2:21. The first example is taken from an earlier work on the relationship 
between film distortion and relative humidity (2). It illustrates the importance of 
standardizing the sampling technique. 
The experimenter recorded among other things the differential shrinkage of 
the two samples of the same thing film under two different humidity conditions, 
as percentage of the dimension (Table 1). 
  
  
Table 1 
Crosswise 14 17 20 34. 42.318 04 .16 
509/o Lengthwise 09. 15: 44 .27. 27 41 22 .10 
Difference +05 +-0.2 +.06+.07 +.15+.05 +.02 +.06 
Crosswise 14 13 14 20 18 190 19 .12 
65% Lengthwise 44 11 43 18 472 425.13. 08 
| Difference +.00+.02 +.01 +.02 +.01 ~.02 +.01 +.04 
  
  
The averages were .060 and .011 per cent respectively. It seems at first sight 
that treatment at 65 per cent relative humidity is superior to treatment at 50 per 
cent. We should however take into consideration the variability within the two 
samples. Assuming for the time being that the variability does not differ from 
one condition of relative humidity to the other, the variance of the difference 
between the two means and the corresponding ¢ value can be computed as follows: 
1 3 po 1 ^, —/ 1 i > 
Pa HE SE] = 7; [S116 + 001] — 00095, 
0488 (xS m 
03130 \ 16 | ms 
with 14 degrees of freedom. The difference is therefore significant on the 1 per 
cent level where t = 2.977. The test therefore reassures that the treatment at 65 
per cent relative humidity is superior to treatment at 50 per cent. There is however 
the possibility that this value of ¢ has been inflated by the apparent difference 
between the scatter of the two samples. But we must first establish the significance 
: : .0016 | .0021 : 
of this difference. Fisher's F-test is the tool. F — uu 5.56, which 
differs from unity significantly on the 1 per cent level. We cannot therefore assume 
equality of the sampling errors. It now remains to find out whether the difference 
between the two means could have arisen entirely from the demonstrated differ- 
ence of the variances. The issue can be readily settled by means of Sukhatme test. 
tn 0 = 4/57 (5.56^ — 236...0 — 67° 
.0116 .0021 
(Eu) = ( A a + oe) 2 = 01736 
d = .0488/ .01736 = 2.81 
The degrees of freedom are 7 and 7. The difference between the sample 
averages is still significant on the 5 percent level®). 
and t = 
  
*) Seen from a somewhat different point of view, the examples given above demonstrate the 
tolerance of the statistical approach to small deviations from the assumptions underlying the 
tests. We have seen that the levels of significance underwent certain changes, but these were 
not drastic. 
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