I'm working through the "Measuring the Value of Information" chapter in Hubbard's How to Measure Anything and am puzzled by the example in "The Value of Information Ranges" section (starting on page 89 of the first edition).
Here's what I'm doing:
Based on the givens, I create a normal distribution with mean of 550,000 and an SD of 273,556 (this gives a 90% CI between 100,000 and 1,000,000). For the opportunity loss of a slice, I'm using:
25*(200,000-j) where j is the mid-point of a slice.
The probability of a slice is computed using the normal distribution mentioned above. I'm pretty sure this is all correct, but please let me know if I've screwed it up!
At this point I'm unsure about which range I should cut into slices.
Originally I used [0, 200,000]. I reasoned that the scenario was focused on the number of additional units sold due to the ad campaign, and the text seemed to indicate that zero additional sales was the lower limit: "If we didn't sell any, we would have lost the cost of the ad campaign, $5 million (you might say the business would lose more than jus the cost of the campaign, but let's keep it simple). However, the computed EVPI in this case comes to $157,647.
If, instead, I slice up the interval -1,500,000 to 200,000, I get an EVPI of $323,090. This is close enough to the value given in the book, $337,500, that I'm tempted to attribute the difference to slicing variances. But I'm not sure why, in this case, it makes sense to include the portion of the tail less than zero. So I doubt this is correct.
If anyone has insight on this, please drop me a line. I'm probably missing something obvious about the method.