Statistics is used in two most common ways: as a tool to describe the world around us, and as a tool used to infer something we have limited information.
While there are several different ways in which raw data can be presented to a reader, most commonly it is done using Line Graphs, Bar Graphs, Pie Charts and Histograms.
For example, the following graphs from Gallup Organization, a national
Do you consider the amount of federal income taxes you have to pay as too high, about right, or too low?
Talk about symmetry:
Most advertisements, political debates, and other public forms of argument are riddled with fallacies, that is, with persuasive but invalid forms of logic. A familiarity with the most common fallacies is important if one is to make informed decisions and generate rational opinions. Although there are a great many fallacies, the ones listed here are used most often.
Fallacies of Relevance:
Subjectivism: "I believe/want something to be true, therefore it is true." This fallacy is often characterized by a refusal to consider evidence contrary to a cherished belief, and in some books is called "the Fallacy of the Irrefutable Hypothesis." This is very common in conspiracy theories. Examples:
"No one with any compassion could possibly believe it
is okay to torture animals."
When the Murrah Federal Building in Oklahoma was bombed, many militia groups claimed the government knew it was going to happen since the FBI had infiltrated their organizations. When it was asked why, in that case, the authorities didn't evacuate the building, it was replied that the government allowed it to kill so many people in order to discredit the milita movement and turn public sentiment against it. Some milita spokespeople even suggested that the FBI had done the bombing itself to achieve this purpose. These militia members have an irrefutable hypothesis.
Appeal to Ignorance: "If it can't be proved false, it must be true." This fallacy is often disguised by the use of very plausible language. Examples:
"Despite thousands of so called 'sightings,' no hard evidence for UFO's has ever been produced. Therefore UFO's don't exist."
"Thousands of studies and millions of dollars worth of research have turned up no cause for Gulf War Syndrome. Consequently, we must conclude that this so called 'syndrome' is not connected with having served during the Gulf War."
This fallacy is closely related to the Fallacy of Limited Choice (or False Dichotomy), in which an argument forces a conclusion based on an artificial "either/or" statement. Examples:
"If you're against the war, you're not supporting our sons and daughters in uniform."
"If you're so smart, why aren't you rich?"
"We must either support animal testing, or give up in the war against cancer."
Appeal to Emotion: This fallacy attempts to evoke an emotional response to convince the listener, and is extremely common in debates over emotionally charged issues like vivisection, abortion, and capital punishment. In can involve not only verbal argument, but the use of graphic and disturbing pictures or other media, for example of animals suffering in a laboratory. Examples:
"Someone who would mutilate and kill a little child deserves to be killed – I'd throw the switch myself with a smile."
This fallacy is closely related to the Appeal to Force, which is an attempt to get one's point of view accepted by an explicit or implied threat. Example:
"If you don't vote with the others, your place on this committee could be placed in jeopardy."
Appeal to Authority:
This is an attempt to get a position accepted by appealing to an inappropriate
or unqualified authority. This is extremely common in advertising, when some
well-known public figure is induced to promote a product. It can also occur
when an authority is corrupt, as when, in Nazi Germany, citizens were persuaded
to go along with many public policies they found abhorrent because they were
dictated by the state. (This example also involved the Appeal to Force, since
there was an ever-present implied threat against dissenters. This is the
situation under many governments in the world today.)
Personal Attack (Ad Hominum ): A very common technique, in which one challenges one's opponent personally, rather than his arguments. Examples:
"That's something only a bleeding-heart liberal would believe."
"Why shouldn't I hunt animals if I want? You eat meat, don't you?"
"Anyone who would support that has no feelings, no heart."
Any time an argument impugns an opponent's motives,
veracity, or qualifications, it is an ad hominum attack, meant to shift
the debate away from considering the merits of the argument itself.
Begging the Question: This occurs more often than one would suspect, and I've noticed that many people argue by use of this fallacy simply out of habit, and are quite surprised when their circular reasoning is pointed out to them. It generally involves a statement of the form, "this is true because it's true." Examples:
"Animals shouldn't be made to suffer to further scientific knowledge, because making animals suffer is wrong."
"Everyone in a wealthy society like ours has a right to health care, therefore health care should be made universally available."
"Freedom of speech is an essential right in a free society, since everyone should have the right to express him or herself with complete freedom."
Non Sequitor: This fallacy is often hard to recognize, because it so often expresses a common bias or appeals to a popular sentiment. It occurs anytime the premises and conclusion of an argument are essentially unrelated. Examples:
"A strong national defense is essential to our freedom. Therefore, we should fund production of the MX missile."
"Sex crimes are often the result of an unrestrained libido, so castration is an appropriate punishment for such crimes."
"Two-thirds of prison overpopulation is a result of long sentences for drug offenses. Drugs should be legalized."
"Almost all drug addicts got started by using milder drugs like marijuana. Therefore marijuana should not be legalized."
False Cause (Post Hoc, Ergo Propter Hoc): The second event followed the first event; therefore the first event caused the second event. The fallaciousness of this reasoning is obvious, yet it is a remarkably easy fallacy to commit, and it is used often in politics. Examples:
"After my opponent took office, the economy plummeted. A vote for me is a vote for restoring the economic engine of this country."
"On our watch, the crime rate has gone down. Obviously, our policies are succeeding in the war against crime."
"After the social liberalization of the 1960's, social ills such as teen pregnancy, urban violence, and rudeness in public discourse skyrocketed. We need to restore some traditional values."
Complex Question: This is the famous "have you stopped beating your wife?" device, in which a conclusion is forced by disguising it in the body of a question. You should be especially suspicious of any question that demands a "yes or no" answer. Examples:
"Is my opponent prepared to renounce negative advertising?"
"Will you commit yourself to greater equity in employment by endorsing my position on affirmative action?"
"Does your procrastination cause your grades to suffer?"
Fallacies of Numbers and Statistics:
Appeal to Popularity (Numbers): This is the "everybody does it" fallacy so often used by school children, to which the wise parent invariably replies, "and if everybody jumped off a cliff, would you do that too?" Examples:
"We have the best selling (fill in the blank) in America. (So you should buy one too.)"
"So many people have seen the Loch Ness Monster – there must be something down there."
Hasty Generalization: This involves drawing a general conclusion on the basis of anecdotal evidence. (It is similar to post hoc, ergo propter hoc.) Examples:
"I've never done well in my math classes. I just don't have a 'math brain.'"
"Two 747's were involved in air disasters in the past year. It must not be a safe plane."
Bias and Availability Error: This is very common in opinion polls, and boils down to the fact that how people will respond to a question often depends very much on how the question is phrased.
These examples by no means exhaust the many varieties of common fallacy, but they are representative of the most common kinds in contemporary advertising and propaganda. Becoming astute at noticing these fallacies when they are used against you is an excellent inoculation against being persuaded to accept ideas and conclusions based on flimsy or deceitful arguments.