Simulations

What is it? Simulation is using a table of random digits, a calculator, or a computer to imitate chance behavior…

The 3 Steps in a Simulation…A Quick List Make a probability model. Assign digits to represent outcomes. Conduct many repetitions. The 3 Steps in a Simulation…A Quick List

Step 1: Make a Probability Model You need to make sure that all the choices are included in your probability model and in the correct proportion.

Disclaimer… For the following example, we are assuming that all categories are the same size. This will not always happen.

Step 1 Examples 1. Heads/Tails 2. A/B/C/I/NC 3. Yes/No/ Undecided 4. Football/ Baseball/ Soccer/ Other Step 1 Examples

Step 2: Assign Digits to Represent Outcomes If there are two outcomes, you can use the numbers 0-9 to represent the outcomes…just make sure all the digits are used… If there are more than two outcomes, you have to be careful, because now you might need to leave out some numbers…

Back to the Examples 1. Heads/Tails 2. A/B/C/I/NC Undecided Can be 0-4 Heads, 5-9 Tails. Any other ways? 2. A/B/C/I/NC Can be 0-1 A, 2-3 B, 4-5 C, 6-7 I, 8-9 NC. 3. Yes/No/ Undecided Can be 0-2 Yes, 3-5 No, and 6-8 Undecided. Why can’t I use the #9? 4. Football/ Baseball/ Soccer/ Other You tell me…

If you said: 0-1 Football, 2-3 Baseball, 4-5 Soccer, and 6-7 Other, that’s great!!! But who said: 00-24 Football, 25-49 Baseball, 50-74 Soccer, and 75-99 Other??

Step 3: Conduct Many Repetitions Just like with samples and experiments, you need more than just a couple of pieces of data in order to draw a conclusion.

HOW DO YOU GET YOUR DATA?

Use a calculator’s randint function. Use the table of random digits Use a computer’s random number generator. Otherwise, draw 1000 numbers from a hat. Your choices…

It’s very important to know that every time you conduct a repetition, you start over again. This makes the outcomes INDEPENDENT. If you are using a table of random digits, the way to make the outcomes INDEPENDENT is to use different rows each time.