Factcheck.org Mislead by the NOAA on Statistics

Here is a link to a Factcheck.org article "Obama and the ‘Warmest Year on Record".


The article includes the following statement.


"For example, NOAA reported that the global average temperature for 2014 was 0.69 degrees Celsius (1.24 degrees F) above the 20th century average. This departure from the average is known as the temperature anomaly. The 2014 temperature anomaly (0.69 degrees C) ranks first among all years dating back to 1880. However, that finding has a margin of error of 0.09 degrees C — which means there is a 95 percent chance that 2014’s temperature anomaly falls between 0.60 degrees C and 0.78 degrees C."

Factcheck got this phrasing from the NOAA.  The NOAA's interpretation of the meaning of its 95% confidence interval is incorrect.

The methodology for constructing confidence intervals only assures that 95% of the 95% confidence intervals constructed from all possible samples will contain the true parameter. Thus, it is correct to say, before a sample is taken, that the probability that the 95% confidence interval computed from the sample will contain the true parameter is 95%. However, it is incorrect to say, after the sample is taken, that the 95% confidence interval computed from that particular sample contains the true parameter is 95%.

By the nature of the confidence interval methodology, 95% of the 95% confidence intervals constructed from all possible samples will contain the true parameter. For these confidence intervals, the probability that they contain the true parameter is 1. For the remaining 5% of the 95% confidence intervals, the probability that they contain the true parameter is 0.