*J. Atmos. Terr. Phys., 57*, 537-556, 1995

(Received in final form 19 May 1994; accepted 27 June 1994)

Copyright © 1995, Elsevier Science Ltd

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*Grebowsky et al.* [1991] did compare their rate of coincidence with that
expected from the burst rate studies of *Ho et al.* [1991]. However the burst rate
studies used a fixed threshold of
2 10
V/m/Hz,
while Grebowsky et al.
counted signals as low as a factor of 2 above background as being bursts. For
reference, the background of the 100 Hz channel is variable, but typically is
around
10
V/m/Hz.
Thus it is difficult to compare the coincidence rate as
reported by *Grebowsky et al.* [1991] with that expected for random coincidence.
Furthermore, Grebowsky et al. did not compare the coincidence rate for
anomalous scans with the rate found for normal scans, again making a comparison
with random coincidence difficult.

Here, we will take a statistical approach to determine if the apparent
association of Langmuir probe anomalies is more than simply random
coincidence. We have used the Langmuir probe anomaly data (J. M. Grebowsky,
personal communication, 1992) for the first three nightside periapsis seasons as a
basis for this determination. As a first step we use the burst counting method of
*Ho et al.* [1991] to calculate the probability that one or more bursts exceeding the
2 10
V/m/Hz
threshold will occur in any 2-s interval. We have chosen this
length of interval since the Langmuir probe anomaly timing is given to the nearest
second. Using that probability we can then compare the coincidence rate for
bursts and Langmuir probe anomalies with that expected through random
coincidence.

The first row of
Table 1
shows the results of this calculation for all the
data acquired within 0.9
*R*
of the Venus-Sun line, and altitudes < 300 km in the
nightside ionosphere. The table shows that 20% of the Langmuir probe anomalies
have one or more 100 Hz bursts occurring within a 2-s interval including the
Langmuir probe sweep. Since the probability that one or more bursts will occur in
any 2-s interval is
7%, the observed degree of coincidence lies in the upper
0.1% of the tail of the Binomial distribution for 150 samples with a 7% event
probability, under the assumption of independent events. Another way of
assessing the significance of the observed degree of coincidence is to note that for
a binomial distribution with event probability of 7%, the mean number of events
is 10 for 150 samples, while the variance is also 10. The standard deviation is
therefore
3, and the observed number of coincident events is at least 6 standard
deviations away from the mean. Thus the 20% coincidence is statistically
significant, but it is much less than that reported by *Grebowsky et al.* [1991].

Table 1. Comparison of burst probability and the coincidence rate for Langmuir probe (OETP) anomalies. The binomial probability gives the probability that the number of coincident events >m, forNLangmuir probe anomalies (corresponding to a one-tail test).

In previous sections, we have emphasized that the 100 Hz waves correspond with vertically propagating whistler-mode waves. In computing the burst probability, however, we have assumed that the bursts occur independently of the underlying ionospheric conditions. In the lower two rows of Table 1 we have tested each interval for whether or not vertical whistler-mode propagation is allowed. The table shows that the probability of a burst occurring in an interval in which vertical propagation is allowed is 9%, somewhat higher than for all intervals, while the degree of coincidence has dropped slightly, 18%. Thus, the coincidence rate lies in the upper 1% of the Binomial distribution for 90 samples with 9% event probability. This again suggests that the coincidence is not random, but is much less than one would expect for a direct causal relation between Langmuir probe anomalies and 100 Hz bursts. For completeness, Table 1 also includes the "non-whistler" intervals.

One interesting feature in the table is that regardless of the selection
criteria, the coincidence rate is roughly constant. This suggests that the
coincidence occurs because of some underlying property of the ionosphere that is
common to both signatures. In the previous section we have shown that low
is
required for whistler-mode propagation. *Huba* [1992] suggested that the Langmuir
probe anomalies may be signatures of the lower hybrid drift instability, and he has
shown that low
also applies to the lower hybrid drift instability. However, in
Table 1
we have included all intervals, irrespective of
.
This will reduce the
predicted probability for 100 Hz bursts. In
Table 2
we show the burst probability
for those intervals for which
< 1. In order to determine
we need to know the
electron density and temperature. We have used Langmuir probe data from the
Unified Abstract Data System (UADS) for this purpose. We have interpolated the
data to the 2-s resolution used earlier. UADS data are not available for all the
intervals, and we have included the probabilities for all intervals for which we
have UADS data, and those intervals for which
< 1.

Table 2. Comparison of burst probability and the coincidence rate for Langmuir probe (OETP) anomalies, using those intervals for which Langmuir probe UADS data are available.

Table 2
shows that the coincidence rate is similar to
Table 1
for all the
intervals, although the probability of random coincidence is higher, because of the
smaller sample. The bottom row of
Table 2
shows that the burst probability is
quite high,
13%, for
< 1, while the coincidence rate is
19%. For the number
of samples, this rate lies in the upper 13% of the Binomial distribution. This is a
"one-tailed" test, while it is usual to use a "two-tailed" test when testing against
random coincidence. For this purpose one can roughly double the percentage, and
there is a less than 75% probability that the observed coincidence is not random.
When testing for a non-random association of events it is usual to require at least
a 95% probability before the null hypothesis of random coincidence is rejected
[e.g., *Pollard*, 1977].

Given the relatively low likelihood of non-random coincidence, and the generally low degree of correlation (< 20%), we conclude that the Langmuir probe anomalies do not explain the 100 Hz bursts. Rather, both 100 Hz bursts and Langmuir probe anomalies tend to occur in regions of low .

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