Types of Devices

Types of Devices

There are six types of devices you can use in the sampler. Here we give a brief overview of them and what each is particularly useful for.

Mixer and Stacks Devices

You can fill mixers and stacks with a certain number of discrete elements.

Mixers are handy when you have a small number of elements to enter, such as in the mixer below designed to model coin flipping. You simply click the + button on the device toolbar to add more elements, and click and edit the element names. They are also useful when you have many distinct elements, such as students listed by name.

For entering a large number of duplicate elements, use the stacks device. Suppose, for example, that you wanted to determine probabilities associated with sampling boys and girls from a school in which there were 41 boys and 45 girls. That would require a lot of work to enter directly into a mixer. In a stacks device, you can simply edit the labels along the bottom axis. Then, using your cursor, you can drag the top of each stack to adjust the number in that stack. You can also choose Show Count from the device's Options menu at the lower-left of the device, and then edit the number that appears above each element type.

After you've created the elements you want, you can replace the stacks with a mixer device by dragging a mixer from the bottom sampler toolbar onto the current stacks device. The mixer will keep the same elements the stacks had, as shown below.

If you made this sampler larger, you could see the labels "boys" and "girls" in the balls. Because the balls are currently too small to display the labels, they show "..." to indicate the labels are clipped.

Because mixer and stacks devices hold fixed numbers of discrete elements, you can sample from them either with (default) or without replacement. To specify sampling without replacement, select Replacement | Without Replacement from the device's Options menu. The top "opening" of the mixer or stacks device will change when set to "without replacement," becoming open to suggest that the elements come out of the top when selected. When running the sampler on slow speed, you can see the elements becoming fewer and fewer as sampling continues.

Spinner and Bars Devices

Spinners and bars consist of elements that have areas rather than frequencies. You can adjust these areas either by dragging directly in the device, or by selecting Show Percent or Show Proportion from the Device Options menu, and editing the values. To make all the elements equal, you can also select Equalize Angles (for spinners) or Equalize Heights (for bars) from the device's Options menu.

Suppose you wanted to model a coin that was slightly biased in favor of heads. One way to do this would be to create, say, 3 h's and 2 t's in a mixer. But if you wanted a very small bias, you'd have to add, say, 100 elements and make 51 of them h's and 49 t's. Using a spinner, you can create a small bias by dragging the boundary between the two slices, as shown below.

Some people find spinners to be the easiest way to model various chance devices, such as dice, which consist of a single object with multiple faces or facets.

Bars are useful when you have many different elements with a variety of probabilities. For example, suppose you wanted to make a distribution of the number of minutes you needed to wait for the next bus. You could enter a range of, say, 0 to 10, which initially gives you a set of bars that are all the same height and thus area (a uniform distribution). By clicking and dragging the cursor over each bar, you can quickly change the height of these bars to draw an approximate shape. The shape in the example here suggests that it is most likely that the next bus will arrive 7 minutes from now.

Because bars and spinner devices are made up of areas rather than discrete numbers of elements, you cannot sample from them without replacement.

Distribution Curve Device

Edit the numbers on the two ends of the axis of this device to specify a continuous range from which to randomly sample. Using the cursor, sketch the shape of the distribution you want. (Choosing Equalize Heights from the device's Options menu will make the distribution uniform (or flat) across the range.)

In a curve device, the elements are continuous rather than discrete. Use this device to create a distribution of continuous values, such as the distribution of heights over some range. The default curve device appears with a range from 0–100, which you can edit. You can change the shape of the distribution using your cursor as a drawing device. Shown here is a distribution of heights ranging from 46 to 75 inches that is roughly normal. Notice that the cursor changes to a plus symbol when positioned over the curve to indicate that it is in draw mode.

Counter Device

Whereas the other devices select elements and values randomly when you click RUN, the counter device selects elements systematically. This can be useful in designing models in which certain variables (or attributes) are not randomly determined. You can also use this device to create sample spaces (see the movie "Creating a Sample Space").

If you place two counter devices next to one another in a sampler, they will behave like the disks in a mechanical odometer. The rightmost device will cycle through all of its elements, then the counter to its left will rotate once.