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Misuse of statistics
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Statistics are supposed to make something easier to understand but when used in a misleading fashion can trick the casual observer into believing something other than what the data shows. That is, a misuse of statistics occurs when a statistical argument asserts a falsehood. In some cases, the misuse may be accidental. In others, it is purposeful and for the gain of the perpetrator. When the statistical reason involved is false or misapplied, this constitutes a statistical fallacy.
The false statistics trap can be quite damaging for the quest for knowledge. For example, in medical science, correcting a falsehood may take decades and cost lives.
Misuses can be easy to fall into. Professional scientists, even mathematicians and professional statisticians, can be fooled by even some simple methods, even if they are careful to check everything. Scientists have been known to fool themselves with statistics due to lack of knowledge of probability theory and lack of standardization of their tests.
Contents
[hide]
1 Importance
2 Definition, limitations and context
3 Simple causes
4 Types of misuse
4.1 Discarding unfavorable data
4.2 Loaded questions
4.3 Overgeneralization
4.4 Biased samples
4.5 Misreporting or misunderstanding of estimated error
4.6 False causality
4.7 Proof of the null hypothesis
4.8 Confusing statistical significance with practical significance
4.9 Data dredging
4.10 Data manipulation
4.11 Other fallacies
4.12 Other types of misuse
5 See also
6 References
6.1 Notes
6.2 Sources
7 Further reading
Importance[edit]
Statistics may be a principled means of debate with opportunities for agreement,[1][2] but this is true only if the parties agree to a set of rules. Misuses of statistics violate the rules.
Or to put it another way:
False facts are highly injurious to the progress of science, for they often long endure; but false views, if supported by some evidence, do little harm, as every one takes a salutary pleasure in proving their falseness; and when this is done, one path towards error is closed and the road to truth is often at the same time opened.
— Charles Darwin, The Descent of Man (1871), Vol. 2, 385.
Definition, limitations and context[edit]
One usable definition is: "Misuse of Statistics: Using numbers in such a manner that - either by intent, or through ignorance or carelessness - the conclusions are unjustified or incorrect."[3] The "numbers" include misleading graphics discussed elsewhere. The term is not commonly encountered in statistics texts and no authoritative definition is known. It is a generalization of lying with statistics which was richly described by examples from statisticians 60 years ago.
The definition confronts some problems (some are addressed by the source):[4]
Statistics usually produces probabilities; conclusions are provisional
The provisional conclusions have errors and error rates. Commonly 5% of the provisional conclusions of significance testing are wrong
Statisticians are not in complete agreement on ideal methods
Statistical methods are based on assumptions which are seldom fully met
Data gathering is usually limited by ethical, practical and financial constraints.
How to Lie with Statistics acknowledges that statistics can legitimately take many forms. Whether the statistics show that a product is "light and economical" or "flimsy and cheap" can be debated whatever the numbers. Some object to the substitution of statistical correctness for moral leadership (for example) as an objective. Assigning blame for misuses is often difficult because scientists, pollsters, statisticians and reporters are often employees or consultants.
An insidious misuse(?) of statistics is completed by the listener/observer/audience/juror. The supplier provides the "statistics" as numbers or graphics (or before/after photographs), allowing the consumer to draw (possibly unjustified or incorrect) conclusions. The poor state of public statistical literacy and the non-statistical nature of human intuition permits misleading without explicitly producing faulty conclusions. The definition is weak on the responsibility of the consumer of statistics.
A historian listed over 100 fallacies in a dozen categories including those of generalization and those of causation.[5] A few of the fallacies are explicitly or potentially statistical including sampling, statistical nonsense, statistical probability, false extrapolation, false interpolation and insidious generalization. All of the technical/mathematical problems of applied probability would fit in the single listed fallacy of statistical probability. Many of the fallacies could be coupled to a statistical analysis, allowing the possibility of a false conclusion flowing from a blameless statistical analysis.
An example use of statistics is in the analysis of medical research. The process includes[6][7] experimental planning, conduct of the experiment, data analysis, drawing the logical conclusions and presentation/reporting. The report is summarized by the popular press and by advertisers. Misuses of statistics can result from problems at any step in the process. The statistical standards ideally imposed on the scientific report are much different than those imposed on the popular press and advertisers; however, cases exist of advertising disguised as science. The definition of the misuse of statistics is weak on the required completeness of statistical reporting. The opinion is expressed that newspapers must provide at least the source for the statistics reported.
Simple causes[edit]
Many misuses of statistics occur because
The source is a subject matter expert, not a statistics expert.[8] The source may incorrectly use a method or interpret a result.
The source is a statistician, not a subject matter expert.[9] An expert should know when the numbers being compared describe different things. Numbers change, as reality does not, when legal definitions or political boundaries change.
The subject being studied is not well defined.[10] While IQ tests are available and numeric it is difficult to define what they measure; Intelligence is an elusive concept. Publishing "impact" has the same problem.[11] A seemingly simple question about the number of words in the English language immediately encounters questions about archaic forms, accounting for prefixes and suffixes, multiple definitions of a word, variant spellings, dialects, fanciful creations (like ectoplastistics from ectoplasm and statistics),[12] technical vocabulary...
Data quality is poor.[13] Apparel provides an example. People have a wide range of sizes and body shapes. It is obvious that apparel sizing must be multidimensional. Instead it is complex in unexpected ways. Some apparel is sold by size only (with no explicit consideration of body shape), sizes vary by country and manufacturer and some sizes are deliberately misleading. While sizes are numeric, only the crudest of statistical analyses is possible using the size numbers with care.
The popular press has limited expertise and mixed motives.[14] If the facts are not "newsworthy" (which may require exaggeration) they may not be published. The motives of advertisers are even more mixed.
"Politicians use statistics in the same way that a drunk uses lamp-posts—for support rather than illumination" - Andrew Lang (WikiQuote) "What do we learn from these two ways of looking at the same numbers? We learn that a clever propagandist, right or left, can almost always find a way to present the data on economic growth that seems to support her case. And we therefore also learn to take any statistical analysis from a strongly political source with handfuls of salt."[15] The term statistics originates from numbers generated for and utilized by the state. Good government may require accurate numbers, but popular government may require supportive numbers (not necessarily the same). "The use and misuse of statistics by governments is an ancient art."[16]
Types of misuse[edit]
Discarding unfavorable data[edit]
All a company has to do to promote a neutral (useless) product is to find or conduct, for example, 40 studies with a confidence level of 95%. If the product is really useless, this would on average produce one study showing the product was beneficial, one study showing it was harmful and thirty-eight inconclusive studies (38 is 95% of 40). This tactic becomes more effective the more studies there are available. Organizations that do not publish every study they carry out, such as tobacco companies denying a link between smoking and cancer, anti-smoking advocacy groups and media outlets trying to prove a link between smoking and various ailments, or miracle pill vendors, are likely to use this tactic.
Ronald Fisher considered this issue in his famous lady tasting tea example experiment (from his 1935 book, The Design of Experiments). Regarding repeated experiments he said, "It would clearly be illegitimate, and would rob our calculation of its basis, if unsuccessful results were not all brought into the account."
Another term related to this concept is cherry picking.
Loaded questions[edit]
Main article: Loaded question
The answers to surveys can often be manipulated by wording the question in such a way as to induce a prevalence towards a certain answer from the respondent. For example, in polling support for a war, the questions:
Do you support the attempt by the USA to bring freedom and democracy to other places in the world?
Do you support the unprovoked military action by the USA?
will likely result in data skewed in different directions, although they are both polling about the support for the war. A better way of wording the question could be "Do you support the current US military action abroad?" A still more nearly neutral way to put that question is "What is your view about the current US military action abroad?" The point should be that the person being asked has no way of guessing from the wording what the questioner might want to hear.
Another way to do this is to precede the question by information that supports the "desired" answer. For example, more people will likely answer "yes" to the question "Given the increasing burden of taxes on middle-class families, do you support cuts in income tax?" than to the question "Considering the rising federal budget deficit and the desperate need for more revenue, do you support cuts in income tax?"
The proper formulation of questions can be very subtle. The responses to two questions can vary dramatically depending on the order in which they are asked.[17] "A survey that asked about 'ownership of stock' found that most Texas ranchers owned stock, though probably not the kind traded on the New York Stock Exchange."[18]
Overgeneralization[edit]
Overgeneralization is a fallacy occurring when a statistic about a particular population is asserted to hold among members of a group for which the original population is not a representative sample.
For example, suppose 100% of apples are observed to be red in summer. The assertion "All apples are red" would be an instance of overgeneralization because the original statistic was true only of a specific subset of apples (those in summer), which is not expected to be representative of the population of apples as a whole.
A real-world example of the overgeneralization fallacy can be observed as an artifact of modern polling techniques, which prohibit calling cell phones for over-the-phone political polls. As young people are more likely than other demographic groups to lack a conventional "landline" phone, a telephone poll that exclusively surveys responders of calls landline phones, may cause the poll results to undersample the views of young people, if no other measures are taken to account for this skewing of the sampling. Thus, a poll examining the voting preferences of young people using this technique may not be a perfectly accurate representation of young peoples' true voting preferences as a whole without overgeneralizing, because the sample used excludes young people that carry only cell phones, who may or may not have voting preferences that differ from the rest of the population.
Overgeneralization often occurs when information is passed through nontechnical sources, in particular mass media.
Biased samples[edit]
Main article: Biased sample
Scientists have learned at great cost that gathering good experimental data for statistical analysis is difficult. Example: The placebo effect (mind over body) is very powerful. 100% of subjects developed a rash when exposed to an inert substance that was falsely called poison ivy while few developed a rash to a "harmless" object that really was poison ivy.[19] Researchers combat this effect by double-blind randomized comparative experiments. Statisticians typically worry more about the validity of the data than the analysis. This is reflected in a field of study within statistics known as the design of experiments.
Pollsters have learned at great cost that gathering good survey data for statistical analysis is difficult. The selective effect of cellular telephones on data collection (discussed in the Overgeneralization section) is one potential example; If young people with traditional telephones are not representative, the sample can be biased. Sample surveys have many pitfalls and require great care in execution.[20] One effort required almost 3000 telephone calls to get 1000 answers. The simple random sample of the population "isn't simple and may not be random."[21]
Misreporting or misunderstanding of estimated error[edit]
If a research team wants to know how 300 million people feel about a certain topic, it would be impractical to ask all of them. However, if the team picks a random sample of about 1000 people, they can be fairly certain that the results given by this group are representative of what the larger group would have said if they had all been asked.
This confidence can actually be quantified by the central limit theorem and other mathematical results. Confidence is expressed as a probability of the true result (for the larger group) being within a certain range of the estimate (the figure for the smaller group). This is the "plus or minus" figure often quoted for statistical surveys. The probability part of the confidence level is usually not mentioned; if so, it is assumed to be a standard number like 95%.
The two numbers are related. If a survey has an estimated error of ±5% at 95% confidence, it also has an estimated error of ±6.6% at 99% confidence. ± x {\displaystyle x} % at 95% confidence is always ± 1.32 x {\displaystyle 1.32x} % at 99% confidence for a normally distributed population.
The smaller the estimated error, the larger the required sample, at a given confidence level.
at 95.4% confidence:
±1% would require 10,000 people.
±2% would require 2,500 people.
±3% would require 1,111 people.
±4% would require 625 people.
±5% would require 400 people.
±10% would require 100 people.
±20% would require 25 people.
±25% would require 16 people.
±50% would require 4 people.
People may assume, because the confidence figure is omitted, that there is a 100% certainty that the true result is within the estimated error. This is not mathematically correct.
Many people may not realize that the randomness of the sample is very important. In practice, many opinion polls are conducted by phone, which distorts the sample in several ways, including exclusion of people who do not have phones, favoring the inclusion of people who have more than one phone, favoring the inclusion of people who are willing to participate in a phone survey over those who refuse, etc. Non-random sampling makes the estimated error unreliable.
On the other hand, people may consider that statistics are inherently unreliable because not everybody is called, or because they themselves are never polled. People may think that it is impossible to get data on the opinion of dozens of millions of people by just polling a few thousands. This is also inaccurate.[a] A poll with perfect unbiased sampling and truthful answers has a mathematically determined margin of error, which only depends on the number of people polled.
However, often only one margin of error is reported for a survey. When results are reported for population subgroups, a larger margin of error will apply, but this may not be made clear. For example, a survey of 1000 people may contain 100 people from a certain ethnic or economic group. The results focusing on that group will be much less reliable than results for the full population. If the margin of error for the full sample was 4%, say, then the margin of error for such a subgroup could be around 13%.
There are also many other measurement problems in population surveys.
The problems mentioned above apply to all statistical experiments, not just population surveys.
Further information: Opinion poll and Statistical survey
False causality[edit]
Main article: Correlation does not imply causation
When a statistical test shows a correlation between A and B, there are usually six possibilities:
A causes B.
B causes A.
A and B both partly cause each other.
A and B are both caused by a third factor, C.
B is caused by C which is correlated to A.
The observed correlation was due purely to chance.
The sixth possibility can be quantified by statistical tests that can calculate the probability that the correlation observed would be as large as it is just by chance if, in fact, there is no relationship between the variables. However, even if that possibility has a small probability, there are still the five others.
If the number of people buying ice cream at the beach is statistically related to the number of people who drown at the beach, then nobody would claim ice cream causes drowning because it's obvious that it isn't so. (In this case, both drowning and ice cream buying are clearly related by a third factor: the number of people at the beach).
This fallacy can be used, for example, to prove that exposure to a chemical causes cancer. Replace "number of people buying ice cream" with "number of people exposed to chemical X", and "number of people who drown" with "number of people who get cancer", and many people will believe you. In such a situation, there may be a statistical correlation even if there is no real effect. For example, if there is a perception that a chemical site is "dangerous" (even if it really isn't) property values in the area will decrease, which will entice more low-income families to move to that area. If low-income families are more likely to get cancer than high-income families (this can happen for many reasons, such as a poorer diet or less access to medical care) then rates of cancer will go up, even though the chemical itself is not dangerous. It is believed[24] that this is exactly what happened with some of the early studies showing a link between EMF (electromagnetic fields) from power lines and cancer.[25]
In well-designed studies, the effect of false causality can be eliminated by assigning some people into a "treatment group" and some people into a "control group" at random, and giving the treatment group the treatment and not giving the control group the treatment. In the above example, a researcher might expose one group of people to chemical X and leave a second group unexposed. If the first group had higher cancer rates, the researcher knows that there is no third factor that affected whether a person was exposed because he controlled who was exposed or not, and he assigned people to the exposed and non-exposed groups at random. However, in many applications, actually doing an experiment in this way is either prohibitively expensive, infeasible, unethical, illegal, or downright impossible. For example, it is highly unlikely that an IRB would accept an experiment that involved intentionally exposing people to a dangerous substance in order to test its toxicity. The obvious ethical implications of such types of experiments limit researchers' ability to empirically test causation.
Proof of the null hypothesis[edit]
In a statistical test, the null hypothesis ( H 0 {\displaystyle H_{0}} ) is considered valid until enough data proves it wrong. Then H 0 {\displaystyle H_{0}} is rejected and the alternative hypothesis ( H A {\displaystyle H_{A}} ) is considered to be proven as correct. By chance this can happen, although H 0 {\displaystyle H_{0}} is true, with a probability denoted α {\displaystyle \alpha } (the significance level). This can be compared to the judicial process, where the accused is considered innocent ( H 0 {\displaystyle H_{0}} ) until proven guilty ( H A {\displaystyle H_{A}} ) beyond reasonable doubt ( α {\displaystyle \alpha } ).
But if data does not give us enough proof to reject that H 0 {\displaystyle H_{0}} , this does not automatically prove that H 0 {\displaystyle H_{0}} is correct. If, for example, a tobacco producer wishes to demonstrate that its products are safe, it can easily conduct a test with a small sample of smokers versus a small sample of non-smokers. It is unlikely that any of them will develop lung cancer (and even if they do, the difference between the groups has to be very big in order to reject H 0 {\displaystyle H_{0}} ). Therefore, it is likely—even when smoking is dangerous—that our test will not reject H 0 {\displaystyle H_{0}} . If H 0 {\displaystyle H_{0}} is accepted, it does not automatically follow that smoking is proven harmless. The test has insufficient power to reject H 0 {\displaystyle H_{0}} , so the test is useless and the value of the "proof" of H 0 {\displaystyle H_{0}} is also null.
This can—using the judicial analogue above—be compared with the truly guilty defendant who is released just because the proof is not enough for a guilty verdict. This does not prove the defendant's innocence, but only that there is not proof enough for a guilty verdict.
"...the null hypothesis is never proved or established, but it is possibly disproved, in the course of experimentation. Every experiment may be said to exist only in order to give the facts a chance of disproving the null hypothesis." (Fisher in The Design of Experiments) Many reasons for confusion exist including the use of double negative logic and terminology resulting from the merger of Fisher's "significance testing" (where the null hypothesis is never accepted) with "hypothesis testing" (where some hypothesis is always accepted).
Confusing statistical significance with practical significance[edit]
Statistical significance is a measure of probability; practical significance is a measure of effect.[26] A baldness cure is statistically significant if a sparse peach-fuzz usually covers the previously naked scalp. The cure is practically significant when a hat is no longer required in cold weather and the barber asks how much to take off the top. The bald want a cure that is both statistically and practically significant; It will probably work and if it does, it will have a big hairy effect. Scientific publication often requires only statistical significance. This has led to complaints (for the last 50 years) that statistical significance testing is a misuse of statistics.[27]
Data dredging[edit]
Main article: Data dredging
Data dredging is an abuse of data mining. In data dredging, large compilations of data are examined in order to find a correlation, without any pre-defined choice of a hypothesis to be tested. Since the required confidence interval to establish a relationship between two parameters is usually chosen to be 95% (meaning that there is a 95% chance that the relationship observed is not due to random chance), there is a thus a 5% chance of finding a correlation between any two sets of completely random variables. Given that data dredging efforts typically examine large datasets with many variables, and hence even larger numbers of pairs of variables, spurious but apparently statistically significant results are almost certain to be found by any such study.
Note that data dredging is a valid way of finding a possible hypothesis but that hypothesis must then be tested with data not used in the original dredging. The misuse comes in when that hypothesis is stated as fact without further validation.
"You cannot legitimately test a hypothesis on the same data that first suggested that hypothesis. The remedy is clear. Once you have a hypothesis, design a study to search specifically for the effect you now think is there. If the result of this test is statistically significant, you have real evidence at last."[28]
Data manipulation[edit]
Informally called "fudging the data," this practice includes selective reporting (see also publication bias) and even simply making up false data.
Examples of selective reporting abound. The easiest and most common examples involve choosing a group of results that follow a pattern consistent with the preferred hypothesis while ignoring other results or "data runs" that contradict the hypothesis.
Psychic researchers have long disputed studies showing people with ESP ability. Critics accuse ESP proponents of only publishing experiments with positive results and shelving those that show negative results. A "positive result" is a test run (or data run) in which the subject guesses a hidden card, etc., at a much higher frequency than random chance.[citation needed]
Scientists, in general, question the validity of study results that cannot be reproduced by other investigators. However, some scientists refuse to publish their data and methods.[29]
Data manipulation is a serious issue/consideration in the most honest of statistical analyses. Outliers, missing data and non-normality can all adversely affect the validity of statistical analysis. It is appropriate to study the data and repair real problems before analysis begins. "[I]n any scatter diagram there will be some points more or less detached from the main part of the cloud: these points should be rejected only for cause."[30]
Other fallacies[edit]
Pseudoreplication is a technical error associated with analysis of variance. Complexity hides the fact that statistical analysis is being attempted on a single sample (N=1). For this degenerate case the variance cannot be calculated (division by zero).
The gambler's fallacy assumes that an event for which a future likelihood can be measured had the same likelihood of happening once it has already occurred. Thus, if someone had already tossed 9 coins and each has come up heads, people tend to assume that the likelihood of a tenth toss also being heads is 1023 to 1 against (which it was before the first coin was tossed) when in fact the chance of the tenth head is 50% (assuming the coin is unbiased).
The prosecutor's fallacy[31] has led, in the UK, to the false imprisonment of women for murder when the courts were given the prior statistical likelihood of a woman's 3 children dying from Sudden Infant Death Syndrome as being the chances that their already dead children died from the syndrome. This led to statements from Roy Meadow that the chance they had died of Sudden Infant Death Syndrome were extremely small (one in millions). The courts then handed down convictions in spite of the statistical inevitability that a few women would suffer this tragedy. The convictions were eventually overturned (and Meadow was subsequently struck off the U.K. Medical Register for giving “erroneous” and “misleading” evidence, although this was later reversed by the courts).[32] Meadow's calculations were irrelevant to these cases, but even if they were, using the same methods of calculation would have shown that the odds against two cases of infanticide were even smaller (one in billions).[32]
The ludic fallacy. Probabilities are based on simple models that ignore real (if remote) possibilities. Poker players do not consider that an opponent may draw a gun rather than a card. The insured (and governments) assume that insurers will remain solvent, but see AIG and systemic risk.
Other types of misuse[edit]
Other misuses include comparing apples and oranges, using the wrong average,[33] regression toward the mean,[34] and the umbrella phrase garbage in, garbage out.[35] Some statistics are simply irrelevant to an issue.[36]
Anscombe's quartet is a made-up dataset that exemplifies the shortcomings of simple descriptive statistics (and the value of data plotting before numerical analysis).
See also[edit]
Deception
Ethics in mathematics
Misleading graph, discusses problems arising from graphical presentations.
Numbers Guy weekly column in The Wall Street Journal by Carl Bialik
References[edit]
Notes[edit]
Jump up ^ Some data on accuracy of polls is available. Regarding one important poll by the U.S. government, "Relatively speaking, both sampling error and non-sampling [bias] error are tiny."[22] The difference between the votes predicted by one private poll and the actually tally for American presidential elections is available for comparison at "Election Year Presidential Preferences: Gallup Poll Accuracy Record: 1936-2012". The predictions were typically calculated on the basis of less than 5000 opinions by likely voters.[23]
Sources[edit]
Jump up ^ Abelson, Robert P. (1995). Statistics as Principled Argument. Lawrence Erlbaum Associates. ISBN 0-8058-0528-1. ... the purpose of statistics is to organize a useful argument from quantitative evidence, using a form of principled rhetoric.
Jump up ^ Porter, Theodore (1995). Trust in Numbers: The Pursuit of Objectivity in Science and Public Life. Princeton, N.J: Princeton University Press. ISBN 0-691-03776-0. Porter considered the history of cost-benefit analysis. While this is perhaps more economical than statistical, it is a quantitative decision-making technique considered to be in the statistical domain.
Jump up ^ Spirer, Spirer & Jaffe 1998, p. 1.
Jump up ^ Gardenier, John; Resnik, David (2002). "The misuse of statistics: concepts, tools, and a research agenda". Accountability in Research: Policies and Quality Assurance. 9 (2): 65–74. doi:10.1080/08989620212968. PMID 12625352.
Jump up ^ Fischer, David (1979). Historians' fallacies: toward a logic of historical thought. New York: Harper & Row. pp. 337–338. ISBN 978-0060904982.
Jump up ^ Strasak, Alexander M.; Qamruz Zaman; Karl P. Pfeiffer; Georg Göbel; Hanno Ulmer (2007). "Statistical errors in medical research-a review of common pitfalls". Swiss Medical Weekly. 137: 44–49. PMID 17299669. In this article anything less than best statistical practice is equated to the potential misuse of statistics. In a few pages 47 potential statistical errors are discussed; errors in study design, data analysis, documentation, presentation and interpretation. "[S]tatisticians should be involved early in study design, as mistakes at this point can have major repercussions, negatively affecting all subsequent stages of medical research."
Jump up ^ Indrayan, Abhaya (2007). "Statistical fallacies in orthopedic research". Indian Journal of Orthopaedics. 41 (1): 37. doi:10.4103/0019-5413.30524. Contains a rich list of medical misuses of statistics of all types.
Jump up ^ Spirer, Spirer & Jaffe 1998, chapters 7 & 8.
Jump up ^ Spirer, Spirer & Jaffe 1998, chapter 3.
Jump up ^ Spirer, Spirer & Jaffe 1998, chapter 4.
Jump up ^ Adler, Robert; John Ewing; Peter Taylor (2009). "Citation statistics". Statistical Science. 24.1: 1–14. doi:10.1214/09-STS285. Scientific papers and scholarly journals are often rated by "impact" - the number of times cited by later publications. Mathematicians and statisticians conclude that impact (while relatively objective) is not a very meaningful measure. "The sole reliance on citation data provides at best an incomplete and often shallow understanding of research—an understanding that is valid only when reinforced by other judgments. Numbers are not inherently superior to sound judgments."
Jump up ^ Spirer, Spirer & Jaffe 1998, chapter title.
Jump up ^ Spirer, Spirer & Jaffe 1998, chapter 5.
Jump up ^ Weatherburn, Don (November 2011), "Uses and abuses of crime statistics" (PDF), Crime and Justice Bulletin: Contemporary Issues in Crime and Justice, NSW Bureau of Crime Statistics and Research, 153, ISBN 9781921824357, ISSN 1030-1046, Archived from the original on June 21, 2014 CS1 maint: Unfit url (link) This Australian report on crime statistics provides numerous examples of interpreting and misinterpreting the data. "The increase in media access to information about crime has not been matched by an increase in the quality of media reporting on crime. The misuse of crime statistics by the media has impeded rational debate about law and order." Among the alleged media abuses: selective use of data, selective reporting of facts, misleading commentary, misrepresentation of facts and misleading headlines. Police and politicians also abused the statistics.
Jump up ^ Krugman, Paul (1994). Peddling prosperity: economic sense and nonsense in the age of diminished expectations. New York: W.W. Norton. p. 111. ISBN 0-393-03602-2.
Jump up ^ Spirer, Spirer & Jaffe 1998.
Jump up ^ Kahneman 2013, p. 102.
Jump up ^ Moore & Notz 2006, p. 59.
Jump up ^ Moore & Notz 2006, p. 97.
Jump up ^ Moore & McCabe 2003, pp. 252–254.
Jump up ^ Moore & Notz 2006, p. 53, Sample surveys in the real world.
Jump up ^ Freedman, Pisani & Purves 1998, chapter 22: Measuring Employment and Unemployment, p. 405.
Jump up ^ Freedman, Pisani & Purves 1998, pp. 389-390.
Jump up ^ Farley, John W. (2003). Barrett, Stephen, ed. "Power Lines and Cancer: Nothing to Fear". Quackwatch.
Jump up ^ Vince, Gaia (2005-06-03). "Large study links power lines to childhood cancer". New Scientist. Archived from the original on August 16, 2014. CS1 maint: Unfit url (link) Cites: Draper, G. (2005). "Childhood cancer in relation to distance from high voltage power lines in England and Wales: a case-control study". BMJ. 330 (7503): 1290. doi:10.1136/bmj.330.7503.1290. PMC 558197  . PMID 15933351.
Jump up ^ Moore & McCabe 2003, pp. 463.
Jump up ^ Rozeboom, William W. (1960). "The fallacy of the null-hypothesis significance test". Psychological Bulletin. 57 (5): 416–428. doi:10.1037/h0042040.
Jump up ^ Moore & McCabe 2003, p. 466.
Jump up ^ Neylon, C (2009). "Scientists lead the push for open data sharing". Research Information. Europa Science. 41: 22–23. ISSN 1744-8026. Archived from the original on December 3, 2013. CS1 maint: Unfit url (link)
Jump up ^ Freedman, Pisani & Purves 1998, chapter 9: More about correlations, §3: Some exceptional cases
Jump up ^ Seife, Charles (2011). Proofiness: how you're being fooled by the numbers. New York: Penguin. pp. 203–205 and Appendix C. ISBN 9780143120070. Discusses the notorious British case.
^ Jump up to: a b Michael Kaplan and Ellen Kaplan, Chances Are (Adventures in Probability), Viking Penguin, 2006, pp. 192-5. ISBN 978-0143038344
Jump up ^ Huff 1954, chapter 2.
Jump up ^ Kahneman 2013, chapter 17.
Jump up ^ Hooke 1983, §50.
Jump up ^ Campbell 1974, chapter 3: Meaningless statistics.
Further reading[edit]
Wikimedia Commons has media related to Misuse of statistics.
Wikiquote has quotations related to: Misuse of statistics
Campbell, Stephen (1974). Flaws and fallacies in statistical thinking. Prentice Hall. ISBN 0-486-43598-9.
Christensen, R.; Reichert, T. (1976). "Unit Measure Violations in Pattern Recognition, Ambiguity and Irrelevancy". Pattern Recognition. 4: 239–245. doi:10.1016/0031-3203(76)90044-3.
Ercan I, Yazici B, Yang Y, Ozkaya G, Cangur S, Ediz B, Kan I (2007). "Misusage of Statistics in Medical Researches" (PDF). European Journal of General Medicine. 4 (3): 127–133. Archived from the original on November 13, 2014. CS1 maint: Uses authors parameter (link) CS1 maint: Unfit url (link)
Ercan I, Yazici B, Ocakoglu G, Sigirli D, Kan I (2007). "Review of Reliability and Factors Affecting the Reliability" (PDF). InterStat. Archived from the original on August 28, 2013. CS1 maint: Uses authors parameter (link) CS1 maint: Unfit url (link)
Freedman, David; Pisani, Robert; Purves, Roger (1998). Statistics (3rd ed.). W.W. Norton. ISBN 978-0-393-97083-8.
Hooke, Robert (1983). How to tell the liars from the statisticians. New York: M. Dekker. ISBN 0-8247-1817-8.
Huff, Darrell (1954). How to Lie with Statistics. W. W. Norton & Company. LCCN 53013322. OL 6138576M.
Kahneman, Daniel (2013). Thinking, fast and slow. New York: Farrar, Straus and Giroux. ISBN 9780374533557.
Moore, David; McCabe, George P. (2003). Introduction to the practice of statistics (4th ed.). New York: W.H. Freeman and Co. ISBN 0716796570.
Moore, David; Notz, William I. (2006). Statistics: concepts and controversies (6th ed.). New York: W.H. Freeman. ISBN 9780716786368.
Spirer, Herbert; Spirer, Louise; Jaffe, A. J. (1998). Misused statistics (revised and expanded 2nd ed.). New York: M. Dekker. ISBN 978-0824702113. The book is based on several hundred examples of misuse.
Oldberg, T. and R. Christensen (1995) "Erratic Measure" in NDE for the Energy Industry 1995, The American Society of Mechanical Engineers. ISBN 0-7918-1298-7 (pages 1–6) Republished on the Web by ndt.net
Oldberg, T. (2005) "An Ethical Problem in the Statistics of Defect Detection Test Reliability," Speech to the Golden Gate Chapter of the American Society for Nondestructive Testing. Published on the Web by ndt.net
Stone, M. (2009) Failing to Figure: Whitehall's Costly Neglect of Statistical Reasoning, Civitas, London. ISBN 1-906837-07-4
Galbraith, J.; Stone, M. (2011). "The abuse of regression in the National Health Service allocation formulae: Response to the Department of Health's 2007 'resource allocation research paper'". Journal of the Royal Statistical Society, Series A. 174 (3): 517–528. doi:10.1111/j.1467-985X.2010.00700.x.
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Siblicide
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A Nazca booby (Sula granti) with a chick and egg. When the second egg hatches, any siblings present will almost certainly kill their younger brother or sister.
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Siblicide (attributed by behavioural ecologist Doug Mock to Barbara M. Braun) is the killing of an infant individual by its close relatives (full or half siblings). It may occur directly between siblings or be mediated by the parents. The evolutionary drivers may be either indirect benefits for the genetic viability of a population or direct benefits for the perpetrators. Siblicide has mainly, but not only, been observed in birds.
The word is also used as a unifying term for fratricide and sororicide in the human species; unlike these more specific terms, it leaves the sex of the victim unspecified.
Siblicidal behavior can be either obligate or facultative. Obligate siblicide is when a sibling almost always ends up being killed. Facultative siblicide means that siblicide may or may not occur, based on environmental conditions. In birds, obligate siblicidal behavior results in the older chick killing the other chick(s).[1] In facultative siblicidal animals, fighting is frequent, but does not always lead to death of a sibling; this type of behavior often exists in patterns for different species. For instance, in the blue-footed booby, a sibling may be hit by a nest mate only once a day for a couple of weeks and then attacked at random, leading to its death. More birds are facultatively siblicidal than obligatory siblicidal.[2] This is perhaps because siblicide takes a great amount of energy and is not always advantageous.
Siblicide generally only occurs when resources, specifically food sources, are scarce.[1] Siblicide is advantageous for the surviving offspring because they have now eliminated most or all of their competition. It is also somewhat advantageous for the parents because the surviving offspring most likely have the strongest genes, and so, will pass these genes onto their offspring later in life, creating a strong line of genetics.
Some parents encourage siblicide, while others prevent it.[citation needed] If resources are scarce, the parents may encourage siblicide because only some offspring will survive anyway, so they want the strongest offspring to survive. By letting the offspring kill each other, it saves the parents time and energy that would be wasted on feeding offspring that most likely would not survive anyway.
Parent–offspring conflict is a theory which states that offspring can take actions to advance their own fitness while decreasing the fitness of their parents and that parents can increase their own fitness while simultaneously decreasing the fitness of their offspring. This is one of the driving forces of siblicide because it increases the fitness of the offspring by decreasing the amount of competition they have.[3] Parents may either discourage or accept siblicide depending on whether it increases the probability of their offspring surviving to reproduce.[3]
Inclusive fitness is defined as an animal's individual reproductive success, plus the positive and/or negative effects that animal has on its sibling's reproductive success, multiplied by the animal's degree of kinship. In instances of siblicide, the victim is usually the youngest sibling. This sibling's reproductive value can be measured by how much it enhances or detracts from the success of other siblings, therefore this individual is considered to be marginal. The marginal sibling can act as an additional element of parental success if it, as well as its siblings, survive. If an older sibling happens to die unexpectedly, the marginal sibling is there to take its place; this acts as insurance against the death of another sibling, which depends on the likelihood of the older sibling dying.
Contents
[hide]
1 Mathematical representation
2 Examples
2.1 In birds
2.2 In other animals
2.3 In humans
3 In fiction
4 See also
5 References
6 Further reading
Mathematical representation[edit]
The cost and effect siblicide has on a brood's reproductive success can be broken down into an algebraic equation. M {\displaystyle M} is the level of parental investment in the entire brood, with an absolute maximum value MH(0 ≤M ≤M"H)." A parent investing M {\displaystyle M} units of parental investment (PI) in its current brood can expect a future reproductive success f ( M ) {\displaystyle f(M)} given by
f H {\displaystyle fH} if M ≤ 0
f(M)= { fH[1-(M/MH)^θ ] if 0 < M < M H {\displaystyle 0<M<MH}
if MH≤M,
f H {\displaystyle fH} is the parents' future reproductive success, if it makes no reproductive attempt. The parameter ᶿ determines the relationship between parental investment and the cost of reproduction. The equation indicates that as M {\displaystyle M} increases, the future reproductive success of the parent decreases.
The probability p(m) that a chick joins the breeding population after receiving M units of PI is
P ( m ) = 1 − M v / m {\displaystyle P(m)=1-Mv/m} if m > m v {\displaystyle m>mv}
if m ≤ mv
Examples[edit]
In birds[edit]
Cattle egrets, Bubulcus ibis, exhibit asynchronous hatching and androgen loading in the first two eggs of their normal three-egg clutch. This results in older chicks being more aggressive and having a developmental head start. If food is scarce the third chick often dies or is killed by the larger siblings and so parental effort is distributed between the remaining chicks, which are hence more likely to survive to reproduce. The extra "excess" egg is possibly laid either due to exploit the possibility of elevated food abundance (as seen in the blue-footed booby, Sula nebouxii) or due to the chance of sterility in one egg. This is suggested by studies into the common grackle, Quiscalus quiscula[4] and the masked booby, Sula dactylatra.[2]
The theory of kin selection may be seen as a genetically mediated altruistic response within closely related individuals whereby the fitness conferred by the altruist to the recipient outweighs the cost to itself or the sibling/parent group. The fact that such a sacrifice occurs indicates an evolutionary tendency in some taxa toward improved vertical gene transmission in families or a higher percentage of the unit in reaching a reproductive age in a resource-limited environment.
The closely related masked and Nazca boobies are both obligately siblicidal species, while the blue-footed booby is a facultatively siblicidal species.[5] In a facultatively siblicidal species, aggression occurs between siblings but is not always lethal, whereas in an obligately siblicidal species, aggression between siblings always leads to the death of one of the offspring.[1][2] All three species have an average brood size of two eggs,[5][6] which are laid within approximately four days of each other.[6][7] In the few days before the second egg hatches, the first-born chick, known as the senior chick or A-chick, enjoys a period of growth and development during which it has full access to resources provided by the parent bird. Therefore, when the junior chick (B-chick) hatches, there is a significant disparity in size and strength between it and its older sibling.[8][9]
In these three booby species, hatching order indicates chick hierarchy in the nest.[1][8] The A-chick is dominant to the B-chick, which in turn is dominant to the C chick, etc. (when there are more than two chicks per brood)[9] Masked booby and Nazca booby dominant A-chicks always begin pecking their younger sibling(s) as soon as they hatch;[9] moreover, assuming it is healthy, the A-chick usually pecks its younger sibling to death or pushes it out of the nest scrape within the first two days that the junior chick is alive.[10] Blue-footed booby A-chicks also express their dominance by pecking their younger sibling. However, unlike the obligately siblicidal masked and Nazca booby chicks, their behavior is not always lethal.[7] A study by Lougheed and Anderson (1999) reveals that blue-footed booby senior chicks only kill their siblings in times of food shortage. Furthermore, even when junior chicks are killed, it does not happen immediately. According to Anderson, the average age of death of the junior chick in a masked booby brood is 1.8 days, while the average age of death of the junior chick in a blue-footed booby brood may be as high as 18 days.[5] The difference in age of death in the junior chick in each booby species is indicative of the type of siblicide that the species practices. Facultatively siblicidal blue-footed booby A-chicks only kill their nest mate(s) when necessary. Obligately siblicidal masked and Nazca booby A-chicks kill their sibling no matter if resources are plentiful or not; in other words, siblicidal behavior occurs independently of environmental factors.
Blue-footed boobies are less likely to commit siblicide and if they do, they commit it later after hatching than masked boobies. In a study, the chicks of blue-footed and masked boobies were switched to see if the rates of siblicide would be affected by the foster parents. It turns out that the masked boobies that were placed under the care of blue-footed booby parents committed siblicide less often than they would normally. Similarly, the blue-footed booby chicks placed with the masked booby parents committed siblicide more often than they normally did, indicating that parental intervention also affects the offspring's behavior.
In another experiment which tested the effect of a synchronous brood on siblicide, three groups were created: one in which all the eggs were synchronous, one in which the eggs hatched asynchronously, and one in which asynchronous hatching was exaggerated. It was found that the synchronous brood fought more, was less likely to survive than the control group, and resulted in lower parental efficiency. The exaggerated asynchronous brood also had a lower survivorship rate than the control brood and forced parents to bring more food to the nest each day, even though not as many offspring survived.
Originally proposed by Dorward (1962), the insurance egg hypothesis (IEH) has quickly become the most widely supported explanation for avian siblicide as well as the overproduction of eggs in siblicidal birds.[2] The IEH states that the extra egg(s) produced by the parent serves as an "insurance policy" in the case of the failure of the first egg (either it did not hatch or the chick died soon after hatching). When both eggs hatch successfully, the second chick, or B-chick, is known as the marginal offspring; otherwise stated, it is marginal in the sense that it can add to or subtract from the evolutionary success of its family members.[1] It can increase reproductive and evolutionary success in two primary ways. Firstly, it represents an extra unit of parental success if it survives along with its siblings. In the context of Hamilton's inclusive fitness theory, the marginal chick increases the total number of offspring successfully produced by the parent and therefore adds to the gene pool that the parent bird passes to the next generation. Secondly, it can serve as a replacement for any of its siblings that do not hatch or die prematurely.
In other animals[edit]
Siblicide (brood reduction) in spotted hyenas (Crocuta crocuta) resulted in the champions achieving a long-term growth rate similar to that of singletons and thus significantly increased their expected survival. The incidence of siblicide increased as the average cohort growth rate declined. When both cubs were alive, total maternal input in siblicidal litters was significantly lower than in non-siblicidal litters.[11] Once siblicide has occurred, the growth rates of siblicide survivors substantially increased, indicating that mothers don't reduce their maternal input after siblicide has occurred. Also, facultative siblicide can evolve when the fitness benefits gained after the removal of a sibling by the dominant offspring, exceeds the costs acquired in terms of decreasing that sibling's inclusive fitness from the death of its sibling.
Some mammals sometimes commit siblicide for the purpose of gaining a larger portion of the parent's care. In spotted hyenas, pups of the same sex exhibit siblicide more often than male-female twins. Sex ratios may be manipulated in this way and the dominant status of a female and transmission of genes may be ensured through a son or daughter which inherits this solely, receiving much more parental nursing and decreased sexual competition.
Siblicidal "survival of the fittest" is also exhibited in parasitic wasps, which lay multiple eggs in a host, after which the strongest larva kills its rival sibling. Another example is when mourning cloak larvae will eat non-hatched eggs.[12]
In humans[edit]
Siblicide can also be seen in humans in the form of twins in the mother's womb. One twin may grow to be an average weight, while the other is underweight. This is a result of one twin taking more nutrients from the mother than the other twin. In cases of identical twins, they may even have Twin to Twin Transfusion Syndrome (TTTS).[13] This means that the twins share the same placenta and blood and nutrients can then move between twins. The twins may also be suffering from Intrauterine Growth Restriction (IUGR), meaning that there is not enough room for both of the twins to grow.[14] All of these factors can limit the growth of one of the twins while promoting the growth of the other. While one of the twins may not die because of these factors, it is entirely possible that their health will be compromised and lead to complications after their birth.
Siblicide in humans can also manifest itself in the form of murder. There was a significantly greater proportion of accidental deaths in half-siblings, stepsiblings, and sibling in-laws than in full siblings. This type of killing (siblicide) is rarer than other types of killings. Genetic relatedness may be an important moderator of conflict and homicide among family members, including siblings. Siblings may be less likely to kill a full sibling because that would be a decrease in their own fitness. The cost of killing a sibling is much higher than the fitness costs associated with the death of a sibling-in-law because the killer wouldn't be losing 50% of their genes.[15] Siblicide was found to be more common in early to middle adulthood as opposed to adolescence.[16] Yet, there is still a tendency for the killer to be the younger party when the victim and killer were of the same sex. The older individual was most likely to be the killer if the incident were to occur at a younger age.
In fiction[edit]
In Jurassic World, the engineered hybrid dinosaur Indominus rex is told to have eaten her sibling before it was even hatched from its egg.
See also[edit]
Parent–offspring conflict
Fratricide, the killing of a brother
Sororicide, the killing of a sister
Infanticide (zoology), a related behaviour
Nazca booby (displays obligate siblicide)
Sibling abuse
Sibling rivalry
Intrauterine cannibalism
References[edit]
^ Jump up to: a b c d e Mock, D. W.; Drummond, H. & Stinson, C. H. (1990). "Avian Siblicide" (PDF). American Scientist. 78: 438–449. [dead link]
^ Jump up to: a b c d Anderson, David J. (March 1990). "Evolution of obligate siblicide in boobies: A test of the insurance egg hypothesis" (PDF). The American Naturalist. 135 (3): 334–350. doi:10.1086/285049.
^ Jump up to: a b Rodríguez-Gironés, M. A. (1996). "Siblicide: The Evolutionary Blackmail" (PDF). The American Naturalist. 148 (1): 101–122. doi:10.1086/285913. Archived from the original (PDF) on September 28, 2010.
Jump up ^ Henry F. Howe (1976). "Egg Size, Hatching Asynchrony, Sex, and Brood Reduction in the Common Grackle". Ecology. 57 (6): 1195–1207. doi:10.2307/1935044.
^ Jump up to: a b c Anderson, D. J. (1995). "The role of parents in siblicidal brood reduction of two booby species" (PDF). The Auk. 112 (4): 860–869. doi:10.1007/BF00302994.
^ Jump up to: a b Drummond, H. & C. Rodríquez (2008). "No reduction in aggression after loss of a broodmate: a test of the brood size hypothesis". Behavioral Ecology and Sociobiology. 63 (3): 321–327. doi:10.1007/s00265-008-0664-7.
^ Jump up to: a b Lougheed, L. W. & D. J. Anderson (1999). "Parent blue-footed boobies suppress siblicidal behavior of offspring". Behavioral Ecology and Sociobiology. 45 (1): 11–18. doi:10.1007/s002650050535.
^ Jump up to: a b Gonzalez-Voyer, A.; T. Szekély & H. Drummond (2007). "Why do some siblings attack each other? Comparative analysis of aggression in avian broods". Evolution. 61 (8): 1946–1955. PMID 17683436. doi:10.1111/j.1558-5646.2007.00152.x.
^ Jump up to: a b c Mock, D. W. (2004). More than kin and less than kind: the evolution of family conflict. Cambridge, Mass: Belknap Press of Harvard University Press. ISBN 9780674012851.
Jump up ^ Clifford, L. D. & D. J. Anderson (2001). "Experimental demonstration of the insurance value of extra eggs in an obligately siblicidal seabird". Behavioral Ecology. 12 (3): 340–347. doi:10.1093/beheco/12.3.340.
Jump up ^ Hofer, H. & East, M. L. (2007). "Siblicide in Serengeti spotted hyenas: a long-term study of maternal input and cub survival". BehavEcolSociobiol. Springer-Verlag. 62 (3): 341–351. doi:10.1007/s00265-007-0421-3. [dead link]
Jump up ^ "The Virtual Nature Trail at Penn State New Kensington". Pennsylvania State University. Retrieved October 4, 2013.
Jump up ^ Sebire, N.; Souka, A.; Skentou, H.; Geerts, L. & Nicolaides, K. (2000). "Early prediction of severe twin-to-twin transfusion syndrome". Human Reproduction. 15 (9): 2008–2010. PMID 10967005. doi:10.1093/humrep/15.9.2008.
Jump up ^ Resnik, R. (2002). "Intrauterine Growth Restriction" (PDF). Obstetrics and Gynecology. 99 (3): 490–496. PMID 11864679. doi:10.1097/00006250-200203000-00020.
Jump up ^ Michalski, R. L.; Russell, D. P.; Shackelford, T. K. & Weekes-Shackelford, V. A. (2007). "Siblicide and genetic relatedness in Chicago, 1870-1930" (PDF). Homicide Studies. 11 (3): 231–237. doi:10.1177/1088767907304098.
Jump up ^ Daly, M.; Wilson, M.; Salmon, C. A.; Hiraiwa-Hasegawa, M. & Hasegawa, T. (2001). "Siblicide and seniority". Homicide Studies. 5 (1): 30–45. doi:10.1177/108876790100500100.
Further reading[edit]
Alcock, J. (1998). Animal Behaviour (6th ed.). Sinauer Associates. ISBN 9781605351957.
Smith R. L.; Smith T. M. (2001). Ecology and Field Biology (6th ed.). Benjamin Cummings. ISBN 9780321068811.
Russell, D. P.; Michalski, R. L.; Shackelford, T. K. & Weekes-Shackelford, V. A. (2007). "A preliminary investigation of siblicide as a function of genetic relatedness" (PDF). Journal of Forensic Sciences. 52: 738–739. doi:10.1111/j.1556-4029.2007.00436.x.
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This page was last edited on 21 April 2017, at 16:25.
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