Applies to: @RISK 5.x and Up

Computing a Confidence Interval on a Simulated Input or Output

Background:

Prediction Interval vs. Confidence Interval in @RISK

Prediction Interval:

• Refers to the middle x% of simulated values (e.g., 2.5–97.5% for a 95% interval).

• Use RiskPtoX() to find percentiles directly.

Confidence Interval about the Mean:

• Estimates the “true population mean” from simulated sample means.

• Calculated as:
  sample_mean ± critical_t_or_z × standard_error

• Standard error = simulated standard deviation ÷ √(iterations).

• Monte Carlo: accurate; Latin Hypercube: overestimates standard error, producing conservative intervals.

Worksheet Functions:

• RiskCIMean(cell, 0.95, TRUE/FALSE) → lower/upper bound of confidence interval about the mean.

• Standard error computed via RiskStdErrOfMean().

Monte Carlo Sampling:

• Standard error = simulated standard deviation ÷ √(sample size).

• Confidence interval: sample_mean ± z × standard error.

Latin Hypercube Sampling:

• Produces less variable sample means than Monte Carlo; standard error using the usual formula is overestimated.

• Confidence intervals using RiskCIMean() are overly conservative.

Accurate Confidence Intervals for Latin Hypercube:

1. Enable Multiple Simulations with different seeds.

2. Run several simulations; record the mean of each.

3. Compute standard deviation of these means ÷ √(number of simulations).

4. Compute margin of error: t_critical × standard_error.

5. Confidence interval = mean of simulation means ± margin of error.

• Latin Hypercube gives much smaller standard errors than Monte Carlo for the same total iterations, producing tighter confidence intervals.

Attachments:
ConfidenceInterval_LH.xlsx
ConfidenceInterval_MC.xlsx
PredictionInterval.xls