By K. A. Brownlee
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Extra info for Industrial Experimentation
The variance tables were constructed for the purpose of testing whether a variance A was greater than a variance B, A being known beforehand as derived in a particular way which distinguished it from B. Here we are testing whether a variance A is greater than a variance A 1 1 and until we have calculated them we do not know which is A and which is A A is that one which turns out to be the larger. 2% respectively. That is to say, unlikely to get the result ^^ , : (b) Averaging of Several Variances Suppose, extending our previous example, we had a number of determinations of variability for each method on a number of different samples.
There may be a systematic difference between these machines ; we wish to test whether such an effect exists, and if it does exist estimate its contribution to the total variance of the final product. Formally what we have to deal with here is a twofold classification; every individual belongs to a particular row and to a particular column. ^ Or, in an to ing n different acid experiment on conditions of nitration of cellulose, we could have x corres concentrations, corresponding to rows, and n 2 different acid temperatures, numbers.
To be those in which the total number of individuals Large samples can be considered 30. than is n 2) greater (na. "" , , , . + Small Samples (i) We calculate the following terms. S denotes summation. ,-2) the table of t with degrees of freedom t, we enter our value of t exceeds that for the 5% level we may take it ( different. with that degree of assurance that the populations are Having found the value of nj + B2 _2). If the Let us consider a specific example. The numbers below represent tons of acid before failure for two sets of pots, one of in hundreds throughputs acid pot con from Foundry A, the other from Foundry B, used in sulphuric is better than the Is there any reason to suppose that one foundry centration.