Statistical Fallacies

• Logical Fallacy of Abuse of Statistics / Lying with Statistics / Statistical Fallacy Misused Statistics: occurs when statistics are used to assert a falsehood.
• Misunderstanding the Nature of Statistics / Innumeracy: occurs when any of the statistical fallacies are committed due to ignorance of the math. These fallacies include the gamblers fallacy, hasty generalization, false precision, biased statistics, the ludic fallacy, and others.
• Clustering Illusion: occurs when the clustering of events that naturally takes place in a random process are not really random events. This fallacy is a statistical fallacy and usually occurs when the sample size is too small or non-representative. One thing that should be noted is the fact that God controls what we call random processes. He uses these processes to bless those who are following Him or to test them and prepare them to rule in the Kingdom of God. That means that there are no truly random processes. However, what we call random processes are merely examples of how, in His faithfulness, God is consistent. We know of God's active role through revelation.
• Bad Statistical Data: occurs when numbers are skewed, giving erroneous results. EXAMPLE When people are asked questions about their past, they may not remember or they may not want to answer honestly.
• Biased Statistical Method: occurs when the methods of getting the data are skewed, either intentionally or unintentionally. EXAMPLE Leading questions. EXAMPLE Making the desired choice the default or putting the desired choice in a position that makes it more likely to be selected. EXAMPLE Many things in science cannot be observed directly, so assumptions are made. Those assumptions may affect statistics.
• Biased Calculation: occurs when calculations are dependent on presuppositions. EXAMPLE In calculating gene mutation rates, secular scientists take the genome of a chimp and compare it to the genome of a human (which only makes sense if you presuppose Darwinism) and then divide the number of mutations by 6 million (the presupposed number of years since chimps and humans are presupposed to have diverged from some kind of unknown ape-like creature).
• Biased Conclusion from Statistics: occurs when presupposition leads the conclusion beyond what can be deduced from the facts.
• Biased Reporting of Statistics: occurs when reports that display statistical data are biased. EXAMPLE Graphics that are not proportioned to the numbers EXAMPLE leaving out vital information EXAMPLE using emotional language EXAMPLE over-stating the case EXAMPLE making ambiguous comparisons EXAMPLE neglecting the base line EXAMPLE playing with mean, median, and mode EXAMPLE misreporting the numbers EXAMPLE failure to report all (supposed) anomalies EXAMPLE failure to report all assumptions, alternative assumptions, and honest evalutations of the ramifications of using the alternative assumptions
• Logical Fallacy of Biased Statistics / Loaded Sample / Prejudiced Statistics / Prejudiced Sample / Loaded Statistics / Biased Induction / Biased Generalization / Unrepresentative Sample / Unrepresentative Generalization / Sampling Bias: occurs when a data set is chosen in way that is designed to get a certain result. EXAMPLE Durex going to popular spring break locations to ask about sexual habits.
• Generalizing from a Hypostatization: To hypostatize is to regard or treat a concept or idea as a distinct substance or reality. A hypostatization is something that is dreamt up and yet considered real: EXAMPLE the Big-Bang-Billions-of-Years-No-Flood-Molecules-to-Man story EXAMPLE Atheism EXAMPLE Agnosticism EXAMPLE Hedonism EXAMPLE Belief in natural human goodness without Christ EXAMPLE Theologies that rationalize beyond what God reveals to us through Scripture EXAMPLE “Theology is a study with no answers because it has no subject matter.” This statement makes the assertion that God does not exist and that God doesn’t speak to His people. It is an assertion contrary to fact. The reason that this assertion contrary to fact is made with such confidence is because of the hypostatization of Atheism or Agnosticism. Both Atheism and Agnosticism are concepts that are treated, by a few people, as facts. Since they seem to be facts to these people, they are very limiting. They disallow exploration of the real fact that everyone who seeks Christ in sincerity, humility, and persistence, and with a will to do His will does find Him.
• Error in Sampling:occurs when a bad data set is chosen, creating a false impression. A sampling error is defined by the differences between the sample and the entire group which the sample is supposed to represent. The sample can be of people's opinions, people's physical condition, people's characteristics, parts coming from an assembly line, plants in the wild, plants on farms, plants on a single farm, fossils, grains of sand, or any other thing. Errors in sampling fallacies can be committed accidentally or purposely for a nefarious purpose. The results of sampling cannot be used to determine truth. It can only result in inductive reasoning. If an attempt to use inductive reasoning as a basis of a premise in deductive reasoning, the deductive reasoning is unsound. EXAMPLE The Kinsey report is a famous example of error in sampling and one that did a tremendous amount of damage.
  
• Avoiding Specific Numbers: occurs when statistics are given with either hedging words surrounding them or using general terms. This is generally a hedging tactic when claims are supported by questionable evidence. EXAMPLE Newspaper Comment: "[a candidate for office] is stressing job growth, but religiously avoiding specific numbers. Evidently, if she wins, she will take a look-back approach in four years, declaring her jobs policy a success, whether 5,000 or 500,000 jobs are created." This is the use of the logical fallacy of avoiding specific numbers for the purpose of making it possible to later declare victory regardless of the outcome.
• Logical Fallacy of Fake Precision / Over Precision / False Precision / Misplaced Precision / Spurious Accuracy: occurs when the language to communicate statistics implies much more accuracy than the data allows. Sometimes, just the comment that one thing is more likely than another is false precision. The word, "likely," implies a percentage of probability. What is the exact percentage that was calculated? How was the research conducted? How were the numbers derived? In many cases, the numbers were pulled from the air (PFA). EXAMPLE “We know that the Earth is 4.54 billion years old.” The methods and the math don’t allow that kind of accuracy, and we know, by revelation, that this is wrong. However, a statistic like this to this level of accuracy sure implies a high level of confidence. EXAMPLE “We know that the Earth is 6,349.5 years old.” Taking the information that God is giving us through the Bible, we can only roughly estimate the age of the Earth using genealogies. It is Divine revelation, but God doesn't get that specific. We can't dogmatically claim to know that the Earth is 6,000 years old. We know that God created the Heavens and the Earth in six days and we know the number of generations between Adam and Christ. That's about it. Even though a plain reading of Scripture seems to indicate a young Earth; even though there is zero observed evidence and only circular reasoning and speculations that support old Earth stories, we can't even deny the possibility that God could have done something that Scripture doesn't hint at and that has left no scientific evidence. It is possible. It just is not worth the time to think about it. We really cannot estimate the age of the Universe except from the standpoint of Earth since God has not told us how He got distant starlight to the Earth. Using Einstein’s Theory of Relativity, God could have caused billions of years to pass in distant space while literally no time passed on Earth during the creation week, but we have no revelation on that. To say that this happened would be pure speculation. Some people speculate about a prior creation between the first and second verse of Scripture; however, there are severe problems with this speculation. It is fairly well falsified. Others speculate that the first few days of the Creation Week were billions of years long. Beyond being very speculative, this story doesn't work scientifically or logically. That being said, if God deems it important for us to know the exact amount of time that passed since the Creation (or any other event that has taken place), He is well able to provide the information. In the mean time, there is no need to commit fallacies of false precision.
• Self-Selected Biased Sample: occurs when return of a survey is voluntary, resulting in a biased sample with those people with strong feeling being over-represented (since these are the ones who are more likely to complete the survey). Internet surveys, texting polls, or phone polls are great for this, and those who want to sway the poll actively recruit people to take the survey. Certain people are less likely to cooperate with a phone survey. People taking surveys door to door are less likely to enter certain neighborhoods.
• Comparing Two Things Statistically that are not Technically Comparable / Statistical Apples and Oranges: occurs when certain element of two unrelated things are compared statistically. By the way, you can indeed compare apples to oranges, but not for some purposes. You can compare which one you would prefer to eat, for instance. You can statistically compare the financial return on farming them. However, there are many times where it is irrational to compare two things depending on what you are trying to prove. EXAMPLE Sandy: "I can tell you that I am a much better person than most Christians that I have seen." Rocky: "Based on what standard?" There are many things wrong with Sandy's claim. First, without God's Law, there is no absolute standard. Agrippa's Trilemma creates a situation in which (without Divine revelation) it is impossible to make any sound conclusion about anything. This is even more true when making conclusions about what is a valid standard of a "good person." Sandy's sample size is far to small as well. Regarding the comparison of two things that cannot be rationally compared, however, Sandy's statement falls apart.
• Logical Fallacy of Ludus / Ludic Fallacy: occurs when statistical models are constructed and applied in complex domains where there are too many variables to account for and know with certainty. It involves applying naive and simplified statistical models in complex domains. The ludic fallacy is very common in supposed predictions in the scientific community. From an anti-Christian website: "If all we have is “God” with no attributes, there is a 50% chance that this God exists.  As soon as we add an attribute though, the chances go lower.  If you have a God that created the universe for instance, you have a 50% chance that God created the universe and you have a 50% chance of God existing.  That means that you actually have a 25% chance.  If that God created man, suddenly it’s a 1/8 chance.  If that God created dogs, it goes to 1/16 and so on.  Let’s say that God created every atom in the universe.  That alone is roughly a 1/10^80 chance that there is a god that created every single atom in the universe." That is what the ludic fallacy looks like. The reality is that God's existence is 100% because He has personally revealed Himself to us. Our own existence would be questionable except for the fact that He has revealed to us that we actually exist and that He holds us responsible for our thoughts, words, and deeds.
• Fishing for Data / Data Dredging / Data Fishing / Data Snooping / Equation Fitting: occurs when patterns in data seem to point to certain conclusions, but those patterns are actually the result of random chance. Data mining is used to uncover relationships. In this process, statistics can yield false relationships, patterns that just happen to fall together when no real relationship exists. This can be especially deceiving when it coincides with an unfounded belief—especially a group-held false belief, which just makes the confirmation bias problem more severe. Often, numbers will be crunched until something pops up that looks like it favors the desired conclusion. Those numbers will be given elevated status over all the other results to create the impression that the desired conclusion has evidence to support it. Another way of equation fitting is to make assumptions that make the data fit a desired conclusion. After crunching numbers, there are some numbers that aren't quite right. They do show promise, though. With a little tweak, they would prove the desired conclusion. Enter the magic of proof by assumption. If we make some assumptions, we can make the numbers fit the desired conclusion very well. Other techniques can be used, such as eliminating some of the results. They must be errors since they don't fit the desired conclusion. EXAMPLE All methods of trying to determine the age of things without an eye witness or written account of what happened and when it happened.
• Logical Fallacy of Base Rate Neglect / Base Rate Fallacy / Neglecting Base Rates / Base Rate Bias / Prosecutor's Fallacy / Ignoring Proportionality: occurs when someone uses specific instances or unrelated instances in favor of verified statistical information. The corresponding fallacy is to try to apply statistical analysis to something that does not yield itself to this type of analysis, such as miracles, God, the spiritual real, Heaven, Hell, etc. In this case, a person who wanted to prove a certain thing would dismiss any and all specific instances in favor of statistics that could not possibly measure what they claim to measure. This is sometimes called the prosecutor's fallacy, although it is not limited to prosecutors. It gets this name from prosecutors who sway juries by pointing out that the defendant matches a very specific description and a very small percentage of the population match that description. However, it doesn’t take into account the large population in which quite a few other individuals also match the same description. If only one in half a million people matches the description and there are 20 million people in the city, then there are 40 other people who also match the description.
• Logical Fallacy of Isolated Examples / Unrepresentative Sample: occurs when non-typical or non-representative examples are used to 'prove' a general claim. This is associated with hasty generalization. This fallacy involves giving some of the facts but leaving out pertinent facts that would change the conclusion.
• Logical Fallacy of Hasty Generalization / False Generalization / Glittering Generalities / Jumping to Conclusions / Hasty Decision / Leaping to Conclusions / Where There’s Smoke, There’s Fire / Lonely Fact / Proof by Example: occurs when a claim is made based on an incomplete or insufficient amount of evidence, which may include claims based on a sample too small or not considering all the variables. Keep in mind that not everything is a debate. Sometimes, people just explain things. When someone uses an example to make an explanation more clear, it is irrational to start an argument with him or her about whether that proves his or her point. Also, making generalizations is always inductive reasoning, which is never as solid as deductive reasoning. And, you rarely (if ever) get to see the actual raw data before it has been monkeyed with, so you have to make decisions based on trust of people whom you don’t know. When generalizations are made that conflict with what God is telling you through Scripture, be very skeptical. You may be reading things into Scripture. Go to prayer about it and see what God says. Eventually, He will answer your question if you persist.
• Argument from Small Numbers / Small Sample Size Bias: occurs when a generalization is made from a small sample size. It is a hasty generalization and a statistical fallacy.
• General Rule Fallacy: occurs when it is assumed that things are a certain way in most cases, and, therefore, it is that way in a particular case. It is a form of hasty generalization.
• Logical Fallacy of Specificity: occurs when an overly specific conclusion is drawn from the evidence. This is a kind of jumping to conclusions. 
• Logical Fallacy of Overwhelming Exception: occurs when an accurate generalization is made, but it has qualifications that eliminate so many cases that what is left to generalize about is much less than one would be led to believe.
• Logical Fallacy of Stereotyping / Association: occurs when an assumption is made that what is considered to be true (or thought to be true) of a larger class/group is true for ALL the members of that class/group. EXAMPLE The liberal news media began using the same word, fundamentalist, to describe Christians who believe the Bible and Muslim terrorists.
• Logical Fallacy of Dicto Simpliciter / Sweeping Generalization: occurs when a statistical syllogism ignores or eliminates an exception that affects the conclusion.
• Gambler's Fallacy / The Monte Carlo Fallacy / The Doctrine The Maturity of Chances / Hot Hand Fallacy: occurs when the odds of a truly random event happening are thought to increase or decrease over time and events.
• Logical Fallacy of Appeal to Possibility / Appeal to Probability: occurs when it is asserted that something is true because it is possible or to say that something is very probable when it is only remotely possible or even impossible.
• Logical Fallacy of Appeal to Infinite Possibilities: occurs when it is asserted that something is possible because nothing is impossible.
• Texas Sharpshooter Fallacy: occurs when cherry-picked data, observations, quotes, etc. are selected and used to support a proposition. EXAMPLE A farmer takes a bunch of random shots at his barn, paints a target around the biggest concentration of bullet holes, and then claims to be a "Texas sharpshooter."
• Misuse of Averages Fallacy: occurs when it is assumed that something is acceptable based on the mean or the average value of the total of all cases. EXAMPLE “Three days a week, I’m aggressive to the point of being obnoxious, and on the other days, I’m so passive that I won’t take action on anything. On average, I’m about right.”