By R.B.G. Williams

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**Extra info for Intermediate Statistics for Geographers and Earth Scientists**

**Example text**

A number of tests have been devised for evaluating the differences between the means of individual classes . One of the easiest to calculate is the least significant difference (or LSD) test. Unfortunately, it can be used to test only selected differences between the class means, and the selection must be made on theoretical grounds without reference to the data. 375 Sing le Factor Analysis of Variance Sc he f f~ (1959) has pr oposed anot her s impl e t est th at can be used to evaluat e the di fferen ces between all the clas s mean s , or differences se lec ted as a r esult of ins pect ion of th e dat a .

If only some of the class means are significantly different, the F ratio for the classes as a whole (that is, for Factor A) may be so reduced as to be non-significant. Duncan's test concentrates on the individual class means, and can pick out significant differences even when the majority of differences are nonsignificant. One should not make the mistake, however, of imagining that Duncan's test is invariably more powerful than single factor ANOVA. If this were the case it would be a waste of time learning about single factor ANOVA.

40881 2 17 . 20441 Ori entat ion (Factor B) 88 . 09069 4. 11841 Er r or 25 . 5 2818 17 Int eracti on (A and B) 14 . The r at io of the vari anc e estimates for the interact ion and the error is F = 2 . 11841/2. 9856 . Since the r atio is le ss than 1 it obviousl y cannot be signifi cant. There is no reason to suppo se that e r os i ona l envi r onment and ori ent ation i nteract to af f ect slope ang l e. 0046 . The numerator has 2 degrees of freedom and the denominator 12. 01 level of significance.