The GRIMMER test
The GRIMMER test is my main contribution to the statistical subfield of granularity testing. A publication of the method is available here.
This method extends granularity testing to measures of variability such as standard deviations, standard errors, variances, and deviations from the mean.
My involvement in granularity testing started when I saw the GRIM test publication. I immediately recognized the importance of the method and added the test to PrePubMed in order to make it easier for researchers to use.
After discussions with the authors I started working on trying to extend the GRIM test to standard deviations and stumbled upon the observation that measures of variability follow a simple repetitive pattern, as do the means.
Mathematicians may scoff at the idea that granularity testing is a "discovery" given that it is obvious that statistics of discrete data will also be discrete, and admittedly applying this fact to a statistic such as a sum or a mean is very simple, but it is not necessarily obvious how to apply granularity testing to more complicated statistics. In addition, the idea of granularity testing has never been formalized before, and this includes establishing the general requirements and limitations for granularity testing for each statistic in addition to providing a simple method for checking the statistic.
Granularity testing for a sum is so obvious that there isn't a name or a publication for it. If your data is reported in whole numbers you would be surprised to see a sum with decimals.
Granularity testing for means is also fairly obvious, but for most sample sizes it is difficult to determine in your head if a mean is consistent. In addition, given how easy it is to calculate a mean it is surprising how many publications have incorrectly reported means.
Going beyond means requires some advanced computing. I was able to extend granularity testing to measures of variability, including establishing the power of the test, but thus far have not tried to extend the test to other statistics.
Given the fact that most researchers find the GRIM test complicated and the test has not been embraced by the scientific community for wide use, I do not expect the much more complicated GRIMMER test to find a home in the hands of the average researcher.
The next step for granularity testing likely is not to apply the observation to more statistics, but rather to try and automate the test similar to what the statcheck people have done. I don't think it will be possible to achieve as much accuracy as statcheck given the specific requirements for granularity testing, but it would be interesting to see how accurate automated testing could get and whether it would be worth reporting such results.
