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Top Five Ideas -- Statistics for Project Management

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Top Five Ideas -- Statistics for Project Management

  1. 1. Quantitative Methods Part I Top Five Ideas from Statistics that help Project Management John C Goodpasture Square Peg Consulting
  2. 2. Top five ideas from statistics that help project management <ul><li>The Bell Curve: In the long run, most real activities, like cost and schedule, have outcomes that cluster around an average according to a bell curve of probabilities </li></ul><ul><li>Expected Value: In the face of uncertainty about the real world outcomes, the best single number to represent the average outcome is a risk-weighted average: Expected Value (EV) </li></ul><ul><li>Distributions: Every project estimate—without exception—has some uncertainty about it, a distribution of possibilities, each possibility having a unique probability. </li></ul>Photo:Tom Gazpacho
  3. 3. Top five ideas from statistics that help project management <ul><li>Monte Carlo: the best and fastest way to get a handle on your project is to simulate the outcomes </li></ul><ul><li>Dependency bias: When otherwise independent actions become dependent upon each other, there is a bias towards extending the schedule </li></ul>
  4. 4. The Bell Curve is ubiquitous—it’s everywhere! <ul><li>The bell curve—aka the Normal curve—is ubiquitous because of the Central Limit Theorem and the Law of Large Numbers </li></ul><ul><li>CLT tells us that the sum of value set—like the sum of work-package costs—will be a value with probabilities that tend towards a bell curve </li></ul><ul><li>LLN tells us that the average of the value set will tend toward the expected value and true mean of the population, even if the value set is only a ‘large enough’ sample </li></ul><ul><li>The consequence of the LLN upon the CLT is that the EV of the bell curve is an excellent estimate of the true mean of the population </li></ul><ul><li>The consequence of the CLT upon the LLN is that the bell curve provides additional information about the quality of the value set. </li></ul>Events or Measurements Outcome Values EV
  5. 5. Expected Value is the one go-to number for everyone <ul><li>Example: 10 work-packages </li></ul><ul><li>3-point estimates with probabilities, ~ 80-20 rule </li></ul><ul><li>EV = value x probability* </li></ul><ul><li>Variance** = Value probability x ( LLN EV – Value ) 2 </li></ul><ul><li>Standard deviation = √( variance ) </li></ul><ul><li>Expected value (budget): $549.7 </li></ul><ul><li>84% confidence the budget will be < $549.7 + $40.8 = $590.5 </li></ul><ul><ul><li>EV + 1 standard deviation </li></ul></ul>* Example: WP1 10% x (60 + 45) + 80% x 50 = 50.5 ** Example: WP1 80% x (55. – 50) 2 +10% x (55-60) 2 + 10% x (55-45) 2
  6. 6. Ban single-point estimates! It’s all about distributions <ul><li>There are no facts about the future—everything that hasn’t happened is only an estimate! </li></ul><ul><ul><li>“If you are going to predict, predict often…” Milton Friedman, Nobel laureate </li></ul></ul><ul><li>Every estimate should be placed within a range of possibilities </li></ul><ul><ul><li>Some possibilities are more probable than others </li></ul></ul><ul><ul><li>Possibilities and probabilities constitute a distribution </li></ul></ul><ul><li>It’s rare that the real distribution is known or can be known </li></ul><ul><ul><li>It’s likely that reasonable 3-point estimates can be made </li></ul></ul><ul><li>3-point estimates constitute a distribution </li></ul><ul><ul><li>Points in between would be handy to know, but not essential </li></ul></ul><ul><ul><ul><li>Its customary to connect the 3 points with straight lines, thereby the Triangular Distribution </li></ul></ul></ul><ul><ul><li>3-point estimates can be used directly in simple arithmetic approximations that provide ‘good enough’ risk adjustments for estimates </li></ul></ul>
  7. 7. Monte Carlo is a simulation technique that gives quick, useful answers <ul><li>Make a 3-point estimate for every outcome—work package or activity </li></ul><ul><ul><li>Most pessimistic, most optimistic and most likely </li></ul></ul><ul><li>Assume a distribution that fits the situation; most quick estimates are made with the Triangular distribution </li></ul><ul><ul><li>The choice of distribution is not as important as picking the three points since the Central Limit Theorem will tend to wash-out the distribution detail </li></ul></ul>Run a simulation using a plug-in tool on your scheduler application* The outcome will tend to be bell-curve distributed in almost every case, so the interesting results are in the cumulative probability distribution—this is in effect a confidence data for your outcome, the so-called S-curve Photo John Goodpasture
  8. 8. Everything stretches out when there are dependencies <ul><li>When there are dependencies, the distributions of each event interact </li></ul><ul><ul><li>At a milestone with paths joining: Probability ( milestone ) = P (path A) x P (path B) </li></ul></ul><ul><ul><ul><li>90% confidence in each path leads to 81% confidence in the milestone </li></ul></ul></ul><ul><ul><ul><li>To raise the milestone confidence, each path must be allowed to stretch out to the right—a phenomenon called ‘merge bias’ </li></ul></ul></ul><ul><li>Dependencies can be created by resource conflicts </li></ul><ul><li>With independent resources the schedule is 5 units </li></ul><ul><li>With resources-to-task dependency, the schedule extends to 6 units </li></ul>Time 4 tasks, 2 resources
  9. 9. Read more about it! <ul><li>Quantitative Methods is a book about numbers and methods for applying them to practical situations in projects </li></ul><ul><li>There is a good tutorial on statistics, accounting, balanced scorecard, and value </li></ul><ul><li>The chapter on estimating is right out of my own experience </li></ul><ul><li>The presentation on earned value makes EV really workable in day-to-day situations. </li></ul><ul><li>If you do contracting, read the chapter on about doing risk management with contracts </li></ul><ul><li>And, best of all, you can buy it at any on-line retailer, and read excerpts on google/books </li></ul>
  10. 10. I hope you liked what you saw here <ul><li>I hope you enjoyed this presentation. </li></ul><ul><li>You can share it with your network </li></ul><ul><li>There is a lot more information in the book, at my company website, and at my BLOG. See the cover page for links </li></ul><ul><li>By the way, there is information on my other books and magazine articles at </li></ul><ul><li>You can contact me from my company website; the information is all there </li></ul>