A minimum sample size required from Schmidt hammer measurements

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. Copyright (C) 2009 John Wiley & Sons, Ltd.