MDC - Simulations Lesson

Simulations Lesson

Simulations

Simulations are valuable tools for generating random data for a variety of reasons.   There are specific steps involved in performing a simulation to ensure that it accurately models the facts of the problem.   Please watch this presentation for an introduction to Simulations.   Remember to advance through the presentation using the forward button and take notes as needed.   Then return to this page to see the steps performed in a real situation that you may find interesting.

Please click to watch the video below:

Completed Simulation Example

NOTE :   Often questions regarding a simulation have a success or failure component to them for COUNTING purposes.  

You take a quiz with 6 multiple choice questions.  After you studied, you ESTIMATED that you would have about 80% CHANCE of getting any INDIVIDUAL question right.

Question: What are your chances of getting them ALL RIGHT? Use a simulation containing at least 20 trials to determine the answer
Thinking...Thinking...Thinking...

This starts out just like any algebra word problem... 

ASSIGN VARIABLES. Let the digits 0 - 7 represent a CORRECT ANSWER. Let the digits 8 and 9 represent an INCORRECT ANSWER 

This is done to insure the 80% success rate GIVEN in the problem will be modeled accurately. 

OKAY...now decide HOW TO MODEL this...this example uses the random number generator on the graphing calculator ... MATH>>>PRB>>>rand (Int) command.

We get exactly what we need by doing randInt (0, 9, 6)

randInt commands establish the range of the digits and tell how many you need.

randInt arguments are: (lower bound, upper bound, count)

Here is a table with the results of the first 4 trials run

Repeating...we are modeling a 6 question MC test having 80% chance of getting a correct answer to ANY question with a GOAL of getting ALL 6 questions correct.

Trial #	result	count	Success/Failure S: all 6 correct
Trial 1	4 4 7 3 3 4	6 correct	S
Trial 2	0 5 0 4 3 3	6 correct	S
Trial 3	2 1 5 4 3 9	5 correct	F
Trial 4	6 8 3 0 8 7	4 correct	F

You need to do more trials than this but this is just to get you started. The MORE trials - the BETTER the estimate!!!

Stopping with just these results and counting the successes there are JUST TWO. Turning that into a PERCENT is done by

2/4 = 50% or #successes /total trials success

Conclusion

According to this simulation we EXPECT to get approximately 50% of the answers correct assuming the conditions stated in the question. Other simulations will have varying results but provide a good estimate of the expected outcome with sufficient repetitions.   For the purpose of this course we will consider 20 trials to be the minimum.

Exploring Categorical Data Review

There are five methods of data collection:

        Census —count or measure an entire population

        Sample survey—count or measure part of the population

        Experiment —collect data on two groups, one with treatment and the other without treatment

        Observational Study —observe subjects without intervention

        Simulation - model random events by using random numbers to specify outcomes

This unit focused on simulations.   Simulations often generate many outcomes of a response variable that are reasonably similar.     These outcomes can be pictured as a distribution of responses.   Typically a data table is constructed to organize the outcomes.   The tools used to display and summarize these outcomes are the same as those used earlier to describe one variable data such as histograms and boxplots.   The results of a simulation can be summarized with measures of center and spread paying careful attention to the spread.  

Always think about your analysis and conclusion.   Simulations can hide subtle errors.   Careful analysis of the responses can save you from erroneous conclusions based on a faulty simulation.   Outliers are less likely to occur in these distributions, but if one or more is found, you should try to determine how that happened.  

A common mistake in constructing a simulation is to adopt a strategy that appears to produce the right kind of results, but that DOES NOT accurately model the situation.

Don't confuse your conclusion statement by suggesting that something that MIGHT happen is CERTAIN to happen.   Always state that future results will not match the simulated results exactly.

Run adequate trials...the more the better...10 trials are better than 5, 20 trials are better than 10 trials, etc.