Spatial conscript body height correlation of Norwegian districts in the 19^th century

Background: We investigated height of Norwegian conscripts in view of the hypothesis of a "community effect on height" using autocorrelation analysis of district heights within a time-span of 20 years at the end of the 19^th century and correlations between neighboring districts at this time. Material and methods: After digitalizing available body height data of Norwegian draftees in 1877-1878, 1880 (averaged as 1878), and 1895-1897 (averaged as 1896) we calculated the magnitude of autocorrelation of body height within the same municipality at different time points. Furthermore, we generated three different neighborhood networks, (1) based on Euclidean distances, (2) a minimum spanning tree build on those distances, (3) a network founded on real world road connections. The networks were used to determine the correlation between body height of neighboring districts depending on the number of edges required to connect two municipalities. Results: The autocorrelation value for body heights was around r = 0.5 (for all p < 0.001) in the years 1878 and 1896. The correlation between neighboring districts varied in the Euclidean distance based network between 0.47 and 0.27 approximately for both years in a sorted order, descending from nearest (0-50 km) to farthest (150-200 km, for all p < 0.001). First order neighbors in the minimum spanning tree network correlation was 0.36 in 1878 and 0.42 in 1896 (for all p < 0.001). The values of neighbor correlation in the road connection based network ranged in 1878 from 0.42 (first order neighbors) to 0.17 (forth order neighbors, for all p < 0.01) and in 1896 from 0.46 (first order neighbors) to 0.12 (forth order neighbors, for all p < 0.05). Conclusion: This initial study of Norwegian conscript height data from the 19^th century showed significant medium sized effects for the within district autocorrelation between 1878 and 1896 as well as medium neighborhood correlation, slightly lower in comparison to a recent study regarding Swiss conscripts. Digitalizing more data from other years in this and later time spans as well as using older road and ship connections instead of the actual road data might stabilize and improve those findings.