How confident are you of your estimate?

This morning I was listening to NPR story on their new estimate of oil spill. The reporter was asking the a professor from Purdue about his now famous estimate that the oil spill is  70,000 barrels a day, way more than the Government estimate of 5000 barrels per day. Here is a snippet of the conversation:

Reporter: What is your estimate?
Professor: 70,000 barrels per day
Reporter: What is the margin of error?
Professor: About 20%
Reporter: That means the spill is anywhere between 56,000 to 84,000 barrels a day
Professor: That’s right.
Reporter: How confident are you of the estimate
Professor:  Pretty confident

Pretty confident?  I was disappointed. I was not sure if the professor deliberately chose a generic language of “pretty confident” vs. what he would normally use with his estimates – using the confidence level of 95%.

Be it estimating oil spill, sales increase, marketing conversion or a person’s height, confidence level (90%, 95% or 99%) and margin of error are very two useful and relevant qualifiers you must provide (and if we assume all the estimates are normally distributed about the real parameter). I particularly prefer 95% confidence level because the margin of error is almost equal to 2 sigmas (standard deviations).

Suppose the professor was 95% confident, he is saying the chances of the oil spill is lower than 56,000 barrels is less than 2.5%. So according to him, the chance that the oil spill is really 5000 barrels a day is 0.0000000000000000000083, a 9 sigma event!

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