Cronbach's alpha is a coefficient of consistency. It tests to what degree the different words in the data set give the same signal of linguistic relationships between the dialect. If all words have a similar geographic distribution of variants the value of Cronbach's alpha is 1, if there is no consistency between the words in the data set the value is 0. A generally accepted threshold for consistency of the data is 0.70.
Generally the Cronbach's Alpha value is higher the more items the analysis comprises. The value can therefore be used for testing if the number of items is enough to obtain consistent results. If the Cronbach's Alpha value is very low it is a good idea to add more items to the analysis in order to get more reliable results.
General references: Nunally 1978
Use in dialectology: Heeringa 2004:170-177
Local incoherence means something like the lack of coherence on a local scale. The smaller the value, the less incoherence and the better the measurements.
Local incoherence is based on the idea that the dialect in one location differs less from the dialect in another location in the near vicinity, than from the dialect of another location, still in the vicinity, but a bit further away. Differences between locations geographically far apart are discarded, because at that level coincidence sets in.
You can only use local incoherence to compare multiple measurements for one and the same area, because the result highly depends on the geography of the area and the exact geographic distribution of the locations. And of course, one dialect area is not like another. And for instance, if you add locations to a previously analyzed area, then the local incoherence can go both up or down, but this says nothing about the relative reliability of the extended set of locations.
Finally, you should note that local incoherence is a simple method. Generally speaking, of two measurements, the one with the best result of local incoherence will be the better measurement. But this doesn't have to be true in each and every case.
Reference(s): Nerbonne and Kleiweg 2007
The aggregate linguistic differences between all pairs of places can be downloaded as a table, as well as in RuG/L04 format. In the table you can look up the linguistic difference between any two sites (exactly like you would look up the distance in kilometers between two places in the distance chart in a road map!).
Shows the distribution of the distances. [Why squared?]
The maps are created by drawing lines corresponding to the aggregate distance between pairs of sites. The darker the color of the line the higher similarity (see whole color range).
In the first map, only neighboring sites are connected by lines. In the second map lines are drawn across a larger geographic area.
Reference(s): Nerbonne (forthcoming), Nerbonne and Siedle 2005