Jökull - 01.12.1994, Page 53

KOLMOGOROV-SMIRNOV ONE SAMPLE TEST
USING STANDARD NORMAL DISTRIBUTION
Variable Maximum Lilliefors
dilference probability
R1156 0.110 0.000
L1156 0.069 0.063
C1156 0.118 0.000
R1157 0.175 0.000
L1157 0.097 0.001
C1157 0.125 0.000
R1161 0.132 0.000
L1161 0.088 0.004
Cll6l 0.096 0.001
R1162 0.103 0.000
L1162 0.073 0.036
C1162 0.066 0.084
R1200 0.143 0.000
L1200 0.078 0.018
C1200 0.116 0.000
R1203 0.114 0.000
L1203 0.094 0.001
C1203 0.103 0.000
R1204 0.112 0.000
L1204 0.095 0.001
C1204 0.105 0.000
R1207 0.094 0.001
L1207 0.095 0.001
C1207 0.067 0.077
R1267 0.065 0.100
L1267 0.085 0.007
C1267 0.028 1.000
R1270 0.113 0.000
L1270 0.096 0.001
C1270 0.082 0.010
R1277 0.138 0.000
L1277 0.072 0.043
C1277 0.079 0.017
R1287 0.092 0.002
L1287 0.060 0.157
C1287 0.064 0.108
R1418 0.222 0.000
L1418 0.078 0.018
C1418 0.155 0.000
R1420 0.080 0.015
L1420 0.066 0.087
C1420 0.095 0.001
R1422 0.196 0.000
L1422 0.057 0.208
C1422 0.133 0.000
Table 4. Kolmogorov-Smirnov one-sample test of the nor-
mality test for each parameter (prefixes R, L, C before sam-
ple numbers refer to ruggedness, elongation, and circularity)
in all samples. The 2-tailed Lilliefors probability values
show the probability of each sample being derived from a
normally distributed population. Values below 0.05 differ
from normal at the 95% level of significance.
4. tafla. Kolmogorov-Smirnov prófun á normaldreifingu
hvers lögunarþáttar í öllum sýnum. EfLilliefors líkindagildi
eru lœgri en 0,05 eru marktœkfrávikfrá normaldreifingu við
95 % öryggismörk.
these tests depend on the assumption that the variable
has a normal distribution. Other, non-parametric tests
are available for comparing samples from non-normal
distributions. The grain shape parameters were there-
fore tested for normality before selecting appropriate
procedures. Table IV shows the results of a normality
test for the three parameters and all samples. Lilliefors
probability (2-tail) was calculated in a Kolmogorov-
Smimov one sample test using standard normal distri-
bution (Wilkinson, 1989). 80 % of the samples and all
the parameters differ significantly from normal distri-
bution (probability values < 0.05). It was therefore
necessary to adopt non-parametric (distribution-free)
tests for comparing mean values for the grain shape
parameters.
Tables 5-7 show the results of a Kolmogorov-
Smimov two-sample test which measures the discrep-
ancy between two sample cumulative distribution
functions. The test assumes that compared samples
came from exactly the same distribution. The results
indicate that there is a statistically significant differ-
ence between mean values of shape parameters mea-
sured in samples from magmatic and hydrovolcanic
emptions.
A visual appraisal of the morphometric parameters
may be obtained by studying SEM images. Grains
from tephra layers belonging to the Reykjanes vol-
canic system display moderate vesiculation and out-
lines that indicate breakage (Fig. 4). The grains are an-
gular but straight edge segments are characteristic.
The morphology of these grains contrasts sharply with
grains generated in strombolian eruptions such as
these displayed in Figs. 5 (sample 1540) and 6 (sam-
ples 1267 and 1287), where vesiculation is much more
pronounced, and the outlines are affected by gas ex-
pansion. Smooth, bubbly surfaces are sometimes pre-
served, but in many cases individual grains carry signs
of breakage with jagged outlines reflecting the intense
vesiculation.
CONCLUSIONS
The results of image analysis of the Reykjanes
tephra and a comparison with several other Icelandic
tephra units show conclusively that there is a signifi-
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