[3], page 276 f.) I£ we then — for each value of 6 — multiply these 
probabilities by the costs in figure 2, we obtain the expected conditional 
risk for the case of a — 30 96 — see the dashed lines in figure 8. The 
next step in our procedure is to take the revised probabilities for certain 
states of nature, figure 7, and compute the expected weighted risk. This 
is equal to the area under the dotted lines in figure 8. These lines are 
thus the product of the values of the dashed lines and the line in figure 
7. 
The described procedure is repeated for all values of all), giving the 
result of figure 10. It can be seen that an a = 85 % gives the lowest ex- 
pected weighted risk. 
8. Compute the Critical Value of the standard error 
. If the null hypothesis is correct, f 52/692 has a distribution which 
may be represented by the Chi?-distribution, see [3], p. 276. Thus we 
get the critical value, C, equal to V (o Chi? = 
1—a 
V (25 Chi2,5/100) — 4.6 um12). 
9. Compute the standard error. Decide 
From our measurements we compute an expected value of the standard 
error of unight weight of the instrument. This figure represents the error 
population. If it is smaller than 4.6 um we decide to accept the accuracy 
of the instrument. According to figure 10 the expected cost of this deci- 
sion is 60 kronor. 
11) In figure 9 is given an other example. There « is equal to 5 96. It can be 
observed that the power of the test, i. e. the area under the right hand fully drawn 
curve in figure 8 and 9, is very important for the expected effects of the possible 
errors of our decision. The effects of the number of degrees of freedom on the 
expected loss is also of the greatest importance, but in the way we have choosen to 
handle the decision process here, this number of degrees of freedom is fixed at 
this stage of the procedure. 
The level of significance is equal to the hight of the right hand end of the left 
hand fully drawn curve in figure 8 and 9. 
12) If we had chosen the alternativ hypothesis as null hypothesis we would 
have got our optimal « equal to 15 96 instead of 85 96, and the critical value 4.6 
um. The expected weighted cost function would have been the mirror of figure 10. 
This choice of which hypothesis to test is arbitrary, if the above method of deter- 
mination of best level of significance is used. 
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