Appendix E
Statistical Tables
I. ONE SIDED az VALUES FOR A NORMAL DISTRIBUTION
One sided ei values, such as class ’A’ and ’B’ structural materials stress limits
are often used for designing. In Fig. E.1 the K¢ values for n-1 degrees of
freedom are plotted so that the K,- value may be estimated. The values
are substituted into the following equation
o~i=~(--KiS
i= A,B,C
(E.1)
where
~( is the Gaussian mean of the data set with n values.
S is the standard deviation of the same data set.
KA values will exceed ~ 99% of the time with 95% confidence.
K~ values will exceed ~ 90% of the time with 95% confidence.
Kc values will exceed ~ 99.999% of the time with 95% confidence.
When more accurate values are not available from Fig. E. 1 the following
equations may be used to compute K factors in lieu of using table values:
[1.18]
KA = 2.236 + exp[1.34 -- 0.522 ln(n) + 3.87/n]
(E.2)
Ke = 1.282 + exp[0.958 - 0.520 In(n) + 3.9/n].
(E.3)
These approximations are accurate to within 0.2% of the table values for n
greater than or equal to 16.
Values for n from 2 to 5 are shown in Table E. 1.
II. STUDENTS t DISTRIBUTION AND Z 2 DISTRIBUTIONS
The following Tables E.2 and E.3 have been reprinted with the permission of
Addison Wesley Longman Ltd.
259