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Welcome back. This is the second installment of statistics for the laboratory. Following our previous discussion on descriptive statistics, we will discuss the way in which the mean could be interpreted.
For example, Table 1 shows an imaginary study on the average length of stay in three services in a hospital.
The average length of stay for the ICU is 8.1 days (3588/443). Similarly, the average lengths of stay for the other two units are 6.3 days and 3.9 days. Averaging these three averages, we get 6.1 days. However, summing the total days from the three units and dividing by the number of admissions we find the weighted average length of stay to be 5.7 days. However, notice the difference of the average of the averages (6.1 days) and the weighted average (5.7 days) is not the same, because the two calculations are different. How would each of the units respond to the average of 5.7 days? The ICU would be irate for they would feel slighted-8.1 days being greater than 5.7. On the other hand, the CCU would be ecstatic! And the NICU would be "okay."
The two charts below are possible charts that demonstrate the data graphically. The left chart is the one that the ICU would use to argue their case for the need of more staff. However, the right chart is the chart that the CCU would rather use. If you were a nurse in the NICU, which one would you like to see?
We will return to this example later when we ask the question, "Is there a statistical difference among these three units?"
In Example 2, the Table lists the number of units blood donors give on average; the weighted average is 4.5 units, whereas the average of averages is 12.2 units. What does that mean? The weighted average considers the fact that most donors give "only" 4.5 units. However, there are those who give substantially many more units as evidenced by the average of the averages. If you were in charge of a blood drive and wanted to encourage people to give more blood, which average would you use? The person in charge may say, "The average donor gives 12.5 units. What are you giving?"
The Moving Mean
The moving mean was "invented" to place more emphasis on recent data more than older data. Imagine that a hospital increased the number of beds and staff in a service (e.g., Labor and Delivery). The hospital is interested in the change in the number of deliveries since the increase in the number of beds has taken place. The "L&D Before and After New Beds" table below shows another imaginary study for the number of births for the past 10 months. The first 3 months are births before the new beds were available.
It appears that the number of newborns has increased in recent months. But it also appears that the number of births each month is increasing faster than the cumulative average. The cumulative average is the average calculated by accumulating the data each month. That is the average of (month1 + month2), then the average of (month1 + month2+ month3), and so on.
Moving averages find applications in various areas in healthcare--in processing samples in the lab (turnaround time), increases in income (or debt), census, spread of disease, to name a few. In the above example, the trend was increasing. Let's consider another example to demonstrate a decreasing trend: turnaround time for a blood test after a Six Sigma procedure was introduced. The data show the change in turnaround time for 3 months before and 6 months after Six Sigma.
Next time, we will discuss other middles, the median and mode. Remember send your questions and comments to David at davidplaut@yahoo.com.
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