What is a log scale?
A typical scale on a chart is linear, which means that the scale increases by a unit of addition. On a really basic chart, you might see a scale that goes 1-2-3-4-5 or 10-20-30-40-50.
A log scale is non-linear and increases by a unit of multiplication. For example, a really common log scale is 1-10-1,000-10,000.
A couple of log scale examples that you might know of are the Richter scale, which measures the severity of earthquakes, and the pH scale, which measures acidity.
When should you use a log scale?
You should consider using a log scale:
- If your data has outliers, then a log scale can be used to capture a larger range of data points
- If the underlying data is exponential, then a log scale can be used to show more detail within the data
Data with outliers
The most common reason to use log scales is to show outliers. In a typical linear chart, outliers will distort the chart and compress all the other values down to the bottom of the chart.
In the chart below, the left side shows how an outlier (Company A) will compress other data down and make it difficult to see (Company C, Company D & Company E):
Alternatively, the log chart on the right side clearly shows the bars for all companies.
In my view, this introduces a more serious problem. The log scale makes it very difficult to quickly estimate the value of each bar and even more difficult to compare values across companies. We’ll discuss this more below.
You might also want to consider using a log scale if your data is exponential in nature. That is, the growth in your data is, in some way, dependent on the current value.
For example, if you want to plot the growth of an investment, then the value of your investment tomorrow depends on two things. Firstly, it depends on the growth rate. Secondly, and more importantly for this discussion, it depends on the value today.
If you don’t use a log scale, even if the growth rate of your investment stays constant, then it will appear that your investment has grown more rapidly on the right hand-side of the chart. Let’s look at this in practice:
Both of the charts above show the exact same thing. They show the value of $1,000 invested at 6% p.a. over 100 years.
The linear scale on the left seems to suggest that growth was larger in the later years. But, as you can see, the log scale on the right shows that the growth rate has stayed a constant 6% from years 0-100.
When should you not use a log scale?
You want to compare between values
In most cases, log scales make it very difficult to estimate and compare values. For example, if a bar sits halfway between the tick marks for $1m and $10m, then your mind will automatically read that as ~$5m. But in reality, it’s closer to ~$3.5m and there’s no simple way to figure that out.
If you’re using a log scale because your data has outliers and you don’t want to compress your other values, then you should consider using an axis break instead. Although an axis break will make it difficult to compare between outliers and other values, you will still be able to compare between non-outliers.
Your data has negative values
Without getting too deep into mathematical details, you cannot have a negative value in a logarithm. If you’re looking for more detailed mathematical rationale, check out this great explanation.
In Think-Cell, if you add a log scale to a chart with negative values, those values will disappear and you’ll see a warning message that says “Value -X cannot be represented on a logarithmic scale”.
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How to add a log scale to a Think-Cell chart
Changing a Think-Cell chart scale from linear to log is very simple. Just right-click on the chart axis and select ‘Set Logarithmic Scale’.
This will change the axis to a log scale with a multiple of 10. Currently, you can only have log 10 scales in Think-Cell.