Pk Tests In A Pre-Sleep State - Psychokinesis experiments - Statistical Data Included

ABSTRACT: In an experiment with a single participant, the author, signals from a weak vibrator were presented at random time intervals to the participant, while he was ready to fall asleep at night. A pilot test of twenty 15-minute sessions indicated that this sleepy attention to the signals produced a reduction of the signal frequency, z = 2.45, p = .014, two-tailed, and a bunching of the signals along the time axis, z = 1.63. The subsequent main experiment, comprising 40 night sessions, confirmed the signal frequency reduction, = 2.24, p = .013, one-tailed, and the bunching effect, z = 2.85, p = .0022, one-tailed. In parallel with the night sessions of the main experiment there were added 40 day sessions in which the participant, exposed to the random vibrator signals, was fully awake and attempting to visualize vivid colors. These sessions gave a smaller reduction in signal frequency, z 1.01, ns, and a slightly negative bunching effect, z = -0.71, ns.

A large number of studies have already explored the PK performance of participants in special mental states, induced by hypnosis, meditation, mental imagery, or other induction procedures (Gissurarson, 1992). A common aim of these studies was the search for ways to produce PK effects more reliably or more strongly, such as to allow for more efficient studies of the basic PK mechanism and perhaps even for PK applications. These studies may be roughly divided into two classes. In the first class, participants are unselected or selected by formal rules (e.g., by the requirement that they be artists, or have meditated for 3 years). The studies of this class aim at particularly objective results that might be replicated by other researchers. However, even if all procedures are well specified and documented, the participants' perceptions of the test situation and their emotional reactions may vary uncontrollably; also, a subtle experimenter effect may be difficult to replicate.

The second class of studies works with a few highly selected participants, sometimes even with the experimenter as the only participant, the hope being that one might get stronger effects and better understand the individual approaches that lead to PK success. The experiment reported in this article belongs to this latter class, with myself acting as the only participant. I used as targets random time intervals. Let us therefore discuss first some previous experiments with random time intervals to get a feeling for the psychological conditions that might favor a lengthening or shortening of the intervals.

PREVIOUS PK TESTS WITH RANDOM TIME INTERVALS

A Geiger counter exposed to a weak radioactive source may appear to be a good source of random time intervals. Under ideal conditions, the signals arrive randomly in time in the sense that the probability of observing a signal in a small time interval dt is proportional to dt and independent of when the previous signal has arrived. A first successful PK experiment with a Geiger counter, in which the participants tried to affect the number of counts in 1-min intervals, was reported by Chauvin and Genthon (1965). Unfortunately, it is difficult to stabilize the base counting rate of a Geiger counter, and the system may need some recovery time after each count so that the observed events are not truly independent. Therefore, Chauvin and Genthon had to alternate high-aim and low-aim runs, and they had to apply less powerful statistics than could have been used for truly random events.

Such imperfections of a Geiger counter are not critical, however, if one uses the Geiger counter (sometimes also an electronic noise source) as the heart of a digital random number generator (RNG; Schmidt, 1970). With the help of the digital RNG one can then produce random time intervals that permit an efficient statistical evaluation and can be made to approximate the distribution of signals from an ideal Geiger counter as closely as desired. The method is simple: One uses the random generator in the form of a k-sided die (with typically k = 16, or 32, or 64), which is activated at a regular rate. And, one takes each appearance of a 1 (or any other selected "target face") as a "signal" or an "event." If k is large enough, the distribution of the signals along the time axis is practically continuous and equal to the distribution of the signals from an idealized Geiger counter.

In a first experiment of this kind (Schmidt, 1973) the RNG was programmed as a 64-sided die and was activated at a rate of 12 trials/s, so that the average spacing between events was 5.3 s. During a run, the participants watched a counter that advanced with each trial and stopped when an event occurred. The participants tried to let the counter advance as many steps as possible to get a high final reading. After the counter had stopped, the next run was manually initiated. The experiment yielded highly significant results, which probably were enhanced by the experimenter's enthusiasm for the new setting.

Initial attempts to shorten the runs in this setting did not succeed. A possible explanation of why the participants could only extend the time intervals might be this: By trying to keep the counter running, the participant could feel always successful during the run. When the counter stopped, an associated element of frustration could arise only after the run, when it was too late to do any harm. When the participant wanted to stop the counter, however, frustration about the failure to stop the counter could build during the whole run and exert a PK-missing effect.

Studies with the aim of shortening time intervals have used different arrangements. In one case (Schmidt, 1976) the time intervals were generated like in the case just described, but the participants did not see a running counter that structured the time interval. Instead, they listened through headphones to a very weak click that would indicate the event at the end of a run. The volume was set so low that the participant had to focus very intensely in order to not miss the click. This intense expectation of the next click produced a PK effect in the direction of shortening the time interval, bringing in the next click earlier than expected by chance. The participants were not instructed to try to exert a PK effect but to merely listen attentively.

The idea that the apprehensive expectation of a chance event might favor the premature appearance of the event was already emphasized by an earlier experiment (Schmidt & Pantas, 1972) that ostensibly tested precognition, even though precognition and PK could not be clearly separated. The test was performed with a 4-choice precognition tester with four pushbuttons and four corresponding lights. In the more conventional tests, the participant tries to guess which lamp will light next and registers his or her guess by pushing the corresponding button. If the pressed button corresponds to the subsequently appearing light, a hit is scored. In this experiment, however, the participants tried to avoid hits; that is, they tried to press a button next to a lamp that would not light. The goal was to make many "safe" steps before a hit occurred. Each participant performed in front of a group so that he or she was kept in slightly nervous anticipation of the feared event, the next hit. In this setting the waiting interv als between hits were significantly reduced, opposite to the participant's intentions.

THE BASIC IDEA BEHIND THE PRESENT TEST'S ARRANGEMENT

In most of the experiments that have been conducted with random time intervals, the experimenter tried to motivate the participants and to bring them into a highly alert mental state, and in all cases the participants focused their attention on the randomly timed events.

It seemed interesting, however, to also study the opposite situation, in which the participant was sleepy and was mentally focused on other things, with the random events happening more at the periphery of consciousness. This situation was realized in a setting in which the participant lay in bed at his regular sleeping time, ready to fall asleep. Attached to the participant's body was a weak vibrator that was activated at random times. In the intervals between signals (which lasted an average of 15 s), the participant let himself drift closer to sleep. This process was momentarily interrupted by the next signal, but the participant immediately continued the drift toward sleep. Thus, the vibrations did not appear as a major irritant, and the participant managed to enjoy the extended experience of falling asleep rather than thinking about the next upcoming signal or the desirability of "good scores."

What makes the pre-sleep state particularly interesting for psi tests is the possible change in the participant's brainwave pattern in this state. But because no brain waves were recorded, one can only speculate in this direction. More apparent was the participant's feeling of body relaxation. Whether such relaxation per se can improve PK performance, however, depends on still-unknown factors. Work by Honorton and Barksdale (1972), who compared PK performance under muscle stress and muscle relaxation, suggests that muscle relaxation produces lower PK scores. On the other hand, work by Braud and Braud (1979) suggests that PK effects may be produced in a very relaxed state. A plausible benefit of relaxation is the reduction of performance anxiety, which can lead to PK missing (Schmidt & Pantas, 1972).

TECHNICAL PROCEDURES

In this experiment prerecorded random numbers were used to determine the target intervals. These numbers were generated by an RNG, described in Appendix A. For each session, a primary file with 960 random numbers in the range from 0 to 15 was prerecorded. Next, with the help of a random number table, a target number in the range from 0 to 15 was selected, and then the primary file was converted into a secondary file by replacing the target numbers with 1 and the nontarget numbers with 0. From these secondary files, the scores of the test runs were later extracted.

An electronic die with k = 16 faces was used because then the event distribution still appeared practically continuous for the participant. Higher values of k have a slight disadvantage in that they require a larger number of prerecorded random numbers. That is particularly relevant for future researchers who might download the random numbers from the Internet (see last paragraph in this section).

During a session, a laptop computer read the secondary file at the rate of 64 numbers/mm. For each "1", in the file the computer generated a signal by briefly activating the vibrator through the printer port. Thus, the signals appeared at an expected average rate of 4/ min, and the session lasted 15 min. The vibrator and its connection to the computer are described in detail in Appendix A. The laptop computer held a floppy disk with the prerecorded secondary file and was completely quiet during a session.

The use of prerecorded random numbers makes the procedure easily replicable even by researchers who do not have a true random generator available, because one can download the required random numbers from the Internet (http://www.fourmilab.ch/hotbits).

THE 20 PILOT SESSIONS

The main experiment was preceded by a pilot study. If this pilot study had yielded no interesting results, then there would have been no main experiment and no published report. Therefore, the results of the pilot study must be excluded when one assesses the total significance of the study; otherwise one would have a problem with selective reporting.

I first played with the setup for some nights to find a comfortable average signal rate and session duration. Also, the placement and strength of the vibrator needed attention. For this kinesthetically oriented participant it seemed, best if I could only feel, but not hear, the vibrator. This can be achieved by wrapping the vibrator in some cloth and placing it far from the head. Typical locations are the side of the body or the area of the solar plexus. Sometimes the vibrations near the solar plexus, however, were felt as too invasive, and then the vibrator's position was changed. Changes of the vibrator position during a run were quite common. The amplitude of the vibrations was intended as a compromise between not disturbing me too much and not letting me fall asleep completely. The end of a session was indicated by continuous activation of the vibrator.

After the initial adjustments I decided to complete 20 sessions for the pilot study, with the tentative hypothesis that my desire to be left undisturbed would reduce the number of signals in a session. These 20 sessions were held on 20 consecutive nights, starting on February 19, 1999. Throughout the sessions I was able to keep a uniform mental attitude, with the desire to fall asleep overriding concerns about the next possible disturbance. Only at the very end did the mounting cumulative score make me somewhat score conscious and distracted.

The total result showed a reduction of the signal frequency with z = 2.45, p = .014, two-tailed, which warranted the continuation of the experiment. It seemed advisable, however, to take a longer break so that I could disperse any stress that might have built up toward the end of the pilot tests. More details about the results of the pilot tests are provided in Figure 1 and in Table B1 (see Appendix B).

40-NIGHT SESSION AT THE CONFIRMATORY STAGE

After noting the success of the pilot study I decided to complete 40 similar sessions at the confirmatory stage and to add 40 somewhat different day sessions. The results of the night and day sessions were to be published independent of their outcomes. I further decided at this stage to use a secondary data evaluation based on a possible bunching of events along the time axis. This was based on a novel evaluation method, discussed below.

The new sessions started on April 16, 1999, about 5 weeks after the end of the pilot study. The first 20 sessions were held on consecutive days, but then a pause, due to a vacation trip, was inserted. The last 20 sessions were begun on June 22, 1999, and held again on consecutive days. The total score of the confirmatory test was z = 2.24, p = .013, one-tailed.

40 ADDITIONAL DAY SESSIONS

With the night sessions lasting only 15 mm before I fell asleep, I decided to add a slightly different test session during the day. In these sessions I sat in a comfortable chair after lunch, in a lazy state. I did not try to fall asleep but focused on a practice of mental visualization of colors while the vibrator was connected as before. The visualization did not come easy to me and required my full attention, only slightly interrupted by the vibrator. It was not difficult for me to focus my attention on the visualization task rather than on the possible interruptions or a final PK score.

On the same days on which the 40 night sessions were held there were now also held the 40 after-lunch sessions. Because I was interested in color visualization, to which I had been introduced by means of a tape by William Braud, I found these sessions generally pleasant. Only toward the end did some disappointment set in, because I felt I had made no progress in my visualization skills.

The result of these 40 day sessions showed also a reduction of the signal frequency, but the total was not statistically significant, z = 1.01.

A SECONDARY DATA EVALUATION METHOD

Observing randomly timed events, one easily gets the subjective impression that the events occur not really at random but in clusters or bunches of events. In most cases this may be a mere illusion, because one has no good intuitive feeling of what genuine randomness looks like. Nevertheless, it is conceivable that a subconscious PK mechanism amplifies this imagined clustering into a real effect. In a previous article (Schmidt, 2000) I proposed a measure to evaluate such a possible effect. Here I briefly describe this measure and then apply it to the data.

Considering a test session with M = 960 random decisions or steps, suppose that one obtained N events, at the step numbers n(1), n(2),... n(N). Then the number N determines the primary score in which we were mainly interested. To measure the possible bunching of the events n(1),... n(N) we consider the expression

Pot = [[[sigma].sup.I,J=1...N].sub.I[less than]J] [e.sup.-[absolute val. of n(I)-n(J)]/R] with R = R = M / N. (1)

Here one sums over all possible pairs of events. The contribution of a pair declines exponentially with the distance in time, with a range R equal to the average distance between events. One sees easily that Pot has a maximum if the events are all bunched together and a minimum if the events are equidistantly spaced. From the secondary files (containing a sequence of 1s and 0s, with the 1s representing events) the value of Pot can be calculated for each run. Furthermore, one can easily calculate the expectation value (Schmidt, 2000).

Pot = N(N - 1)/M(M - 1) * r/1 - r * [M - 1/1 - r]

With (2)

R = [e.sup.-N/M]. (2)

Now one can define the bunching measure, with positive values indicating increased bunching,

B = Pot - Pot. (3)

For a statistical evaluation one still needs the variance of B. The exact equation for the variance, given in a recent article of mine (Schmidt, 2000), simplifies for large values of N and M to

[[sigma].sup.2] = [r.sup.2]/1 - [r.sup.2] * N/M * [(1 - N/M).sup.2] * N. (4)

For the calculation of the z values z(B) derived from the bunching measure, the exact equation for the variance was used, but the use of Equation 4 would have made only a very slight difference.

RESULTS

Figure 1 shows the increase of the cumulative score over the 20 sessions of the pilot study, the 40 sessions for the night tests of the confirmation, and the 40 sessions of the day tests. Here the score of a session is defined as the reduction of the number of events below its expectation value of 60.

The total z values for the three categories are listed in Table 1. The values z(N) were derived from the total numbers of observed events, with positive z values indicating a reduction of the signal frequency. Statistically independent of the z (N) are the z values derived from the bunching measures. To obtain the total z(B) values, first the z values for the sessions were calculated and then the sum of the z values was divided by the square root of the number of sessions. With positive values of z(B) indicating a positive bunching, one sees that there was highly significant bunching in the confirmatory night sessions. Comparing the 40 confirmatory night sessions with the 40 day sessions, one sees that the difference in the main scores (first column in Table 1) is not significant, with a z(diff) = (2.24- 1.01)/SQR(2) = 0.87. The difference in the bunching measures (second column in Table 1) gives a more significant z(diff) = (2.85 + 0.71) /SQR(2) = 2.52, with an associated probability of p= .012.

It also seemed interesting to check if the scoring varied during the course of the sessions. Was there a decline effect, or did I perhaps need some time to get settled down? The last four columns of Table 1 list the score deviations (reduction of events below the chance level) for the four quarters of the sessions. The low values of DN1 in the night sessions suggest that indeed I did need some time (about 4 mm) to adjust to the situation.

Further details about the outcomes of the individual sessions are provided in Appendix C.

CONCLUDING DISCUSSION

In this study I have explored the question of whether PK effects could be efficiently obtained in a pre-sleep state. For a participant such as myself, who falls asleep easily, this state felt different from mere relaxation. In addition, there was the pleasant feeling of drifting actively deeper and deeper into true sleep. The randomly timed signals did interrupt the process of falling asleep, but I did not mind these interruptions too much, because they also acted as a means to extend the pleasant pre-sleep state. In trying to replicate this study one should select participants who report similarly pleasant feelings about the test arrangement.

The relative ease with which the experiment can be set up is attractive. One needs only a laptop computer and a few electronic parts to connect to the computer's printer port. The use of prerecorded random numbers obviates the need for a true random generator, because the required random numbers can be obtained from the Internet.

This kind of test could be easily converted into a home test in which the participant uses his or her own laptop computer with the inexpensive additional equipment supplied by the experimenter and, with the random numbers prestored on a floppy disk, the setting is completely safe against potential cheating attempts by the participant.

For the purpose of a replication one might explore a small addition to prevent the participant from falling asleep completely. Although this was not a problem for me, other participants might simply ignore the weak signals and soundly sleep during part of the session. To prevent this, one might let the participant hold a pushbutton switch that requires only very slight pressure to operate, connected to the computer. Then one would make arrangements such that each vibration signal continues until the participant presses the switch. Then the extended signal would most likely waken a sleeping participant and, if the participant has fallen asleep too deeply, at least the computer could register the absence of a response.

The positive PK effects observed might result from a combination of factors, such as an altered brain state in the pre-sleep period, the relaxation of the body, the absence of performance anxiety, and the general feeling of pleasure associated with a pre-sleep session.

The pre-sleep sessions were grouped into a pilot study of 20 sessions and a confirmatory study of 40 sessions. An additional exploratory group of 40 day sessions, during which the participant practiced color visualization, was added as an afterthought. Although the scoring difference between day tests and pre-sleep tests in the end was not statistically significant (see Figure 1), the higher evidence for PK in the pre-sleep tests (pilot and confirmation) suggests that pursuing the pre-sleep test in the future might be most rewarding.

Drawing firm conclusions, apart from the existence of a psi effect, is notoriously difficult in psi experiments, because the conscious or subconscious wishes and expectations of the experimenter may have an overriding effect. Thus the finding that the results of the pre-sleep state were slightly better than the results from the day tests may simply reflect my preference for the pre-sleep tests. Similar doubts can be raised about the previous experiments with altered mental states (Gissurarson, 1992). Therefore one cannot know whether, say, a meditative state per se improved psi performance, or whether the higher expectation of the participant or the experimenter improved performance.

In view of a possible experimenter effect the observed significant bunching effect also should be viewed with caution. Because I had just developed the new bunching measure I was certainly most motivated to find an effect. It may well be that the tendency of a participant to perceive randomly spaced events in clusters may direct the subconscious PK effort toward producing statistically significant clustering. However, we have to wait for the outcome of other tests with other experimenters whose participants are unaware that a clustering will be later evaluated.

REFERENCES

BRAUD, L. W., & BRAUD, W. G. (1979). Psychokinetic effects upon a random event generator under conditions of limited feedback to volunteers and experimenters. Journal of the Society for Psychical Research, 50, 21-32.

CHAUVIN, R, & GENTHON,J. (1965). Eine Untersuchung Uber die Moglichkeit psychokinetischer Experimente mit Uranium und Geigerzahler. (On the possibility of psychokinetic experiments with Uranium and a Geiger counter.) Zeitschrift fur Parapsychologie und Grenzgebiete der Psychologie, 8, 140-147.

GISSURARSON, L. R. (1992). Methods of enhancing PK task performance. In S. Krippner (Ed.), Advances in parapsychological research 5 (pp. 89-125). Jefferson, NC: McFarland.

HONORTON, C., & BARKSDALE, W. (1972). PK performance with waking suggestions for muscle tension versus relaxation. Journal of the American Society for Psychical Research, 66, 208-214.

SCHMIDT, H. (1970). Quantum mechanical random number generator. Journal of Applied Physics, 41, 462-468.

SCHMIDT, H. (1973). PK effect on random time intervals [Abstract]. Research in parapsychology 1973 (pp. 46-48). Metuchen, NJ: Scarecrow Press.

SCHMIDT, H. (1976). PK effect on pre-recorded targets. Journal of the American Society for Psychical Research, 70, 267-291.

SCHMIDT, H. (1991). Search for a correlation between PK performance and heart rate. Journal of the American Society for Psychical Research, 85, 101-117.

SCHMIDT, H. (2000). A proposed measure for psi-induced bunching of randomly timed events. Journal of Parapsychology, 64, 301-316.

SCHMIDT, H., & PANTAS, L. (1972). Psi tests with internally different machines. Journal of Parapsychology, 36, 222-232.

                               MAIN RESULTS
Experiment                       z(N)  z(B)  DN DN1 DN2 DN3 DN4
Pilot test (20 night sessions)   2.45  1.63  81   0  29  42  10
Night confirmation (40 sessions) 2.24  2.85 106 -32  74  41  23
Day test (40 sessions)           1.01 -0.71  48  27 -14  28   7
Note: z(N) = the z values derived from the total number N
of events; z(B) = the z values derived from the bunching
measures B; DN = the deviatoin of N from chance in the
expected direction; DN1,..., DN4 = the contributions to
DN from the four quarters of the sessions.

APPENDIX A

DRIVING THE VIBRATOR MOTOR FROM THE COMPUTER'S PRINTER PORT

A standard printer port with its 25-pin output jack may be used to drive the vibrating motor with the help of a single transistor. Figure A1 shows the wiring. The Darlington transistor (2N 6725, bought from JAMEGO Electronics - www.jameco.com) needs only a small driving current from the printer port. The 1 k resistor protects against overload. The vibrating motor can be built from a small regular 3-volt motor by gluing a small piece of lead onto one side of its drive shaft. A ready-made vibrating motor, used in pagers, can be obtained from JAMEGO (Part No. 163539 or 169421). In order to approach the conditions of the reported experiment, however, one should check that the vibrator makes not too much audible noise, so that the participant feels, rather than hears, the signal. The value of the resistor R may have to be adjusted for the particular motor.

If the computer's printer port is located, as seems most common, at H378 = 888 (decimal), then in QuickBasic the instructions for turning the motor on and off are OUT 888,1 and OUT 888,0 respectively. The printer location may be displayed during the startup routine of the computer.

APPENDIX B

RANDOM GENERATOR AND RANDOMNESS TESTS

The random number generator to produce the prerecorded data was identical to those used in many previous experiments. Radioactive decays are its basic source of randomness. A detailed description, including a circuit diagram, can be found in Schmidt (1991).

Like in previous work, one final random number was obtained by combining two consecutively generated initial random numbers and one quasi-random number by means of the XOR operation. The lowest four bits of the final random number were used as output of the 16-sided die. In addition to these precautions, the following randomness check was specifically tailored to the situation in which the random generator was to be used.

The experiments were structured into blocks of M = 960 random numbers (0, ..., 15) with one randomly selected number (0, ..., 15) specified as the target. For the randomness check the computer generated a total of 20,000 such blocks. For each block the locations of the targets, among the M possible slots, were determined as n(1), n(2), ... n(N).

With the help of Equations 1-3 each block provided two numbers: the score deviation DN = N - 60 and the bunching measure B. Adding the values DN, B, DN x DN, and B x B over all blocks, the average values per run could be obtained and compared with the theoretical values; the results are shown in Table BI.

For calculating the theoretical value for the last line of the table one has to remember that the exact equation for the variance, like the approximation given by Equation 4, provides the variance for B for a specified value N of events. To obtain the theoretical value for Aver (B x B), one therefore has to sum over all possible N values with their known probabilities.

The good agreement between the theoretical values and the ones observed in the 20,000 blocks of the computer simulation can confirm our confidence in the random number generator, with an accuracy much higher than required for the experiments.

                      RESULTS OF THE RANDOMNESS TESTS
               Observed value Theoretical value
Aver (DN)          0.048              0
Aver (DN x DN)     56.20            56.25
Aver (B)          -0.022              0
Aver (B x B)       23.52            23.44
Note: Aver = average

RESULTS FROM THE INDIVIDUAL SESSIONS

The tables in this appendix list for each session: (I) the session number, (II) the number N of events, (III) the corresponding z value z(N,) (IV) the bunching measure B, and (V) the corresponding z value z(B).

                    RESULTS FROM THE 20 PILOT SESSIONS
    I     II   III    IV     V
Session #  N  z(N)     B  z(B)
    1     51  1.20  4.27  0.95
    2     56  0.53 -0.78 -0.17
    3     60  0.00  0.27  0.06
    4     61 -0.13  0.87  0.18
    5     56  0.53 -0.05 -0.01
    6     52  1.07 -3.39 -0.74
    7     60  0.00 -0.35 -0.07
    8     48  1.60  1.30  0.30
    9     45  2.00  1.24  0.29
   10     66 -0.80  8.16  1.62
   11     62 -0.27  4.71  0.96
   12     62 -0.27 -2.15 -0.44
   13     54  0.80  5.50  1.19
   14     72 -1.60  0.32  0.06
   15     56  0.53 11.94  2.54
   16     36  3.20 -0.50 -0.13
   17     52  1.07  0.87  0.19
   18     57  0.40 -1.37 -0.29
   19     54  0.80  0.98  0.21
   20     59  0.13  2.84  0.59
        RESULTS FROM THE CONFIRMATORY NIGHT TESTS AND THE DAY TESTS
Night Tests                      Day Tests
     I      II   III    IV     V     I     II   III    IV     V
             N  z(N)     B  z(B)            N  z(N)     B  Z(B)
     1      56  0.53  4.21  0.90     1     66 -0.80 -1.80 -0.36
     2      70 -1.33 10.03  1.94     2     63 -0.40 -6.21 -1.25
     3      51  1.20 10.11  2.24     3     48  1.60 -0.07 -0.02
     4      50  1.33  2.16  0.48     4     56  0.53 -0.32 -0.07
     5      59  0.13 -4.40 -0.91     5     60  0.00 -2.68 -0.55
     6      58  0.27  1.54  0.32     6     60  0.00  7.45  1.54
     7      51  1.20 -2.81 -0.62     7     55  0.67 -3.94 -0.85
     8      64 -0.53 -4.75 -0.95     8     57  0.40  2.91  0.61
     9      49  1.47  0.15  0.03     9     60  0.00 -5.67 -1.17
    10      57  0.40 -7.10 -1.50    10     62 -0.27 -3.93 -0.80
    11      69 -1.20  1.62  0.31    11     58  0.27  3.18  0.67
    12      60  0.00  9.89  2.04    12     49  1.47  0.96  0.22
    13      58  0.27 -2.91 -0.61    13     62 -0.27  0.90  0.18
    14      48  1.60  2.19  0.50    14     56  0.53  4.54 -0.97
    15      62 -0.27  3.22  0.65    15     53  0.93  1.11  0.24
    16      56  0.53  5.93  1.26    16     59  0.13 -3.63 -0.75
    17      66 -0.80  0.95  0.19    17     66 -0.80 -5.08 -1.01
    18      63 -0.40 -2.36 -0.48    18     57  0.40 -5.61 -1.18
    19      55  0.67  0.92  0.20    19     62 -0.27 -0.35 -0.07
    20      55  0.67 -5.58 -1.20    20     52  1.07 -3.50 -0.77
    21      52  1.07 11.24  2.47    21     64 -0.53 -4.95 -0.99
    22      53  0.93  7.65  1.67    22     55  0.67  0.92  0.20
    23      47  1.73 -1.01 -0.23    23     65 -0.67 -8.99 -1.79
    24      55  0.67  7.34  1.57    24     72 -1.60  2.32  0.44
    25      71 -1.47  9.23  1.77    25     63 -0.40  3.06  0.62
    26      54  0.80 -6.77 -1.46    26     61 -0.13  0.32  0.07
    27      33  3.60  4.82  1.32    27     52  1.07 -0.84 -0.18
    28      59  0.13  2.02  0.42    28     46  1.87  1.05  0.24
    29      57  0.40 -2.10 -0.44    29     66 -0.80 -2.60 -0.52
    30      59  0.13  1.21  0.25    30     61 -0.13 -8.34 -1.71
    31      70 -1.33  7.66  1.48    31     49  1.47  9.94  2.24
    32      64 -0.53 -2.35 -0.47    32     62 -0.27 10.97  2.23
    33      61 -0.13  4.90  1.00    33     63 -0.40 -1.98 -0.40
    34      72 -1.60  5.61  1.07    34     56  0.53  1.36  0.29
    35      51  1.20  3.54  0.78    35     52  1.07  3.79  0.83
    36      61 -0.13  0.64  0.13    36     59  0.13  4.13  0.86
    37      53  0.93 14.22  3.10    37     70 -1.33 -5.88 -1.14
    38      64 -0.53 -5.80 -1.16    38     58  0.27  3.20  0.67
    39      47  1.73  1.43  0.33    39     58  0.27 -2.41 -0.50
    40      54  0.80 -1.80 -0.39    40     59  0.13  2.06  0.43

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COPYRIGHT 2001 Gale Group