WMOD00440

• Title: HIPLEX-1: Statistical Evaluation
• Date: 4/4/1984
• Weather Modification - Doc Type: Report

1\PRIL 1984

MIELKE ET AL.

519

I

hand, the individual response variable raw values were
made commensurate with one another by rescaling
from 0 to 1, i.e., dividing the difference between an
individual observed value and the minimum value by
the difference between the maximum and minimum
values.
The MRPP P-values based on raw and rank order
response variable values are presented separately for
Class A-I clouds, Class B clouds, and pooled A-I and
B clouds. Such pooling was not discussed in the HI-
PLEX-l design, but has been effected for exploratory
analysis mainly because of the small sample sizes
available.
Exact P-values are presented for the A-I clouds (M
= 35) and B clouds (M = 1287), whereas approximate
P-values are presented for the pooled A-I and B clouds
(M = 125970). The smallest possible P-value for a
category is l/M; in particular, for Class A-I clouds (M
= 35), the smallest possible P-value is 1/35 = 0.029.
[If Case 16 is deleted because of the selection error
discussed in Section 6 of Smith et al. (1984), then the
remaining sample of four seeded and two nonseeded
Class A-I clouds would have yielded M = 15 with the
smallest possible P-value being 1/15 = 0.067.] The
MRPP are analogous to two-sided tests: thus a P-value
of 1.0 indicates no separation of the response variables
for the experimental units of the two groups in r-space,
while a small P-value suggests a separation between
the two groups.
The only primary response variables indicating con-
sistent differences (larger ~alues for seeded cases) are
CIC2, CIC5, and CCR5. These are the three response
variables associated with the development of ice crystals
in the clouds during the first 5-min interval following
treatment (i.e., a "placebo" or a dry ice seeding). Even
for CCR5 in the A-I clouds (for which the physical
hypothesis was developed) the seeding "signature" is
not strong. The reason that the rank tests for the first
5-min period responses yielded stronger results than
the tests based on raw data is that the contributions

i

it

of a few large raw data measurements (in response
variables which apparently have long-tail distributions)
are subdued. A strong indication of accelerated for-
mation of precipitation, du(: to seeding, also appears
in the TFPI for the Class A-I clouds (P-value is 0.029).
There are a few other instances suggesting possible
effects, for example PIC8 for Class A-I clouds or AER
for Class B clouds, but the P-values are not small
enough to be regarded as significant (a possible con-
sequence of the small sample sizes). However, in all
cases except A WC8 (where the values were very small),
the directions (despite the small sample sizes) are con-
sistent with those suggested by the HIPLEX-l physical
hypotheses.
Table 7 and Figs. 3 and 4 present progressive mul-
tivariate comparisons of non seeded and seeded ex-
perimental units for the HIPLEX-l primary response
variables; the order in which the response variables
are added corresponds to the chain of events described
by the physical hypothesis. Thus, each successive P-
value in a column of Table 7 is a measure of the
separation of the two subgroups (nonseeded and
seeded) in an r-space where r equals the number of
response variables included up to that point. Figure 5
illustrates the "perfect" separation (P-value is 0.029)
of the Class A-I nonseeded and seeded subgroups in
the ranked data 3-space (CIC2, CIC5, CCR5). The P-
values in the bottom row provide an evaluation of the
degree to which seeded clouds of a particular class are
distinct from nonseeded clouds in a 12-dimensional
space representing all 12 of the response variables.
Thus, the Class B seeded clouds may be said to differ
from the Class B nonseeded clouds, considering rank-
ordered response variables, With a P-value of 0.170.
The univariate values presented in Table 6 help show
which response variables are responsible for most of
the difference. The multivariate sequence in Table 7
helps show how far down the chain of events in the
physical hypothesis marked differences can be traced.
The P-values of Table 7 become substantially larger

TABLE 7. Summary of multivariate MRPP P-values for HIPLEX-I primary response variables.
Class A-I clouds Class B clouds Class A-I and B clouds
t3 NS, 4 S) (5 NS, 8 S) (8 NS, 12 S)
Variables
CIC2 thru: Raw data Ranks Raw data Ranks Raw data Ranks
CIC2 0.057 0.029 0.0396 0.0109 0.00939 0.00034
CIC5 0.057 0.029 0.0365 0.0124 0.0118 0.00 123
CCR5 0.057 0.029 0.0295 0.0225 0.0108 0.00174
PIC8 0.057 0.029 0.0365 0.0412 0.00553 0.00306
MVD8 0.371 0.057 0.0412 0.0319 0.0201 0.00483
AWC8 0.257 0.086 0.162 0.0427 0.0930 0.00810
TFPI 0.114 0.029 0.353 0.0793 0.0678 0.00820
TFE 0.114 0.029 0.439 0.103 0.112 0.0104
TIPA 0.171 0.029 0.549 0.121 0.145 0.0126
TIPR 0.17'1 0.029 0.637 0.143 0.161 0.0141
AER 0.171 0.029 0.594 0.148 0.168 0.0198
RERC 0.171 0.029 0.607 0.170 0.169 0.0221