Designing Simulations

Question 1

Define simulation

Answer 1

The imitation of chance behavior based on a model that reflects the experiment.

Question 2

What is the first step in designing a simulation?

Answer 2

State the problem/ experimental design

Question 3

What is the second step in designing a simulation?

Answer 3

State assumptions

Question 4

What is the third step in designing a simulation?

Answer 4

Assign digits to represent the possible outcomes

Question 5

What is the fourth step in designing a simulation?

Answer 5

Simulate many repetitions

Question 6

What is the 5th and final step in designing a simulation?

Answer 6

State your conclusions

Question 7

Simulation Practice problem: On average, suppose a baseball player hits a home run once in every 10 times at bat, and suppose he gets exactly two “at bats” in every game. Using simulation, estimate the likelihood that the player will hit 2 home runs in a single game.

Answer 7

Solution:
Describe the possible outcomes. For this problem, there are two outcomes - the player hits a home run or he doesn’t.

Link each outcome to one or more random numbers.

Since the player hits a home run in 10% of his at bats, 10% of the random numbers should represent a home run. For this problem, let’s say that the digit “2” represents a home run and any other digit represents a different outcome.

Choose a source of random numbers. For this problem, we used Stat Trek’s Random Number Generator to produce a list of 500 two-digit numbers (see below).

Choose a random number. The list below shows the random numbers that we generated.

Based on the random number, note the “simulated” outcome. In this example, each 2-digit number represents two “at-bats” in a single game. Since the digit “2” represents a home run, the number “22” represents two home runs in a single game. Any other 2-digit number represents a failure to hit consecutive home runs in the game.

Repeat steps 4 and 5 multiple times; preferably, until the outcomes show a stable pattern. In this example, the list of random numbers consists of 500 2-digit pairs; i.e., 500 repetitions of steps 4 and 5.

Analyze the simulated outcomes and report results. In the list, we found 6 occurrences of “22”, which are highlighted in red in the table. In this simulation, each occurrence of “22” represents a game in which the player hit consecutive home runs.

Question 8

What are the three types of observational studies?

Answer 8

Cross-Sectional
Case-Control
Cohort

Question 9

Cohort Studies

Answer 9

Analytical study in which a group having one or more similar characteristics (such as habit of smoking or a particular disease) is closely monitored over time simultaneously with another group (whose member do not smoke or are free from the disease). Although more tedious, this method is used where case study approach is not feasible, creates too many statistical problems, or generally produces unreliable results. Also called follow up study.

Question 10

Case-Control Study

Answer 10

an epidemiological research method in which people who have developed a disease such as cancer are studied alongside people who have not, and the differences and possible causes analysed