simulation

Examples of simulation in the following topics:

• Using simulation for goodness of fit tests

  • Simulation methods may also be used to test goodness of fit.
  • In short, we simulate a new sample based on the purported bin probabilities, then compute a chi-square test statistic $X^2_{sim}$.
  • We do this many times (e.g. 10,000 times), and then examine the distribution of these simulated chi-square test statistics.
  • Would our findings differ if we used a simulation technique?
  • Figure 6.21 shows the simulated null distribution using 100,000 simulated values with an overlaid curve of the chi-square distribution.

• Simulating the study

  • In this simulation, we thoroughly shuffle 48 personnel files, 24 labeled male sim and 24 labeled female sim, and deal these files into two stacks.
  • The randomization of files in this simulation is independent of the promotion decisions, which means any difference in the two fractions is entirely due to chance.
  • Table 1.45 show the results of such a simulation.
  • What is the difference in promotion rates between the two simulated groups in Table 1.45?
  • Simulation results, where any difference in promotion rates between male sim and female sim is purely due to chance.

• Simulating a difference under the null distribution

  • The expected difference between the two proportions under this simulation is zero.
  • We run this simulation by taking 40 treatment fake and 50 control fake labels and randomly assigning them to the patients.
  • We use a computer program to randomly assign these labels to the patients, and we organize the simulation results into Table 6.24.
  • Caution: Simulation in the two proportion case requires that the null difference is zero
  • Simulated results for the CPR study under the null hypothesis.

• Generating the null distribution and p-value by simulation

  • Each client can be simulated using a deck of cards.
  • There were 5 simulated cases with a complication and 57 simulated cases without a complication, i.e. = 5/62 = 0.081.
  • One simulation isn't enough to get a sense of the null distribution; many simulation studies are needed.
  • Figure 6.20 shows the results of 10,000 simulated studies.
  • There were 1222 simulated sample proportions with ≤ 0.048.

• Checking for independence

  • While in this first simulation, we physically dealt out files, it is more efficient to perform this simulation using a computer.
  • Repeating the simulation on a computer, we get another difference due to chance: -0.042.
  • Figure 1.46 shows a plot of the differences found from 100 simulations, where each dot represents a simulated difference between the proportions of male and female files that were recommended for promotion.
  • Note that the distribution of these simulated differences is centered around 0.
  • Two of the 100 simulations had a difference of at least 29.2%, the difference observed in the study.

• Monte Carlo Simulation

  • Monte Carlo simulation uses statistical data to figure out the average outcome of a scenario based on multiple, complex factors.
  • The Monte Carlo method solves a problem by directly simulating the underlying process and then calculating the average result of the process.
  • Then, he essentially uses the distributions to run many many simulations of all the inputs to see how they affect the output and then finds the average output .
  • As the number of factors increases, it becomes harder to figure out the "base case. " Statistical analysis through Monte Carlo simulations is great at handling problems with multiple, inter-related, and uncertain factors.
  • By running many simulations based on the probability or distribution of an input (x), the analyst can see the average output (y).

• Modeling Ecosystem Dynamics

  • Conceptual models describe ecosystem structure, while analytical and simulation models use algorithms to predict ecosystem dynamics.
  • In these cases, scientists often use analytical or simulation models.
  • Like analytical models, simulation models use complex algorithms to predict ecosystem dynamics.
  • These simulations are considered to be the most accurate and predictive of ecosystem dynamics.
  • Compare and contrast conceptual, analytical, and simulation models of ecosystem dynamics

• Application of Knowledge

  • A business game (also called business simulation game) refers to a simulation game that is used as an educational tool for teaching business.
  • Business games (also called business simulation game) refer to simulation games that are used as an educational tool for teaching business.
  • Often the term business simulation is used with the same meaning .
  • The activities carried out during a simulation game training session are:
  • Business game (also called business simulation game) refers to simulation games that are used as an educational tool for teaching business.

• Hypothesis testing for two proportions exercises

  • A simulation was conducted to test if people react differently under the two scenarios. 10,000 simulated differences were generated to construct the null distribution shown.
  • In order to conduct the simulation, a researcher wrote yawn on 14 index cards and not yawn on 36 index cards to indicate whether or not a person yawned.
  • He counted how many participants in each simulated group yawned in an apparent response to a nearby yawning person, and calculated the difference between the simulated proportions of yawning as.
  • This simulation was repeated 10,000 times using software to obtain 10,000 differences that are due to chance alone.
  • The histogram shows the distribution of the simulated differences.

• Randomization for two-way tables and chi-square

  • We repeat this many times using a computer, and then we examine the distribution of these simulated test statistics.
  • When the minimum threshold is met, the simulated null distribution will very closely resemble the chi-square distribution.