be used to determine the number of replications required to obtain the de- 

 sired precision in Phase II. Somewhat arbitrarily, the minimum number of 

 samples required at each sampling station in Phase I has been set at four. 

 This number of samples per station is more a concession to ever-present 

 analytical resource limitations than anything else. More samples should be 

 taken if possible. 



The number of samples required to detect a specified difference in the 

 concentration of the spilled substance at two different sampling stations, 

 or at the same station at different times, can be estimated using tables 

 developed by Kastenbaum, Hoel , and Bowman (1970). These tables were de- 

 veloped to aid in the selection of sample size for one-way analysis of vari- 

 ance (ANOVAR) of up to six groups. Since one-way ANOVAR of two groups is 

 mathematically equivalent to a t-test (Sokal and Rohlf 1973), the two group 

 one-way ANOVAR tables can also be used to select sample size for a compari- 

 son of two groups by the unpaired t-test. 



The two-group one-way ANOVAR tables presented in Figure 2 contain the 

 maximum values of the standardized range, t , when the means of k=2 groups, 

 containing N observations, are compared at various levels of risk. In most 

 experiments the level of significance (a ) is usually assigned a value of 

 5 percent and B is normally not even computed. Vanderhorst, Anderson, 

 Wilkinson, and Woodruff (1978) recently suggested that error risks of at 

 least 10 percent for both a and 3 be adopted in biological assessment stud- 

 ies. Since analytical data from environmental samples also often contain 

 considerable variation, we too recommend 10 percent as the minimum error 

 risks for both a and 3 in analytical documentation studies. A 10 percent 

 value for 3 sets the power (1-3 ) of the statistical test at 90 percent. 

 This means that there is a 90 percent probability that a value which differs 

 from the mean by an amount exceeding limits specified by the analyst will be 

 detected. In this situation the analyst specified limits determine the 

 sensitivity of the test and must be expressed as the standardized range 

 using the following formula: 



T = ( ymax - umin ) 



where t is the standardized range, umax - pmin is the specified range about 

 the sample mean, and S is the sample standard deviation. 



Once values for a and 3 are selected and the standarized range is calcu- 

 lated, the tables in Figure 2 can be used to estimate the number of samples 

 required to achieve the desired sensitivity. As an example, suppose that 

 the mean concentration of petroleum hydrocarbons detected in a series of 

 sediment samples taken at a particular sampling station in Phase I was 150 

 parts per million (ppm) and the standard deviation of the measurements was 

 53 ppm. Also, suppose that the analyst wanted to be able to detect a 



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