样本正态分布对降低空间抽样数量的重要性

【研究目的】样本总体的分布特征是影响抽样样本数量的主要因素，对于样本总体为非正态分布的情况，正态转换是降低抽样样本数量、提高抽样调查效率的有效手段。【方法】该文采用中国大陆区域2005年耕地空间分布数据，以1:10万地形图图幅框作为抽样单元，统计每个图幅框内耕地面积占比。分别采样1.5次开方、2次开方、2.5次开方、3次开方和4次开方运算的方式对原始数据进行正态转换。在此基础上对比分析了转换前后数据的峰度及偏度、抽样个数及抽样结果误差等。【结果】结果表明，基于2.5次开方运算后的分层抽样可以大大降低抽样率，由92.26%降低为22.55%，耕地面积指数平均值相对误差由7.06%降低为5.66%。利用2015年耕地面积指数进行抽样方法的精度检验，抽样平均值相对误差仅为3.27%。【结论】研究提出的抽样方法具有较高的适用性，同时也表明空间抽样中数据分布正态转换是非常必要的。本研究成果为广大学者在空间抽样调查方面的研究提供了有益的借鉴。

Importance of Sample Normal Distribution for Decreasing the Spatial Sampling Number

Objective]Sample general distribution feature is a major factor to impact sample size, and normal transformation for non-normal distribution of general samples is an effective means to reduce sample size and improve survey efficiency. Method]By using the special distribution data of the cultivated land of Mainland China of 2005 and by taking 1:100,000 topographic map frames as sampling units, the paper calculates the proportion of cultivated land area in each map frames. The normal transformation of original data is conducted by calculating 1.5 times square root, 2 times square root, 2.5 times square root, 3 times square root, and 4 times square root of them. Based on above transformation, a contrastive analysis on the factors of kurtosis and skewness, the number of samples and sampling error before and after the transformation is conducted. Result]The result shows that, the stratified sampling based on 2.5 square root operation can dramatically reduce sampling rate. The sampling rate is reduced from 92.26% to 22.55%, and the average relative error of cultivated area index is reduced from 7.06% to 5.66%. The accuracy of sampling method is verified by using the 2005 cultivated land area index, and the average relative error of the sampling is only 3.27%. Conclusion]The sampling method proposed by the study is highly applicable, and it is necessary to make normal transformation on the data distribution in spatial sampling. The study result has provided useful reference for the researches of scholars on space sampling survey.