Logarithmic Scale for Time Series Charts

 In posting about Loss Aversion, Derek at Information Ocean, presented an alternative to the dot plot approach I suggested in a previous post.  Derek got the idea from a post by Dr. Nicolas Bissantz on his blog. Nicolas asked the question, “Do time series charts really compare time series?”, a very important question considering the widespread use of time series charts.  Nicolas has done us a great favor by discussing the critical role of the Y axis scale in time series data and reminding us of high school math that some us may have forgotten. If you use time series charts, I suggest you read his post.

Derek used a logarithmic Y axis scale chart to evaluate the % income distribution by total household data set that Jorge Cameos , Derek, Andreas at  XLCubed and I have been discussing recently.  Derek and Andreas have both shed considerable light on this data set, helping to show why chart type selection is so critical for effective charting.

While I’ll have more posts on chart selection later, right now I’d like to concentrate on the use of logarithmic scales in time series charts.

Derek applied a logarithmic scale to the cumulative % distribution of household income to produce this chart.

Derek’s discussion on his chart …”The surprising result is that the <$5k income level contains almost as many households in 2005 as in 1967, and significantly more than in the 70s, after a fall in the 60s. After a modest fall in the 90s, it rises again after 2000, as do all the other income levels below $100k. ”

Derek’s log scale chart definitely shows fluctuations in the <$5,000 series. Here’s my chart to help take a closer look at just the <$5,000 series to better understand what happened.

  Let’s review Derek’s observations with my chart:

• “<$5k income level contains almost as many households in 2005 as in 1967“ - 1967 shows 4.9%, 2005 shows 3.3%, a 32% decline in the proportion of households < $5,000 income.
• “significantly more than in the 70s” - True
• “After a modest fall in the 90s”  - The 1990’s started at 2.7%, increased to 3.2% in 1993, dropped to 2.5% in 1999. This seems to have continued the see-saw effect that started in 1974.
• “it rises again after 2000″ - It rises to 3.4% in 2004, it drops to 3.3% in 2005.

Based on his comments on several data visualization sites, I think that Derek is a careful chart reviewer. What happened with his interpretation of this data series?
 

No Y axis grid lines?
 

Interpreting a log scale axis is more challenging than a linear scale because the magnitude of a change per unit measure (cm, inch) varies by location along the axis, this can lead to misinterpretation of the magnitude of changes.  
 

Grid lines and axis labels are important when using a logarithmic scale so that the chart reader is helped to adjust to the non-linear scale along the axis with grid guidelines and intermittent labels across each log cycle. This is particularly true if you use Excel’s default log scale without a custom axis.