UPDATE: As I originally mentioned at the end of this post, I thought we should “give the benefit of the doubt” to GISS as there may be a perfectly rational explanation. Steve McIntyre indicates that he has done an analysis also and doubts the other analyses:

I disagree with both Luboš and David and don’t see anything remarkable in the distribution of digits.

I tend to trust Steve’s intuition and analysis skills,as his track record has been excellent. So at this point we don’t know what is the root cause or even if there is any human touch to the data. But as Lubos said on CA “there’s still an unexplained effect in the game”.

I’m sure it will get much attention as the results shake out.

UPDATE2: David Stockwell writes in comments here:

Hi,

I am gratified with the interest in this, very preliminary analysis. There’s a few points from the comments above.

1. False positives are possible, for a number of reasons.

2. Even though data are subjected to arithmetric operations, distortions in digit frequency at an earlier stage can still be observed.

3. The web site is still in development.

4. One of the deviant periods in GISS seems to be around 1940, the same as the ‘warmest year in the century’ and the ‘SST bucket collection’ issues.

5. Even if in the worst case there was manipulation, it wouldn’t affect AGW science much. The effect would be small. Its about something else. Take the Madoff fund. Even though investors knew the results were managed, they still invested because the payouts were real (for a while).

6. To my knowledge, noone has succeeded in exactly replicating the GISS data.

7. I picked that file as it is the most used – global land and ocean. I haven’t done an extensive search of files as I am still testing the site.

8. Lubos relicated this study more carefully, using only the monthly series and got the same result.

9. Benfords law (on the first digit) has a logarithmic distribution, and really only applies to data across many orders of magnitude. Measurement data that often has a constant first digit doesn’t work, although the second digit seems to. I don’t see why last digit wouldn’t work, and should approach a uniform distribution according to the Benford’s postulate.

That’s all for the moment. Thanks again.

This morning I received an email outlining some work that David Stockwell has done in some checking of the GISS global Land-Ocean temperature dataset:

Detecting ‘massaging’ of data by human hands is an area of statistical analysis I have been working on for some time, and devoted one chapter of my book, Niche Modeling , to its application to environmental data sets. The WikiChecks web site now incorporates a script for doing a Benford’s analysis of digit frequency, sometimes used in numerical analysis of tax and other financial data.

The WikiChecks Site Says:

‘Managing’ or ‘massaging’ financial or other results can be a very serious deception. It ranges from rounding numbers up or down, to total fabrication. This system will detect the non-random frequency of digits associated with human intervention in natural number frequency.

Stockwell runs a test on GISS and writes:

One of the main sources of global warming information, the GISS data set from NASA showed significant management, particularly a deficiency of zeros and ones. Interestingly the moving window mode of the algorithm identified two years, 1940 and 1968 (see here ).

You can actually run this test yourself, visit the WikiChecks web site, and paste the URL for the GISS dataset

http://data.giss.nasa.gov/gistemp/tabledata/GLB.Ts+dSST.txt

into it and press submit. Here is what you get as output from WikiChecks:

GISS Frequency of each final digit: observed vs. expected

0 1 2 3 4 5 6 7 8 9 Totals Observed 298 292 276 266 239 265 257 228 249 239 2609 Expected 260 260 260 260 260 260 260 260 260 260 2609 Variance 5.13 3.59 0.82 0.08 1.76 0.05 0.04 4.02 0.50 1.76 17.75 Significant * . *

Statistic DF Obtained Prob Critical Chi Square 9 17.75 <0.05 16.92

Significant management detected.

RESULT:Significant variation in digit 0: (Pr<0.05) indicates rounding up or down. Significant variation in digit 1: (Pr<0.1) indicates management. Significant variation in digit 7: (Pr<0.05) indicates management.

Stockwell writes of the results:

The chi-square test is prone to produce false positives for small samples. Also, there are a number of innocent reasons that digit frequency may diverge from expected. However, the tests are very sensitive. Even if arithmetic operations are performed on data after the manipulations, the ‘fingerprint’ of human intervention can remain.

I also ran it on the UAH data and RSS data and it flagged similar issues, though with different deviation scores. Stockwell did the same and writes:

The results, listed from lowest deviation to highest are listed below. RSS – Pr<1 GISS – Pr<0.05 CRU – Pr<0.01 UAH – Pr<0.001 Numbers such as missing values in the UAH data (-99.990) may have caused its high deviation. I don’t know about the others.

Not being familiar with this mathematical technique, there was little I could do to confirm or refute the findings, so I let it pass until I could get word of replication from some other source.

It didn’t take long. About two hours later, Lubos Motl, of the Reference Frame posted his results obtained independently via another method when he ran some checks of his own:

David Stockwell has analyzed the frequency of the final digits in the temperature data by NASA’s GISS led by James Hansen, and he claims that the unequal distribution of the individual digits strongly suggests that the data have been modified by a human hand. With Mathematica 7, such hypotheses take a few minutes to be tested. And remarkably enough, I must confirm Stockwell’s bold assertion.

But that’s not all, Lubos goes on to say:

Using the IPCC terminology for probabilities, it is virtually certain (more than 99.5%) that Hansen’s data have been tempered with.

To be fair, Lubos runs his test on UAH data as well:

It might be a good idea to audit our friends at UAH MSU where Stockwell seems to see an even stronger signal.

… In plain English, I don’t see any evidence of man-made interventions into the climate in the UAH MSU data. Unlike Hansen, Christy and Spencer don’t seem to cheat, at least not in a visible way, while the GISS data, at least their final digits, seem to be of anthropogenic origin.

Steve McIntyre offered an explanation in the way rounding occurs when converting from Fahrenheit to Centigrade, but Lubos can’t seem to replicate the same results he gets from the GISS data:

Steve McIntyre has immediately offered an alternative explanation of the non-uniformity of the GISS final digits: rounding of figures calculated from other units of temperature. Indeed, I confirmed that this is an issue that can also generate a non-uniformity, up to 2:1 in the frequency of various digits, and you may have already downloaded an updated GISS notebook that discusses this issue. … I can’t get 4,7 underrepresented but there may exist a combination of two roundings that generates this effect. If this explanation is correct, it is a result of much less unethical approach of GISS than the explanation above. Nevertheless, it is still evidence of improper rounding.

Pretty strong stuff, but given the divergence of the GISS signal with other datasets, unsurprising. I wonder if it isn’t some artifact of the GISS Homogenization process for surface temperature data, which I view as flawed in its application.

But let’s give the benefit of the doubt here. I want to see what GISS has to say about it, there may be a perfectly rational explanation that can be applied that will demonstrate that these statistical accusations are without merit. I’m sure they will post something on RC soon.

Stay tuned.

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