1. Simulations

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

3. 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

4. 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.

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

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

7. 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…

8. 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, No, and 6-8 Undecided.
Why can’t I use the #9?
4. Football/ Baseball/
Soccer/ Other
You tell me…

9. 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??

10. 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.

11. HOW DO YOU GET YOUR DATA?

12. 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…

13. 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.