Simpson’s Paradox and Data Interpretation

NB: We do not resell your papers. Upon ordering, we do an original paper exclusively for you.

NB: All your data is kept safe from the public.

Table of Contents

Introduction
Simpson’s Paradox
Nuclear Tests Sites in Nevada
“The Conqueror” Paradox
Conclusion
References

Introduction

Interpreting information is a rather complicated process. Statistical data are to be properly analyzed and structured to be interpreted. The same is true about historical data. To assure the proper data interpretation, the human thought have developed lots of concepts and hypothesis and means of it, and one of them is the so-called Simpson’s Paradox (Graff & Birkenstein, 2007, pp. 5 – 8).

The aim of this paper is to examine the essence of the Simpson’s Paradox and its role in the interpretation of information. Another purpose of this work is to consider the possible implementation of the Simpson’s Paradox to the events that took place at Nuclear Tests Sites in Nevada, and namely the events that happened to the cast of the film “The Conqueror” by Howard Hughes. I am going to consider Simpson’s Paradox in the context of those events so that to see its practical use.

Simpson’s Paradox

The very paradox bears the name of Edward H. Simpson who formulated it in 1951 but did not think that his theory would amount to such a worldwide known paradox. The very term “Simpson’s Paradox” was developed much later, in 1972, by Colin R. Blyth. Drawing from this, numerous scholars avoid calling it “Simpson’s Paradox” and use the term “reversal paradox” instead. But, in any case, the essence of the phenomenon remains the same independent of the term which is used to call it. The authorship of the theory also can not be doubted because it was Simpson who discovered the phenomenon, while Blyth only named it after him (Clifford, 1982, pp. 46 – 48).

Simpson’s Paradox is a statistical phenomenon according to which a result which is typical of several separate groups of people, things, phenomena, etc. acquires completely different meaning when these separate groups are combined. Thus, for example, the rate of recovery which is observed in patients that undergo treatment is higher than the rate of recovery in patients who do not undergo treatment. But, at further consideration, it may turn out that the rate of recovery of treated males is lower than in untreated ones. The same can turn out to be true about the female patients who, respectively, undergo and do not undergo treatment.

But, the above presented paradigm is mistaken in its essence because the sum of elements can not contradict their separate meanings. In other words, if female treated patients have higher rate of recovery that those who were not treated, and treated males have higher recovery rate than untreated ones as well, than the recovery rate of overall treated patients can not be lower than the one of untreated patients (Clifford, 1982, pp. 46 – 48).

Thus, the Simpson’s Paradox can be used to explain to controversial phenomena. On the one hand, it describes and explains the mistake interpretation of information based on the failing criterion. On the other hand, it considers the improper use of information and its inaccurate analysis due to which the conclusions made from the information about single whole can contradict the conclusions made from information about its parts. Use of the Simpson’s Paradox is a great chance for scientists to interpret the information in a right way and not to allow its misinterpretation (Clifford, 1982, pp. 46 – 48).

Nuclear Tests Sites in Nevada

The interesting question is the interpretation of data connected with the Nevada Nuclear Tests Sites with the help of Simpson’s Paradox. It is a rather challenging matter because one has to avoid misinterpretation of facts and statistical data. But to have a better understanding of the above mentioned phenomena, it would not be out of place to take a brief look at the history and essence of Nevada Nuclear Tests Sites. These sites were founded in 1951 for the conduct of Nuclear Weapons tests and comprised over 1, 350 square miles in the desert of Nevada close to the city of Las-Vegas (Malone, 1999, p. 116).

Numerous tests of nuclear weapons and A-bombs were carried out on the territory of the Nevada Sites during over forty years, and caused a lot of controversy and actions of public protest. The main argument of those who protested was that the fall outs of the nuclear weapons that remained in the air after the explosions caused terrible cases of cancer to a lot of people living downwind the Sites in Nevada. After the powerful activities of public organizations the nuclear tests were officially stopped in Nevada and the numerous court trials made the Government pay considerable compensations to the victims of the cancer caused by nuclear fall outs.

Nevertheless, the controversy about the causes of the cancer cases still exists, and it is an example of the Simpson’s Paradox. The essence of the paradox in this case lies in the fact that the obvious relation of the increase in cancer cases in the area close to the Nuclear Tests Sites is doubted, especially in the context of the situation of “The Conqueror” which was filmed at the Sites (Malone, 1999, p. 116).

“The Conqueror” Paradox

The movie of 1956 filmed by Howard Hughes caused a lot of dispute after the so-called “epidemic” of cancer killed one after another a great part of the cast and personnel of the film. The very motion picture was shot exactly at the Nuclear Tests Sites in Nevada. This fact caused considerable worrying among the staff and cast but the filming process nevertheless began. In some years after the film was displayed on the major screens of the country, its major stars, like for example John Wayne, Susan Hayward, etc. died of cancer (Olson, 2002, p. 32).

The use of the Simpson’s Paradox in this situation becomes necessary when the exact numbers of those who contracted cancer and died of it become available. The cast amounted to 220 among which 91 person got cancer after the filming and 46 of them died of cancer before 1980. However, numerous scientists claim that the cancer cases and nuclear fall outs at Nevada Sites are not interconnected. According to their hypothesis, if fall outs of nuclear tests were the reasons for cancer, only 30 persons could have been affected by it.

And this is the brightest example of the Simpson’s Paradox, because the numerous cancer cases among the population of Nevada were accepted as results of nuclear tests. It can not be understood why the supposed rate of actors affected by cancer should be about 13%, while the actual rate of cancer cases among ordinary people was over 40%. The reported rate of cancer cases among “The Conqueror” cast was over 40% which is more credible then the above expressed hypothesis (Olson, 2002, p. 49).

Conclusion

The Simpson’s Paradox is a rather specific way of interpreting information. It is based on the principles of reverse equality, i. e. on the illusion of the fact that the sum of the meanings of the components of a single whole is reverse to the meaning of the single whole. In this paper, I exemplified it with theoretical and actual examples and proved that the Simpson’s Paradox is a useful means of information interpretation.

In the cases with the cancer cases at the territories close to the Nuclear Tests Sites in Nevada, and especially in the case of “The Conqueror” cast, the Simpson’s Paradox was especially evident and only precise and attentive consideration of data allowed me to interpret the information in a right way and avoid data misinterpretation, based on improper analysis and wrong conclusions.

References

Clifford H. Wagner. 1982. “Simpson’s Paradox in Real Life”. The American Statistician 36 (1982) (1): 46–48.

Graff, G. & Birkenstein, C. 2007. They Say/I Say: The Moves that Matter in Persuasive Writing. W. W. Norton.

Malone, Charles R. 1999. Integrated Weapons-Site Cleanup: The Department of Energy Is Using Ecosystem Management to Help Clean Up Our Nation’s Nuclear Weapons Sites. Forum for Applied Research and Public Policy 14, no. 2: 116+.

Olson, James. 2002. Bathsheba’s Breast: Women, Cancer and History. Baltimore, Maryland: Johns Hopkins University Press.

Click Here To Order Now!