Benchmark Six Sigma Expert View by Venugopal R
When we have two sets of data having different averages, if we move one data point from one set to another, an increase in the average could be seen for both the sets, subject to conditions. The conditions are - the data point is moved from the set that has higher average to the one with lower average. The data point happens to be lower than the average of its original set, but higher than the average of the set to which it is moved.
Will Rogers phenomenon could thus cause an improvement on the average values of both the groups by just doing a reclassification, all the values remaining same.
Let me illustrate this using a simplified practical example. The table below gives the outstanding dues of loans from customers. There are two groups based on age. For simplicity we are considering only 5 data points for each group.
From the above table, it is seen that the average for group1 is 4600 and for group2 is 1370.
Assume that one customer in group1, who has outstanding of 3200, turns 60 and thus gets moved to Group2. The table will get revised as below:
The group1 average has increased to 4950. The group2 average has also increased to 1675.
It appears as if there is a increase in the average outstanding for both the groups, whereas none of the individual values has changed. The effect was only due to a re-grouping. Such re-groups whether done intentionally or unintentionally, could alter the average value of a group. We need to be careful in interpreting such business results and confirm whether the changes are genuine or are a result of “Will Rogers” phenomenon.
We see articles about how the Will Rogers effect impacts certain practices in the healthcare world. For example, advancements in the methods to detect growth of cancer has resulted in classifying more cases as ‘stage-3’, whereas they were earlier classified as ‘stage-2’, based on the prevailing detection methods. Such a shift in classification has resulted in moving certain cases from stage-2 to stage-3. These cases are ‘high sick’ as per stage-2, but ‘low sick’ as per stage-3. By this reclassification, the average mortality rates showed improvement for both the stages, whereas there is no change in the overall situation. However. While mortality rates could have genuinely improved due to advancement in treatments, Will Roger’s effect from re-classification could make the benefits appear further boosted.