; however, the use of median and mode reveal a concern that can now be addressed.
The moral of this statistical story? Carefully select your MCT when evaluating your performance. What works in one instance may not make sense in another. As such, your QAPI team should carefully discuss these issues when evaluating your data. Of course when it comes to quality, you want to be statistically better than just ‘Average.'
Steven Littlehale is a gerontological clinical nurse specialist, and executive vice president and chief clinical officer at PointRight Inc.