2 . One-way Analysis of Variance . 



This is a parametric statistical test which tests for differences 

 among more than two groups of samples classified by a single criterion, 

 e.g., to see if more of the total variability in the data is among the 

 several different samples or within the individual samples. A signifi- 

 cant difference means that more of the variability is among groups 

 rather than within groups. 



The significant test used was an F test, a test of variance. This 

 test was used^ because testing was one among several groups, and there 

 were few tests outside of analyses of variance which were available to 

 do such tests. 



Formulas for the test are: 



Source of 

 variation 



Among group 



Degrees of 

 freedom 



c-1 



Sums of squares 



Mean square 



r^y)' 



(^z"Ey)^ SS_ 

 n c-1 



Within group n-c 



Total -among group 



SS 

 n-c 



Total 



n-1 



Cz"Ey2 _ li-iZl 



n 



where: c = number of columns 



n = number of observations 

 The test is an F test where: 



Mean square among group 

 Mean square within groups 



F is compared to tabled F values for the appropriate degrees of 

 freedom. An F value exceeding the tabled value indicates significant 

 differences among groups. 



3. Student -Newman- Keuls Multiple Range Test . 



This an a posteriori step-wise test used to measure differences amonj 

 several means. It differs from the one-way analysis of variance by 

 testing means not variances, and is used after the analysis of variance 

 has indicated the need for the test. 



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