The Ruler Tool

Using the ruler tool, you can measure the distance between points on a continuous axis. It's useful for quickly computing, for example, the range of a distribution or the difference between the averages of two groups. You can also use it to create a measure of variability around an average by measuring the distance between the average and one case, and then having TinkerPlots compute the difference between the average and all the cases in a distribution.

1.	Click the Ruler button in the upper plot toolbar.
2.	Drag the dashed lines on the ends of the ruler to the locations you want to measure between (assuming you have a fully-separated numeric axis). The distance between locations is displayed on the arrow end of the ruler. In the example below, we have determined the range of the values of PulseRate to be 74 beats per minute.
3.	Change the location of the ruler by click and dragging the solid purple part of the ruler.

In the Ruler Options menu (found by clicking to the right of the Ruler button) are commands for flipping the ruler (moving the arrow to the opposite end), and changing between vertical and horizontal orientations.

You can snap the ruler ends onto specific spots. In the graph below, we've used the ruler to measure the difference between the medians of male and female pulse rates. To make sure that the ruler ends are exactly on the medians, the ends have been snapped to the medians, as indicated by the purple circles around the median icons.

1.	While dragging a dashed end line, bring the cursor over the case or icon you want to snap to. As you drag, a circle will appear around objects you can snap to. Release the cursor when you are over the desired object or location.

Change the object the ruler is locked to by clicking on either the dashed line or the edge of the lock circle and dragging the circle off the current location.

You can use the ruler tool to construct various measures of variability, such as the mean absolute deviation (MAD), and even to invent new ones. Creating such measures step by step, and testing and critiquing them, can help build an understanding of how such measures work and how to interpret them.

1.	Fully separate a numeric attribute on one of the axes.
2.	Add the mean (or median) to the plot by clicking the appropriate button.
3.	Add a ruler to the plot by clicking the Ruler button.
4.	Snap one end of the ruler to the mean (or median) and the other end to any other case icon.

At this point, your plot will look something like the one shown below. The ruler shows the distance from the median (or mean) to the case that you snapped on. This difference is displayed both at the arrow end of the ruler and in the status field at the lower left of the plot window. When you have snapped onto both an average and a case, a Measure All button appears in the lower right corner of the graph.

1.	Click the Measure All button at the lower right of the plot.

The ruler will animate and show all of the distances being computed (you can instead step though them manually using the Next button.) As the animation progresses, the display at the lower left accumulates the sum of these differences.

Hint: This animation is often more effective if you have stacking turned off. This allows you to see more clearly the individual difference lines as the animation progresses. It can also be informative to order the cases vertically by x-axis attribute.

This sum of the differences is not, by itself, a very useful measure of variability. When measuring around the mean, for example, the sum of these differences, by definition, is always 0. But the sum is a good place for students to start, and investigations can uncover its weaknesses. They will usually suggest as a remedy looking instead at the absolute values of those differences. The Ruler Options menu has this as an option (choose Absolute Difference).

Future discussion can lead to the insight that the mean (or median) of these differences will work better than the sum, because the latter will depend on the number of values. Again, options for computing Mean of Differences and Median of Differences are in the Ruler Options menu.

Either before or after clicking Measure All, separate the distribution into two or more groups. The computations will create separate measures for the averages of each group. You can compare these measures in the status field in the lower left of the plot.

If you have created a fit through a scatterplot (see, for example, Line Trace), you can use Measure All as described above to compute a measure of variability around the line or curve of fit. (For examples of summarizing scatterplots with lines or curves, see the TinkerPlots movie "Exploring Relationships 2.") These fits can include hand-drawn lines, the diagonal line, and a line trace from the color meter.

Here is a scatterplot of Body_Mass_Index and Weight. The line of fit is a running mean that was created using the trace option of the Color Meter. After doing a Measure All around it, you can see lines displayed that show the distance from each case to the line.

To measure the difference between a line/curve of fit and the cases in a scatterplot,

1.	Add a ruler to a scatterplot (It should by default appear in the vertical orientation).
2.	Snap one end of the ruler on the line/curve of fit and the other end to any point, as described above.
3.	Click the Measure All button that appears in the lower right of the graph.
4.	In the Ruler Options menu, select the desired settings (for example, Absolute Difference or Mean of Differences).

To create an attribute of the differences (residuals) between each value and the average (or fitted line/curve),

1.	Choose Difference Attribute from the Ruler Options menu.

Note: This attribute is not formula based, so if you change anything in the plot, the difference values will not dynamically update.

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