On a semi-log plot any rate change must absolutely, positively, show up as a change in slope. If you can draw a stright line that passes through all of the last three or more points, then those points all represent essentially the same rate of change, and the extension of that line provides a context for interpreting future values. Points below the extension will represent a lower rate of change. Points above the extension will represent a higher rate of change. When interpreting a phenomenon that is growing exponentially, it is the rate of growth that is the question of interest.
Additionally, when working with cumulative totals we have the same smoothing mechanism in place that works to smooth out averages. So if we have only a few values in our total we may find tht the cumulative curve on a semi-log plot will wander around a bit. These changes in slope will tell us that the variation in the day-to-day values is still affecting the total, and that any attempt to draw a projection line is inherently uncertain. So the smoothness of the curve plotted will provide a graphic answer the question about the stability of the rates.
There are also issues with abberations in the data collection process. When groups of formerly uncounted cases are added to the database in a "one-time correction" there will be a discontinuity in the curve. However, except for the point of discontinuity, the slope before and after the break will tell the same story if the rate remains the same.
So, rather than trying to find a way to use our general purpose statistical tool of the process behavior chart, here we simply need to let the data speak for themselves. Does this require judgment? Yes, it does. But then any successful use of a process behavior chart also depends upon judgment in terms of rational sampling and rational subgrouping. When the changes are obvious to the naked eye, the running record is all that we need to see how things are changing over time.
On a semi-log plot any rate change must absolutely, positively, show up as a change in slope. If you can draw a stright line that passes through all of the last three or more points, then those points all represent essentially the same rate of change, and the extension of that line provides a context for interpreting future values. Points below the extension will represent a lower rate of change. Points above the extension will represent a higher rate of change. When interpreting a phenomenon that is growing exponentially, it is the rate of growth that is the question of interest.
Additionally, when working with cumulative totals we have the same smoothing mechanism in place that works to smooth out averages. So if we have only a few values in our total we may find tht the cumulative curve on a semi-log plot will wander around a bit. These changes in slope will tell us that the variation in the day-to-day values is still affecting the total, and that any attempt to draw a projection line is inherently uncertain. So the smoothness of the curve plotted will provide a graphic answer the question about the stability of the rates.
There are also issues with abberations in the data collection process. When groups of formerly uncounted cases are added to the database in a "one-time correction" there will be a discontinuity in the curve. However, except for the point of discontinuity, the slope before and after the break will tell the same story if the rate remains the same.
So, rather than trying to find a way to use our general purpose statistical tool of the process behavior chart, here we simply need to let the data speak for themselves. Does this require judgment? Yes, it does. But then any successful use of a process behavior chart also depends upon judgment in terms of rational sampling and rational subgrouping. When the changes are obvious to the naked eye, the running record is all that we need to see how things are changing over time.
Thanks for the question. Hope this helps.