26 March 2020

Determining the growth rate of a published chart

A friend drew my attention to this page comparing the Bay Area COVID-19 cases to New York. But it can be hard to judge visually how steep a log chart is.

To calculate the growth rates, for example of New York on the following chart:

  1. Take a screen capture
  2. Paste it into MSPaint, or similar
  3. Drag the selection box from one log-axis marker to the next.
  4. Use MSPaint's ruler indicator (bottom left corner) to see how high the selction is.
    1. E.g. in the following example, measure from the 1,000 grid line to the 10,000 grid line.
    2. The distance is 198 pixels for a 10x multiplication 
    3. Let's call this PixelsPerTenfold
  5. Pick two date lines around the slope being measured
    1. Start dragging the selection box from the point where the data line intersects the first date line.
    2. Drag to a point where the data line intersections the last date line.
    3. Use the ruler in the corner to measure the vertical distance.
    4. Call this PixelsIncreased
    5. In the example below it is 240 pixels.
  6. Apply calculations as follows:
PixelsIncreased  = 240
PixelsPerTenfold  = 198
Days = 3
Daily Multiplier = 10(PixelsIncreased / PixelsPerTenfold / Days) = 2.54
Daily % Increase = 100 * (DailyMultiplier-1) = 154%
Days to Double = loge2 / logeDailyMultiplier = 0.75 days
Days to 10x = loge10 / logeDailyMultiplier = 2.47 days

No comments: