 Risk Analysis Tip (a sample ModelAssist topic)
Presenting your Risk Analysis Model and Results (3 of 3)
The following Risk Analysis tip has been drawn from material in ModelAssist®, Vose Consulting's risk analysis training, reference and template software. ModelAssist users can consult the ModelAssist-references (in the form of Mxxx)
for additional information. To read more about ModelAssist and download the free demo version, go to http://www.vosesoftware.com/software.htm.
Introduction
Two Risk Analysis Tips ago, we explained the importance of guiding the reader or you risk analysis report or presentation guides the reader through the assumptions, results and conclusions in a manner that is transparent, efficient and interesting. In the same Tip, we also gave an introduction to how to best explain your risk analysis model assumption. In the last Risk Analysis Tip and this Risk Analysis Tips, we discuss how to best presenting your Monte Carlo simulation results.
Two main ways
There are two main ways of describing a model's outputs:
- Graphical Descriptions (M0212)
- Statistical Descriptions (M0419)
In the last Risk Analysis Tip, we discussed the use of Graphical descriptions for a model's output. In this Risk Analysis Tip, we will discuss the use of Statistical descriptions.
Statistical Descriptions
Monte Carlo simulation software offer a number of statistical descriptions to help analyze and compare results. There are also a number of other statistical measures that you may find useful. We have categorized the statistical measures into three groups:
- Measures of location (read more at M0420) -
where the distribution is 'centered';
- Measures of spread (M0422) - how broad the distribution is;
- Measures of shape (M0344) -
how lopsided (M0421) or peaked (M0256) the distribution is.
The most useful ones.
However, in general, at Vose Consulting we use very few statistical measures and descriptions of outputs in our reports (we prefer using Graphical descriptions). In fact, we mostly restrict our use of statistical description to the following few statistics, which are easy to understand. In addition, for nearly any problem, they communicate all the information one needs to get across:
1. The Mean
The mean (M0282) tells you where is distribution is located because it is the average of all the generated output values. It has less immediate intuitive appeal than the mode or median but it does have far more value. One can think of the mean of the output distribution as the x-axis point of balance of the histogram plot of the distribution. The mean is also known as the expected value though we don't recommend using the term as it implies for most people the mode (i.e. the value with the highest probability). The mean is sometimes also known as the first moment about the origin, which engineers will recognize from the idea of a turning moment about the origin. The mean of a data set {xi} is often given the notation x-bar.
The mean is particularly useful because:
1) the mean of the sum is the sum of their means; and
2) the mean of their product is the product of their means.
These two results are very useful if one wishes to combine risk analysis results (e.g. from partial models) or look at the difference between them.
2. Cumulative percentiles
Cumulative percentiles (M0116) give the probability statements that decision-makers need (like the probability of being above, or below X or between X and Y);
Often used notation for the Pth percentile is xP e.g. x75 is the value we estimate from the model to have a 75% probability of being below.
In addition, differences between cumulative percentiles are often used as a measure of the variable's range e.g. x95 - x05 would include the middle 90% of the possible output values and x80 - x20 would include the middle 60% of the possible values of the output. x25, x50 and x75 are sometimes referred to as the quartiles. The median is the 50th percentile and a stable measure of location.
Finally, the easiest way to illustrate and present cumulative percentiles is to quote the most interesting percentiles in combination with showing them on a cumulative distribution plot as discussed here [insert link].
3. Relative measures of spread
Two examples of relative measure of spread are:
- Normalized standard deviation (M0334) occasionally for comparing the level of uncertainty of different options relative to their size (i.e. as a dimensionless measure) where the outputs are roughly normal, and
- Normalized inter-percentile range (M0334) (more commonly) for the same purpose where the outputs being compared are not all normal.
For more information about how to calculate and use these two relative measures of spread, please consult ModelAssist.
What's next?
If you like to know more about how to present your model results, using Graphical or Statistical descriptions, download the free demo of ModelAssist. This comprehensive risk analysis reference and training tool gives you a more complete list of how to present your simulation model and its results.
ModelAssist
- The material within this 'Risk Analysis Tip' comes from one of the over 500 risk analysis topics available in ModelAssist, which gives a more detailed explanation of the above methods and any risk analysis techniques involved.
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