The Concept of Sampling Error
Because the mean and standard deviation of a probability distribution are based on the sampling of Monte Carlo simulations, they are only estimates and, therefore, have a possible error.
Obviously, the more simulations Open Plan performs, the more likely the estimated mean and standard deviation would approach the theoretically correct values for that distribution.
However, it is possible to estimate the likely error in the estimate of a mean. To estimate the sampling error of a mean value arrived at by multiple simulations, it is necessary only to divide the standard deviation by the square root of the number of simulations performed to calculate the standard error of the mean.
Just as one standard deviation on either side of a mean defines a 68% probability of occurrence of an outcome within that range, one standard error on either side of the mean defines a 68% probability that the theoretical value of the mean will fall in this range. Similar confidence levels of 95% based on two standard errors and 99% based on three standard errors can also be calculated in this way.
Example
Assume that the probability distribution of the early start date of an activity has a mean value of December 12 and a standard deviation of 3 days. At the 99% confidence level, the sampling error of our estimated mean is as follows.
| Number of Simulations | Estimated Sampling Error (99% Confidence) |
|---|---|
| 10 | ± 3 days |
| 100 | ± 0.9 days |
| 1000 | ± 0.3 days |
Related Topics
- Overview of Probability
- Using Risk Analysis
- Activity Details Risk Tab
- Probability in Durations
- Risk Analysis Output Files
- How Risk Analysis interprets Durations
- The Effect of Risk Analysis on Start Dates
- How Risk Analysis Calculates Finish Dates
- Progress and Duration Probability
- Using the Risk Analysis Options Tab
- Using the Risk Analysis Advanced Tab