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A minimum sample size required from Schmidt hammer measurements

机译:施密特锤测量所需的最小样本量

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摘要

The Schmidt hammer is a useful tool applied by geomorphologists to measure rock strength in field conditions. The essence of field application is to obtain a sufficiently large dataset of individual rebound values, which yields a meaningful numerical value of mean strength. Although there is general agreement that a certain minimum sample size is required to proceed with the statistics, the choice of size (i.e. number of individual impacts) was usually intuitive and arbitrary. In this paper we show a simple statistical method, based on the two-sample Student's t-test, to objectively estimate the minimum number of rebound measurements. We present the results as (1) the 'mean' and 'median' solutions, each providing a single estimate value, and (2) the empirical probability distribution of such estimates based on many field samples. Schmidt hammer data for 14 lithologies, 13-81 samples for each, with each sample consisting of 40 individual readings, have been evaluated, assuming different significance levels. The principal recommendations are: (1) the recommended minimum sample size for weak and moderately strong rock is 25; (2) a sample size of 15 is sufficient for sandstones and shales; (3) strong and coarse rocks require 30 readings at a site; (4) the minimum sample size may be reduced by one-third if the context of research allows for higher significance level for test statistics. Interpretations based on less than 10 readings from a site should definitely be avoided.
机译:施密特锤是地貌学家用来测量野外条件下岩石强度的有用工具。现场应用的本质是获得足够大的单个回弹值数据集,这将产生有意义的平均强度数值。尽管人们普遍同意进行统计需要一定的最小样本量,但是选择大小(即单个影响的数量)通常是直观而随意的。在本文中,我们展示了一种基于两个样本的学生t检验的简单统计方法,可以客观地估算回弹测量的最小数量。我们将结果表示为(1)“均值”和“中位数”解决方案,每个解决方案均提供一个估计值,以及(2)基于许多现场样本的此类估计的经验概率分布。假设不同的显着性水平,已经对14种岩性的施密特锤数据进行了评估,每种13-81个样品,每个样品包含40个单独的读数。主要建议是:(1)对于弱和中等强度的岩石,建议的最小样本量为25; (2)砂岩和页岩的样本数量为15就足够了; (3)坚硬和粗糙的岩石需要在现场读取30个读数; (4)如果研究范围允许检验统计数据具有更高的显着性水平,则最小样本量可能会减少三分之一。绝对应避免基于站点的少于10个读数的解释。

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