“Worst Bound” of the 90% CI; this is the undesirable end of the range “Best Bound” of the 90% CI; this is the desirable end of the range Threshold: Below this point is losing money A B Relative Threshold (RT)=B/A Computing a “Relative Threshold” Use this result as input to the following slide for computing the value of measuring an uncertain range. Example: You might invest in a new system if you get a productivity improvement of over 10%. But your current range for this value is 5% to 20%. Compute the RT.

The EOLF Chart Use the RT from the previous slide to compute the value of information. Example: You invested in the system in the example on the previous slide. Let’s say if the system does not get a productivity improvement greater than 10%, then you lost $100,000 for each percentage point you are under the threshold. Use this information and the RT to compute the value of reducing uncertainty about the range of potential productivity improvements.

Samples Below Threshold 20% 30% 40% 50% 0.1% 1% 10% Number Sampled Chance the Median is Below the Threshold % 5% 0.2% 0.5% 0 1. Find the curve beneath the number of samples taken 3. Follow the curve identified in step 1 until it intersects the vertical dashed line identified in step Identify the dashed line marked by the number of samples that fell below the threshold 4. Find the value on the vertical axis directly left of the point identified in step 3; this value is the chance the median of the population is below the threshold Measuring to the threshold Use this chart when using small samples to determine the probability that the median of a population is below a defined threshold Example: You want to determine how much time your staff spends on one activity. You sample 12 of them and only two spend less than 1 hour a week at this activity. What is the chance that the median time all staff spend is more than 1 hour per week? Look up 12 on the top row, following the curve until it intersects the “2” line on the bottom row, and look up the number to the left. The answer is just over 1%.

10% 20% 30% 0% 2% 4% 6% 8% % 12% 16% 20% 30% 40% 50% 60% 70% Find the total sample size; then find the diagonal line that starts on the small circle beneath it 2. Follow the diagonal line until it intersects the vertical line that corresponds to the number of samples in the subgroup; at that point lookup the number on the vertical scale to the left labeled “90% CI Lower Bound” 90% CI Upper Bound 90% CI Lower Bound # of Samples in subgroup 3. Repeat the process for the upper bound, using the diagonal line above the sample size; follow the diagonal line until it intersect the same vertical line as before; follow it to the number on the vertical axis to the left labeled “90% CI Upper Bound” # of Samples in subgroup % 40% Sample Size Population Percentage Estimate Use this chart to estimate the percentage of a population that falls within a subgroup, given a small sample Example: you want to measure how many of your customers have shopped at a competitor in the last week. You sample 20 and 10 of them said they did shop at a competitor. The chart shows how to compute the 90% confidence interval for the share of all customers who shopped there.

Upper bound Lower bound Mean A 1. Subtract the smallest serial number in the sample from the largest 2. Find the sample size on the horizontal axis and follow it up to the point where the vertical line intersects the curve marked “Upper Bound” 3. Find the value for “A” on the vertical axis closest to the point on the curve and add 1; multiply the result by the answer in step 1. This is the 90% CI UB for total serial numbered items 4. Repeat steps 2 and 3 for the Mean and Lower Bound Sample Size The “Enemy Tank” case This chart shows how the WWII statisticians estimated German tank production based on serial numbers of captured tanks