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Fig. 2.6 Graphical normality test for 76 biotite ages from Grenville Province, Canadian Shield
(After Agterberg
1974
). Observed cumulative frequencies (
solid dots
) are not all contained within
95-% confidence belt on the theoretical normal curve (plotting as
straight line
on this
Q
-
Q
plot),
indicating some departure from normality that is strongest in the upper tail (Source: Agterberg
1974
, Fig. 24)
refinement consists of plotting the data against so-called plotting percentages by
using the equation:
3
cumulative frequency
1
Plotting percentage
¼
ð
3
n
þ
1
Þ=
100
where
n
represents number of data (Tukey
1962
; Koch and Link
1971
). In most
practical applications, the preceding refinement is not used and cumulative
frequencies are used for plotting percentages. This is because the improvement
gained by the refinement generally is very small.
Secondly, a straight line was plotted for the normal biotite distribution. This line
passes through two points with (1) the mean (
954.5 Ma) with cumulative fre-
quency of 50 %, and (2) the point with abscissa equal to the mean (
¼
¼
954.5 Ma)
minus one standard deviation (
¼
91.3 Ma), and value of 15.9 % along the proba-
bility scale.
Thirdly, an approximate 95 % confidence belt was constructed as previously
used by Hald (
1952
) and Vistelius (
1960
). If
z
t
represents the standardized value for
a point on the straight line for the theoretical normal distribution and
z
an observed
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