The difference between the Linear and the Logarithmic Scales

MoreVisibility - March 4, 2009

By now, mostly everyone has tried using a Motion Chart by clicking on the “Visualize” button, toward the top of several Google Analytics reports at least one time.

…What? What do you mean “No!“? What do you mean “I didn’t even know it existed!“? Well, if you haven’t taken a look, I strongly suggest doing so. For example, go to your Traffic Sources >> Keywords report and click on “Visualize” towards the top – you should see something like this:

Motion Chart using the Linear Scale

There you go – you have just been visualized! :). You can increase the number of circles (or “bubbles”) that appear by going back to the regular report and increasing the number of rows, toward the bottom-right of the report table.

One update to Motion Charts that happened a few months ago which flew a bit under the radar was the option for you to define your viewing scale – Linear, or Logarithmic. I can get into a complex mathematical / statistical explanation of the differences between the two – which I’m sure will satisfy some of you – but for the masses, the easiest possible explanation I can use to differentiate the two is:

Linear Scale – Based on Addition
Logarithmic Scale – Based on Multiplication

The first image above is an example of a Motion Chart using the Linear Scale. Notice on the X axis (going from left to right, the “Pages / Visit” metric), the values from left to right increase by 5 on each point – 5, 10, 15, 20, etc… The values in the Y axis (Visits) increase by 100 on each point – 100, 200, 300, and so on.

Now let’s change “Lin” to “Log” and watch what happens to our Motion Chart:

Motion Chart using the Logarithmic Scale

The motion chart data is exactly the same, but much different looking now, is it not? Notice how the bubbles are much more spread out and more “all over the place” using the Logarithmic Scale. The Motion Charts in Google Analytics use what is known as a base 10 sequence, as each point in the scale is multiplied by 10. A little tough to notice here in the X axis (Pages / Visit), but noticeable on the Y axis (Visits) – 1, 10, 100, 1,000, and it continues off the chart infinitely.

When to use the Linear Scale? When to use the Logarithmic Scale?

A good rule of thumb is to use the scale that best shows off your data. If you are only using the motion chart for the top 10 rows of your report, chances are that the linear scale will work just fine. If you’re going to be using 25 or more rows, you’ll most likely find it much easier on the eyes if you use the logarithmic scale. So, less data = linear; more data = logarithmic. But, please, play with the Motion Charts and decide for yourself what’s easier for your chart.

“The Difference Between” Series:

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