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203

TABLE 6.
Values of the Probability Tntegral for Argument 0.4 tOy; that is, when the unit

of measurement = the Probable error.

 

Multiples

of the

Probable

Error.

.0

'1

'2

'3

-

'4

'5

   6

'7

'8

9

0

0.00

0.85

0.11

0.16

0'21

0.26

0.31

0.36

0.41

0.46

1.0

'50

   54

'58

'62

   66

'69

'72

'75

'78

80

2.0

'82

'84

'86

.88

   89

'91

   92

'93

'94

'95

3.0

'957

.964

   969

'974

'978

   982

985

987

990

992

4.0

   9930

.9943

'9954

'9963

   9970

'9976

9981

'9985

'9988

'9990

5.0

'9993

'9994

'9996

   9997

   9997

'9998

'9998

'9999

   9999

   9999

infinite

1.000

 

Tables 5 and 6 show the proportion of cases in any Normal system, in which the amount of Error lies within various extreme values, the total number of cases being reckoned as 1.0. Here no regard is paid to the sign of the Error, whether it be plus or minus, but its amount is alone considered. The unit of the scale by which the Errors are measured, differs in the two Tables. In Table 5 it is the 00 Modulus," and the result is that the Errors in one half of the cases, that is in 0'50 of them lie within the extreme value (found by interpolation) of 0.4769, while the other half exceed that value. In Table 6 the unit of the scale is 0.4769. It is derived from Table 5 by dividing all the tabular entries by that amount. Consequently one half of the cases have Errors that do not exceed 1.0 in terms of the new unit, and that unit is the Probable. Error of the System. It will be seen in Table 6 that the entry of •50 stands opposite to the argument of 1.0.

If it be desired' to transform Tables 5 and 6 into others that shall show the proportion of cases in which the plus Errors and the minus Errors respectively lie within various extreme limits, their entries would have to be halved.

Let us suppose this to have been done to Table 6, and that a new Table, which it is not necessary to print, has been thereby produced and which we will call 6cr. Next multiply all the entries in the new Table by 100 in order to make them refer to a total number of 100 cases, and call this second Table 6b. Lastly make a converse Table to 6b; one in which the arguments of 6b become the entries, and the entries of 6b become the arguments. From this the Table 7