365 Days of Climate Awareness 74 - Confidence Intervals

A confidence interval is the estimated certainty with which a given value can be stated. It is easily confused with the standard deviation, but the two are not the same. (Confidence intervals can be provided for the standard deviation of a sample set.)

The desired level of confidence is most often known ahead of time: is a high level (90-99%) of confidence desired? Then the interval of values will be larger, as the possible range will be larger. A confidence interval of 95% does not indicate that 95% of the sample values are within those limits--that is the standard deviation curve. A confidence interval of 95% states that there is a 95% chance that the given mean value occurs within those limits. It says nothing about the rest of the sample set.

Confidence intervals (numbers along horizontal axis represent standard deviations).

The calculation of a confidence interval is very different, and more complex, than that for a standard deviation, but since it can be represented with the same bell curve the two are often conflated. Whether the value in question is a data point from field or lab work, or is the result of predictive model runs, the confidence estimate speaks only to the projected reliability of that data point.

The IPCC employs a system of confidence estimates for its statements of fact and model predictions. A summary:

Virtually certain: > 99% probability (within 3 sigma)
Extremely likely: > 95% probability (within 2 sigma)
Very likely: > 90% probability (within 1.645 sigma)
Likely: >66% probability (within ~1 sigma)
More likely than not: > 50% probability (within 0.675 sigma)
About as likely as not: 33-66% probability (~0.4-1 sigma)
Unlikely: <33% probability (outside one sigma)
Extremely unlikely: <5% probability (outside two sigma)
Exceptionally unlikely: <1% probability (outside three sigma)

Tomorrow: uncertainty.

Be well!