本文主在探討人口在時空分布下的自我組織特性，借重本島人口區域分布之時間及空間二因子變異數分析，以發現冪次定律是否受到該二因子之影響，亦即檢驗冪次定律的普遍性與恆常性。由於冪次定律代表都市層級與人口聚散的關係，因此就本研究之人口時空分布資料經都市排序與規模法則 (City Rank-Size Rule)或Zipf's Law，檢證人口聚散差異性與冪次定律顯著性二者在時間與空間的變化。為瞭解人口差異迴歸係數與冪次定律顯著性之解釋性關係，並進行更進一階的相關分析。從本研究中發現冪次定律的存在不受時間與空間之限制，亦即其具有普遍性及恆常性，且在人口聚散差異大的地區具高強度。同時發現高速公路興建之公共政策對於人口分布冪次係數具有影響。

The paper investigates the characteristics of self-organization of population distributions across time and space. Based on two-way ANOVA analyses for regional population distributions on the Taiwan Island across time and space, we intend to discover whether the power law of the distribution structure is affected by the two factors, that is the research is grounded on the hypothesis that the power law of population distribution is both invariable and universal across time and space. Because the power law represents the relation between the formation of urban hierarchies and the level of population aggregations, drawing on the population distribution data of the Island in time and space we examine the evolutionary pattern of and relation between population aggregation trends and levels of significance of the power law through the city rank-size rule or Zipf's Law. In order to understand the explanatory relation between population distribution variations in terms of the coefficient of regression and levels of significance of the power law, a simple regression analysis is further conducted. The resulting evidence shows that the power law not only exists, but also persists in time and space; therefore our hypothesis is confirmed that it is both invariable and universal across time and space. The power law relation of population distributions is more evident in areas where population aggregations are more diverse. Public policies, such as highway constructions, have impact on the characteristics of the power law distribution of populations.