Statistical Analysis in Geomorphic Research

Statistical analysis plays an essential part in quantitative geomorphic investigations using numerical data obtained by random sampling. The sample is represented graphically by a histogram and is described in terms of the arithmetic mean, standard deviation, variance, and form of distribution curve-whether normal, log-normal, or other. From the sample it is possible to estimate the standard deviation of the population and the standard deviation of the sample means. A difference between two sample means may be tested by deriving the statistic t, which will indicate the probability of obtaining the observed difference by chance alone if no real difference in population exists. Differences in sample variances can be tested, using the statistic F, which is the ratio of the larger to the smaller variance. Where three or more sample means are to be compared, analysis of variance using the statistic F affords a means of testing the hypothesis that no significant difference exists. The interrelationship between two sets of variables may be determined by regression analysis, in which equations of both linear and nonlinear types are fitted to the data and tested by a t-test under the hypothesis that no significant departure from a zero trend actually exists. Where no functional relationship is to be established, the degree of correlation between two sets of data is determined in terms of a correlation coefficient which can be tested by a t-test under the hypothesis that no correlation actually exists. Examples of applications of each of the above methods in current geomorphic research show that statistical analysis is a powerful tool in investigation of fundamental problems of land-form development.