Bauhaus-Universität Weimar

Experimental Psychology: A Manual of Laboratory Practice, Vol. II: Quantitative Experiments, part 1: Student's Manual
Titchener, Edward B.
§ 15- The Law of Error 
From these values, you will be required to 
calculate h, the measure of precision, and the corresponding DL. 
It is essential, then, that you understand what t really is.1 
The value hx is, of course, the product of the measure of pre¬ 
cision into a determinate magnitude of error. This product is 
identical with the ratio x: that is, it is ur measured in terms 
of L . Now L is called, technically, the ‘modulus’ of the curve 
of error : a ‘ modulus ’ being, in general, any constant coefficient 
or multiplier whereby a given series or system of quantities may 
be reduced to another similar series or system. When, there¬ 
fore, you are looking up a value of t in the Table, you are asking 
how many times (whole or fractional) the given error x contains 
the modulus. If t = i, the error is equal to the modulus; if t 
= 1.5, the error is half as great again as the modulus ; if t = 
0.5, the error is half the modulus. In all cases, the modulus is 
the unit to which you are referring. 
To make the idea of the modulus still more concrete, let us 
call to mind the fact that it is =2.1 PEX. In looking up t, then, 
you are also asking how many times the given ;r contains (ap¬ 
proximately) twice the probable error. 
(3) Our last point is of a psychological nature. It is tempt¬ 
ing to regard the phrase ‘ degree of probability ’ as equivalent to 
‘degree of expectation’ or ‘amount of belief.’ We give expres¬ 
sion, in daily life, to various degrees of expectation : we say that 
an event is ‘ practically certain,’ ‘ very probable,’ ‘ not unlikely,’ 
‘ as likely as not,’ ‘ hardly possible,’ ‘ almost beyond belief.’ Do 
these judgments correspond to certain numerical fractions, rep¬ 
resenting degrees of objective or mathematical probability ? Is 
the mathematical scale of probabilities simply a more finely 
graded scale of subjective degrees of expectation ? 
1 The following Table illustrates the facts that the integral (which we will term 7) 
varies between the limits o and i, and that it rapidly approaches 
t increases : 
the latter limit 
0.75 0.711 
1.00 .843 
1.25 .923 


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