Repeated Trips to the Wheel (Collecting Measures)

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Now an even more powerful idea:

Every time we resample, we can tell how much we made. But we'd like to record those amounts so that we can do this, say, 100 times, and see the distribution of people's performances at the wheel. (That is, imagine 100 people each going to the wheel and playing ten times, betting on red every time. What's the distribution of amounts that the people make?)

The Goal:

To do this, we need to

• Calculate the amount that we make in the sample collection.
• Collect these measures in a new (measures) collection

What to Do:

Make sure you can see the inspector of your sample collection. (If not, double-click it.)

Click the Measures tab to bring up the measures panel.

Click where it says <new> and type the name netWinnings.

This creates a new measure. Think of a measure as an attribute that applies to the entire collection rather than to each case. Now we need to give this measure a value; to do that we'll define a formula.

Double-click the cell in the Formula column in the same row as your new attribute. The formula editor appears.

Enter the formula sum(winning) (assuming that your "winning" attribute has that name). Click OK to close the formula editor. The value should appear -- and if you resample, that number should change. It should equal your net winnnings -- how much you made in your ten trips to the wheel.

You can resample by switching over to the Sample panel. Or you can select the collection and choose Sample Cases from the Analyze menu. Or you can open the collection and press the Sample More Cases button.

Add another new attribute, this one called PlaysPerSession, whose formula is count( ). This will record how many times we went to the wheel, for future reference.

Now (finally) we're ready to collect these measures, automating how the sampling repeats, collecting the measures we created as attributes for the whole collection, and stuffing them into regular cases in a third collection:

Select the sample collection and choose Collect Measures from the Analyze menu.

Fathom creates a new collection, Measures from Sample of wheel. While the sample collection has regular attributes of color and winning, this one has regular attributes of netWinnings and playsPerSession -- the same as the measures in its "source" collection.

This is a good time to clean up your screen by closing inspectors or making tables, etc., smaller.

By default, Fathom collects five measures. We want more. As with sampling, the controls for collecting measures are in the inspector. And as with a sample collection, a measures collection knows that it collects measures, and from whom.

Double-click the new measures collection, and make sure its inspector is showing the Collect Measures panel. Change the panel to look like this (100 measures, no animation):

Click the Collect More Measures button. Now you'll have 100 measures -- the results from 100 sets of 10 spins of the wheel.

Graph netWinnings to see the distribution, It should look something like this:

So this graphs shows 100 trips to the wheel. While people generally lost money, some people won.

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