Analyse de schémas

Cette étude a été conçue dans le but de faire d'une telle analyse le point de focalisation de son travail. Contingency tables were constructed for these characteristics: UFO sound, size, and colors; type of EM effect; physiological effect; presence of a light beam; and type of UFO. Chi-square tests were then run on each table to test the null hypothesis that the two particular characteristics were independent. Due to low expected frequencies in some cells, it was impossible to use the chi-square statistic in every test. Saunder's Remarkability statistic was substituted in those cases.

Before tables were constructed, a decision was made that, for the null hypothesis to be rejected, the chi-square value should fall within the .02 confidence or significance level. The corresponding R value is about 6, though that depends on the number of degrees of freedom. This level of significance is more rigorous than that chosen by other investigators; it is in fact a compromise between the .01 and .05 levels. Since over 250 contingency tables were tested in this section, a .05 confidence level implies that there will be a possibility of finding about twelve spurious correlations. In order to reduce such Type 1 error, the .05 level was therefore considered not rigorous enough. Conversely, due to the uncertainties in witness reporting of UFO events, the .01 confidence level was believed too rigorous for the purposes of this study, which seeks to locate any possible relationships between event characteristics. The .02 confidence level was then chosen to minimize Type 1 error but still allow for a significant possibility to discover actual correlations. Even at this level, five spurious correlations might be expected.

The above considerations also played a role when choosing R=6 as the significance level for Saunder's statistic. Refer to the Appendix for additional details. The R statistic was not used throughout this study because of reader familiarity with the chi-square statistic. Conversion from one to the other is possible, as described in Appendix A.

When examining the contingency tables, the reader will observe that totals in each category don't equal totals previously recorded. To explain why, consider the contingency table for UFO color and physiological effect. Ninety-eight cases including a physiological effect were reported. For the color yellow, forty-two events were reported. However, there were seven events where there was a physiological effect but no color was reported. There were also sixty-nine cases where no effect was felt by the witness and no color was reported. The totals in each cell must be adjusted accordingly so that the actual contingency table looks like Table 22.

This distribution is observed to be random upon inspection, and thus the null hypothesis is supported.

For the remainder of this section of the text, only those tables that demonstrate significant correlations will be discussed.

Chi-square = 8.15Chi-square(.02 significance level) = 5.41

Tables 23 and 24 represent the results for the two colors (here "metallic" is considered a separate color) that are significant at the .02 level.

Chi-square = 9.83 Chi-square(.02 significance level) = 5.41

For only these two colors do we reject the null hypothesis that color and physiological effect act independently. We find a positive correlation between the color blue and the presence of a metallic surface with a physiological effect on the witnesses. It is interesting to reflect that blue is at the more energetic end of the visible spectrum, and might be an indication of higher energies involved which extend into the ultraviolet and beyond.

Analysis was then undertaken relating UFO color to the largest dimension of the UFO. Again, two possible correlations were discovered, listed in Tables 25 and 26.

Chi-square = 12.16

Chi-square(.02 significance level) = 7.82

TABLE 26 - UFO COLOR METALLIC BY UFO SIZE
	SIZE
COLOR	0-15 ft.	15-33 ft.	Over33 ft.
Metallic	10	32	29
Other Colors	18	13	47

Chi-square = 14.23

Chi-square(.02 significance level) = 7.82

By inspection, the dependence of the variables UFO size and the color red is observed to be due to the relatively larqe number of small, red UFOs. The dependency of the variable of UFO size and metallic "color" is due to the larqe numbers of-metallic UFOs in the fifteen to thirty-three foot size range. This range corresponds exactly to the classic diameter of most disc-shaped. metallic UFOs reported since 1947 (2). In fact, only one metallic-appearing UFO was reported to have a diameter exceeding 100 feet. It is unclear what these correlations may imply about UFO origin or generating mechanisms.

The next analysis was done for UFO color and UFO sound. No attempt was made to differentiate among the reported sounds; it was either recorded as present or absent. Tables 27 and 28 list the correlations located.

Chi-square = 6.00

Chi-square(.02 significance level) 5.41

TABLE 28 - UFO COLOR METALLIC BY UFO SOUND
	SOUND
COLOR	Present	Absent
Metallic	47	79
Other Colors	36	198

Chi-square = 22.16

Chi-square(.02 significance level) 5.41

For both green and metallic, there is a positive correlation, such that when they are reported, a sound is also more likely to be reported. Significantly, well over one-half of the UFOs with associated sound were reported to be metallic (57%). The color metallic has now been found to be positively correlated with UFO size, sound, and the physiological effect.

An analysis was then attempted for UFO color and EM effect. To remind the reader, EM effect has been subdivided into these categories:

1. EM: interference with operation of engine or electrical equipment

2. Control: vehicle under seeming control by outside forces

3. Destruction: engine components or electrical equipment damaged

4. Re-start: engine resumes operation by itself without the help of the driver

Only one possible correlation was discovered, as displayed in Table 29. The numbers in this table are particularly low because of the many events when the engine did not fail completely, hence could not re-start by itself.

TABLE 29 - UFO COLOR METALLIC BY ENGINE RESTART
	EFFECT
COLOR	Restart	No Restart
Metallic	1	72
Other Colors	18	121

Chi-square = 7.85Chi-square(.02 significance level) = 5.41

This association between metallic-appearing UFOs and engine re-starts is an odd, negative relationship. It implies that vehicle engines do not re-start in the presence of a metallic UFO. No ready explanation comes to mind to help us understand this relationship.

The hypothesis that UFO color and UFO actions are not correlated was next tested. Table 30 presents the only interesting result for the color yellow.

TABLE 30 - UFO COLOR YELLOW BY UFO DISAPPEARANCE
	UFO ACTION
COLOR	Disappearance	No Disappearance
Yellow	8	34
			R=11.62
Other Colors	10	303

The remarkability of this table ensues from the larger than expected number of yellow disappearing UFOs. Almost half of the UFOs observed to disappear were yellow.

TABLE 31 - UFO COLOR WHITE BY UFO LEAVING INSTANTLY
	UFO ACTION
COLOR	Leave Instantly	Not Leave Instantly
White	10	59
Other Colors	15	271
	Chi-square = 5.91	Chi-square (.02 significance level)= 5.41

No interesting results were found for the colors red, blue, orange, or green.

Tables 31 and 32 then display the significant correlations for the color white.

TABLE 32 - UFO COLOR WHITE BY UFO CHASING VEHICLE
	UFO ACTION
COLOR	Chase Vehicle	Not Chase Vehicle
White	20	49
Other Colors	44	242

Chi-square = 6.95

Chi-square (.02 significance level) = 5.41

The number of white-colored UFOs that chase vehicles and leave instantly are both higher than expected by chance.

The metallic "color" was found to be correlated with a number of UFO actions. Tables 33, 34, 35, 36, and 37 below will present the data. First Table 33:

Chi-square = 12.40

Chi-square (.02 significance level) = 5.41

Over 50% of all UFOs reported to land are metallic-appearing, as was true for events involving sound. Now Table 34:

TABLE 34 - UFO COLOR METALLIC BY UFO LEAVING INSTANTLY
	UFO ACTION
COLOR	Leave Instantly	Not Leave Instantly
Metallic	16	110
Other Colors	9	220

Chi-square = 9.55

Chi.square (.02 significance level) = 5.41

Again, well over 50% of all UFOs exhibiting a specific characteristic, in this case, leaving instantly, are metallic-appearing. Then Table 35:

TABLE 35 - UFO COLOR METALLIC BY UFO TRAJECTORY
	UFO ACTION
COLOR	Straight Trajectory	Erratic Trajectory
Metallic	4	122
Other colors	23	206

Chi-square = 5.46

Chi-square (.02 significance level) = 5.41

By inspection, we see that the cause of this deviation from expected values is the fact that relatively few metallic UFOs are reported to follow straight trajectories. Then Table 36:

TABLE 36 - UFO COLOR METALLIC BY UFO CHASING VEHICLE
	UFO ACTION
COLOR	Chase Vehicle	Not Chase Vehicle
Metallic	35	91
Other colors	29	200

Chi-square = 12.55	Chi-square (.02 significance level) = 5.41
Metallic UFOs are positively associated with the action of chasing the witnesses' vehicles. Finally, Table 37:

TABLE 37 - UFO COLOR METALLIC BY UFO DISAPPEARANCE
	UFO ACTION
COLOR	Disappearance	No Disappearance
Metallic	1	125
Other colors	17	212

Chi-square = 7.42

Chi-square (.02 significance level) = 5.41

In Table 37, the null hypothesis of independence of the two characteristics is rejected because of a lower-than-expected number of metallic UFOs that disappear. It is revealing that those UFOs that are reported to be metallic tend to act in a manner consistent with that expected of a real physical object in the atmosphere. They do not simply disappear, but leave in a continuous trajectory ? albeit very swiftly at times. They land on the ground, but rarely move in a simple straight trajectory. Such relationships may shed light on the origin of these UFOs.

An investigation was then made concerning the connection between UFO color and shape or type. Here UFO type was subdivided into only four categories: light, disc, oval (like a sphere), and "other" (where some shape was observable). These may be compared to the finer distinctions of Table 6. Table 38 displays the only relationship deemed significant. There is no "light" category because, by definition, metallic UFOs could not be classified as a light.

TABLE 38 - UFO COLOR METALLIC BY UFO SHAPE
	UFO SHAPE
COLOR	Disc	Oval	Other
Metallic	62	20	38
Other Colors	52	39	54

Chi-square = 7.50

Chi-square (.02 significance level) = 7.82

The chi-square value does not quite meet our criterion of significance. However, the computed value for R is 6.37, which indicates that this distribution may be non-random. By computing expected frequencies, we can observe that there are more metallic, disc-shaped UFOs than expected by chance, with slightly lower-than-expected numbers for other categories.

While it is not strictly permissible to use two statistical tests at once under our ground rules, a later discussion will explain more fully the reason why I wish to include Table 38 in this section as an important result.

The final analysis involving color was then done with the presence or absence of a light beam. Table 39 presents the only contingency table for which a correlation was found.

TABLE 39 - UFO COLOR BLUE BY PRESENCE OF A LIGHT BEAM
	LIGHT BEAM
COLOR	Present	Absent
Blue	12	65
Other Colors	15	263

Chi-square = 7.51

Chi-square (.02 significance level) = 5.41

Almost half of the EM events with a light beam involved a blue-colored UFO. This may be an indication of the higher energies that are necessary to generate a beam, which is actually a rather rare feature of EM events.

To continue with our investigation of light beams, Tables 40, 41, and 42 display the interesting results.

TABLE 40 - PRESENCE OF A LIGHT BEAM BY UFO CHASING VEHICLE
	UFO ACTION
LIGHT BEAM	Chase Vehicle	Not Chase Vehicle
Present	16	15
Absent	57	350

Chi-square = 19.98

Chi-square (.02 significance level) = 5.41

There is a tendency for UFOs with light beams to chase vehicles. In most of these cases, the beam falls directly on the vehicle (see the October 31, 1967 case from Boyup Brook, Australia, for an example).

TABLE 41 - PRESENCE OF A LIGHT BEAM BY CONTROL OF VEHICLE
	UFO ACTION
LIGHT BEAM	Control	No Control
Present	7	24
			R=9.41
Absent	20	387

The distribution of cases in Table 41 is a fairly remarkable result, with the deviation from randomness occurring because of the high number of UFOs both controlling the vehicle and emitting a light beam. It is intriguing that a correlation has been found for both chasing and controlling vehicles, for, a priori, we might expect that to gain control of a vehicle, the UFO would need to be relatively close, thereby requiring a chase to get into position. This has been borne out in the statistics.

TABLE 42 - PRESENCE OF A LIGHT BEAM BY PHYSIOLOGICAL EFFECT
	UFO ACTION
LIGHT BEAM	Present
Present	15	16
Absent	83	324

Chi-square = 12.97

Chi-square (.02 significance level) = 5.41

In almost half of the events involving a light beam, the witness was affected. This compares to an overall rate of about 20%. Of course, this is not too surprising if light beams involve higher energies, as suggested by their association with the color blue. Vanackeren and Windey have described how the combination of bright lights, witness fear, modulated sound, and negative ionization will cause paralysis in many people (3). Since light beams are reported to be quite bright, it is possible that some of the reported physiological effects can be attributed to this phenomenon rather than to some specific effect of the light beam. No three-way analysis of UFO sound, light beams, and physiological effect was attempted in this study.

The relation of UFO type with various characteristics was then investigated. Table 43 lists the one correlation located.

TABLE 43 - PRESENCE OF UFO SOUND BY UFO SHAPE
		UFO SHAPE
SOUND	Disc	Light	Oval	Other
Present	30	6	14	21
Absent	56	66	34	59

Chi-square = 15.70

Chi-square (.02 significance level) = 9.84

By calculation of expected frequencies, it can be determined that the large chi-square value is due to a large number of noisy discs and very few lights that emit sound. Most of this variance can be attributed to the paucity of noisy lights.

A non-random relationship was also discovered between the reported UFO size and UFO type. Table 44 presents the data.

TABLE 44 - UFO SIZE BY UFO SHAPE
		UFO SHAPE
SIZE	Disc	Light	Oval	Other
0-15 ft.	6	10	1	12
15-33 ft.	15	0	11	13
33-100 ft.	19	2	11	16
Over 100 ft.	6	0	2	8

Using the remarkability statistic, R is found to be approximately 20 (an exact figure cannot be determined due to limitations on tabular values in Saunder's book). This is an extremely high value for R and indicates that the data in Table 44 is very non-random. By computation of expected cell frequencies, we can observe that most of the deviation from expected values occurs because of the ten lights which are less than fifteen feet in size, and the single oval UFO that is small. A possible explanation for the small size of lights will be discussed in the concluding section.

For the moment, we will continue the investigation of UFO type. Two possible relationships were located between UFOs as lights and certain actions. The first is in Table 45.

TABLE 45 - UFO AS A LIGHT BY UFO LEAVING INSTANTLY
	UFO ACTION
SHAPE	Leave Instantly	Not Leave Instantly
Light	0	81
Other Shapes	20	245

Using informational statistics, this table yields an R value of 10.13, a significant result. In fact, there are no cases of UFOs as lights which leave instantly. Then consider Table 46:

TABLE 46 - UFO AS A LIGHT BY UFO TRAJECTORY
	UFO ACTION
SHAPE	Straight Trajectory	Erratic Trajectory
Light	13	68
Other Shapes	17	248

Chi-square = 7.28

Chi-square (.02 significance level) = 5.41

By inspection, we see that a higher-than-expected number of lights tend to move in straight trajectories.

The fact that no correlations were found for the "other" category of UFO type versus other variables is not surprising, as this group was hardly homogeneous. Lumping together the remainder of UFO types in one category probably masked whatever significance may reside in the data.

The relationship between UFO action and other characteristics not yet tested was next investigated. For the presence of a physiological effect, only once was the null hypothesis rejected, in Table 47.

TABLE 47 - UFO CHASING VEHICLE BY PHYSIOLOGICAL EFFECT
	PHYSIOLOGICAL EFFECT
UFO ACTION	Present	Absent
Chase Vehicle	29	44
Not Chase Vehicle	69	269

Chi-square = 12.33

Chi-square (.02 significance level) = 5.41

This result might be considered to be another confirmation of the theory of Vanackeren and Windey, because one can well imagine that a UFO which chases a vehicle, or appears to chase it, will induce witness fear. Since light beams occur frequently in such cases, the conditions would be conducive for witness paralysis.

One possible correlation was found for the presence of sound and UFOs that land, as displayed in Table 48.

TABLE 48 - UFO LANDING BY UFO SOUND
	UFO SOUND
UFO ACTION	Present	Absent
Landing	32	72
No Landing	58	246

Chi-square = 6.16

Chi-square (.02 significance level) = 5.41

A higher-than-expected number of events included both the emission of sound and the landing of the UFO on the ground. One might speculate that since it is probably only possible to determine whether or not a UFO has landed if it is relatively near the witness, this deviation from chance occurs as an artifact of the event. If there is a minimum threshold above which the sound emitted can be detected, it will more likely be detected the closer the UFO. And, as discussed above, UFOs observed to land might be expected to be closer because of physical requisites. Therefore, we may tentatively conclude that this observed tendency for landed UFOs to emit sound is not an association requiring an appeal to obscure mechanisms for an explanation.

One possible correlation was discovered for UFO action and UFO size in Table 49.

TABLE 49 - UFO CHASING VEHICLE BY UFO SIZE
		UFO SIZE
UFO ACTION	0-15 ft.	15-33 ft.	33-100 ft.	over 100 ft.
Chased Vehicle	13	13	11	1
Not Chase Vehicle	15	32	45	19

Chi-square = 12.17

Chi-square (.02 significance level) = 9.84

The departure from randomness in this table occurs because of the higher numbers of small UFOs that chase vehicles and almost no UFOs larger than 100 feet that do so. No reason comes immediately to mind to explain this result.

Tables 50 and 51 then present the results of an analysis of UFO action and type of EM effect.

TABLE 50 - UFO CHASING VEHICLE BY CONTROL OF VEHICLE
	EM EFFECT
UFO ACTION	Control	No Control
Chased Vehicle	14	59
Not Chase Vehicle	13	325

Using the informational statistic, we find R~=14.7 a significant result. Indeed, over one-half of the cases involving vehicle control occurred when the UFO chased the car or truck. As discussed before, if control of the vehicle necessitates being relatively near the vehicle, then it perhaps implies a chase to get into range.

TABLE 51 - UFO DISAPPEARANCE BY ENGINE RESTART
	EM EFFECT
UFO ACTION	Restart	No Restart
Disappearance	4	10
No Disappearance	16	238

The total number of events is only 268 in Table 51. This is because of the many events where the engine did not stop completely ? such events cannot be included in this analysis. The computed value for R is 6.19, which just does meet our criterion for significance. A higher-than-expected number of UFOs which disappear occur simultaneously with engines which start by themselves.

Finally, correlations were investigated between UFO action and other actions. The first interesting result is displayed in Table 52:

TABLE 52 - UFO LANDING BY UFO DISAPPEARANCE
	UFO ACTION
UFO ACTION	Disappearance	No Disappearance
Landing	10	94
No Landing	9	301

Using remarkability, R is found to be 6.87, well into the significant range. Over one-half of the objects that disappear also landed. This is a somewhat problematical result; why there should be such an association is unclear.

One additional result was important, in Table 53:

TABLE 53 - UFO TRAJECTORY BY UFO CHASING VEHICLE
	UFO ACTION
UFO ACTION	Chased Vehicle	Not Chased Vehicle
Straight Trajectory	0	39
Erratic Trajectory	73	302

Chi-square = 9.22

Chi-square (.02 significance level) = 5.41

This clear association between UFOs that chase vehicles and an erratic trajectory, or conversely, a disassociation between chasing and straight trajectories, can be readily explained. One cannot chase a vehicle by simply moving in a straight line, unless the vehicle is on a straight road. Even then, the initial and final trajectories must follow the same path before and after interaction with the vehicle. It is not surprising, then, that UFOs that follow a straight trajectory do not chase vehicles. Nevertheless, this explanation is predicated on the hidden assumption that the UFO is physically present in the environment of the witness, i.e., that it must follow physical laws.

The various categories of the EM effect were then analyzed in conjunction with all remaining variables. Only one possible association was discovered, which seems quite likely not to be spurious. It is presented in Table 54.

TABLE 54 - CONTROL OF VEHICLE BY PHYSIOLOGICAL EFFECT
	PHYSIOLOGICAL EFFECT
EM EFFECT	Present	Absent
Control	16	11
No Control	82	329

Chi-square = 22.54

Chi-square (.02 significance level) = 5.41

From inspection we see that the large chi-square value is attributed to the large proportion of UFOs that control a vehicle and also affect the witness. We might suppose that, isolated from previous results, this correlation could be explained by some type of fear reaction on the witness' part, inasmuch as his or her vehicle is out of control, a phenomenon likely to cause various physiological symptoms to appear. However, the symptoms which appear in EM control events are rarely reported in traffic accidents, which are their closest analogy. In any case, this is a definite correlation which must be explained in any theory of EM events.

It is of interest to mention in passing that no correlation was found between UFO size and type of EM effect. We might have expected larger UFOs to occur more frequently in cases with destruction of engine components. Such is not the case.

Remaining possible relationships between characteristics not yet mentioned were all found not to reject the null hypothesis that the characteristics acted independently. Specifically, UFO size was not related to the presence of sound or the physiological effect; neither were the last two characteristics correlated. After the many reported positive results noted above, we might be tempted to think of this lack of an association as somewhat unexpected.

The several associations between variables that have been discovered may, at this point, be rather confusing to the reader. A diagram will be constructed in the next section to make readily discernible these relationships.