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Table 4 Community-related differences in the time lag Δt1 until first citation

From: Community structure in co-inventor networks affects time to first citation for patents

   Infomap Prop. Lbls. Rand. Wlks. Greedy Louvain
In raw data \(\overline {\Delta t_{1}}\) 19.4 19.7 20.8 21.6 21.7
  raw data \(\widetilde {\Delta t_{1}}\) 16 16 17 17 17
  raw dataFootnote

abinned into 2-months-wide bins as shown in Figs. 3 and 4

\(\phantom {\dot {i}\!}\text {Mo}_{\Delta {t}_{1}}\)
0 0 10 10 12
  lognorm fit \(\overline {\Delta {t}_{1}}\) 18±2 18±2 18.8±0.9 19.5±0.9 19.5±0.9
  lognorm fit \(\widetilde {\Delta {t}_{1}}\) 16±1 16±1 16.7±0.7 17.4±0.7 17.4±0.7
  lognorm fit \(\phantom {\dot {i}\!}\text {Mo}_{\Delta {t}_{1}}\) 12±2 12±2 12.6±0.9 12±2 13.3±0.9
Out raw data \(\overline {\Delta {t}_{1}}\) 24.6 24.5 24.8 24.7 24.7
  raw data \(\widetilde {\Delta {t}_{1}}\) 19 19 20 20 20
  raw data \(\phantom {\dot {i}\!}\text {Mo}_{\Delta {t}_{1}}\) 15 15 15 15 15
  lognorm fit \(\overline {\Delta {t}_{1}}\) 21.5±0.9 21.5±0.9 21.5±0.9 21.5±0.9 21.5±0.9
  lognorm fit \(\widetilde {\Delta {t}_{1}}\) 19.4±0.7 19.4±0.7 19.4±0.7 19.4±0.7 19.4±0.7
  lognorm fit \(\phantom {\dot {i}\!}\text {Mo}_{\Delta {t}_{1}}\) 15.3±0.9 15.4±0.9 15.3±0.9 15.3±0.9 15.4±0.9
  t-test full dataset 8.4 6.6 6.8 8.7 7.6
  av. t-score subset 2.9 1.7 1.7 2.3 2.6
  1. The mean (\(\overline {\Delta {t}_{1}}\)), median (\(\widetilde {\Delta {t}_{1}}\)), and modal (\(\phantom {\dot {i}\!}\text {Mo}_{\Delta {t}_{1}}\)) values derived from the raw data for the empirically observed distributions of time until the first citation that is not a self-citation and either originates from within (In) or outside (Out) co-inventor communities are listed for community structures obtained using five different detection algorithms. Corresponding values derived from fits of the empirical distributions to log-normal form are also given for comparison. Welch’s t-test scores (Welch 1947) establish the statistical significance for the observed differences between mean time lags for in-community and out-of-community citations. We give t-values obtained from tests applied to the full datasets of in-community and out-of-community citation lags, as well as the average t-score found when comparing 500 independently and randomly chosen subsets of 300 citations from the in- and out-of-community datasets