An Explanation of Statistical Tools from

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Sound, Effective, Appropriate Reasoning

Fallacious Reasoning

Reasoning is the use of information to arrive at a conclusion. The challenge of reasoning is applying logical judgment to arrive at an appropriate conclusion. For example, what is enough evidence? When is a comparison or analogy appropriately applied and when is it a false analogy?   The outcomes of the reasoning process, the process of critically thinking, evaluating, logically considering information are conclusions. Sound, effective reasoning results is a supported, accurate, appropriate conclusion, and fallacious reasoning results in an error.


It is up to YOU to distinguish sound and appropriate reasoning from fallacious reasoning. 

Sound, Effective, Appropriate Reasoning:

Strong, effective reasoning uses one or more of the following approaches.

  1. EXPERIMENT OR DIRECT DEMONSTRATION: Direct demonstration is one of the most conclusive methods of proof. However, just as a demonstration may support a conclusion, support from one demonstration does not prove a general conclusion. Sound reasoning involves the application of supporting evidence which is representative of all the cases. Failure to meet an appropriate standard of supporting evidence can result in the fallacy of hasty or over generalization.
  2. STATISTICS, INSTANCES, AND EXAMPLES: Using figures, data, and statistics relevant to a situation is another method of supporting a conclusion. Such statistics must, however, apply in all important respects to the statement we are supporting; otherwise they are pointless and misleading. Reading, interpreting, and evaluating statistical information can sometimes be difficult. It is also possible to use representative, though not exceptional, examples to illustrate or support a conclusion. On the other hand, unreliable evidence may lead to fallacious reasoning.
  3. COMPARISON OR ANALOGY: Comparing two or more things or ideas which are alike in most respects is one method of inferring support for a conclusion. If they are similar in several important ways, one might assume that they are similar in other ways. This is reasoning by comparison or analogy; however, a false analogy may arise when the compared items are both similar in some ways, and very different in other ways and an inappropriate extension of an analogy may lead to unwarranted conclusions.
  4. INFERENCE: Often one assumes something to be true but finds it difficult to give clearly demonstrable proof for the conclusion. In such cases one may show the conclusion to be in all probability true by inference from definite facts and concrete details called circumstantial evidence. Inference or circumstantial evidence is perhaps the weakest method of attempting proof because it is not conclusive. Such evidence merely increases the probability of trust as we are able to increase the number of attendant circumstances. So, although it is sometimes necessary and acceptable to use inference, it is important to recognized a conclusion based on inference which may not be as strong as one based on direct evidence.
  5. ACCEPTING THE STATEMENT OF AUTHORITY: The opinion, conclusion, or statement of a specialist or expert can support or verify a conclusion. Such support must come from an acknowledged authority in the field of thought from which the conclusion is drawn. While the opinion of Michael Jordan should be considered as strong support for a conclusion about basketball, his ideas about medical treatment of the aging process are not. Remember, the expert's opinion is respected by us because the expert is recognized by others as an authority. Beware of the self-proclaimed expert, the person who claims authority for themselves.
  6. CAUSE AND EFFECT: One of the most logical methods of proving a statement true is to reason from one or more known facts or circumstance to their probable future effect.
    1. Building a logical argument from the specific details to the general conclusion is called the inductive method of reasoning. For example, the temperature outside is below freezing, and there is water in the bird bath; therefore that water will soon freeze to ice. The inductive method of reasoning would allow one to conclude that the water in the birdbath will freeze. This is logical given the conditions, however it is a conclusion based on the logic not an observation. The compliment, moving from a known or accepted conclusion (the general) out to find what specifics must also be true is labeled the deductive method of reasoning. In this case we might see the ice in the birdbath. Thus the conclusion is an observed and accepted fact. The deductive logical method would then allow one to conclude that the outside temperature must be (or have been) below freezing. Positing a cause and effect relationship requires three logical conditions.
      1. The cause must occur before the effect. This is most evident, but often ignored in some social science research and in everyday arguments. The cause must be statistically connected to the effect. This concordance of cause and effect may be probabilistic. That is, it does not always need to occur. For example, a difference in percent of falls leading to broken bones being higher among older people does not mean that every old person who falls ends up with a broken bone.
      2. There must be no alternative or spurious causes. This is the hardest condition to meet. In actuality, it cannot be met. However, finding that an observed statistical connection between two variables is spurious (sharing a common relationship to a third unanalyzed variable and not causally related to each other) is frequently the focus of on-going scientific debate and the scientific method.
    2. There are instances where one may mistake the cause.

Fallacious Reasoning:

The most common type of errors made in reasoning fall into one of the following general mistakes.

  1. HASTY or OVER GENERALIZATION: A conclusion drawn from an insufficient number of facts, instances, examples, or statistics results in an error of reasoning. Evidence supporting a conclusion needs to be broadly based and generally representative of the total defined population. So, in the case of much research using "college students" the conclusions were drawn from samples of college, male, freshmen, but the conclusions were presented as representative of adults (both male and female, college educated and not, etc.). When the evidence is sufficient and representative of the larger situation then sound reasoning has occurred.
  2. UNRELIABLE EVIDENCE: Testimonial evidence of an authority is trustworthy only when the person who gives the evidence has full and accurate knowledge and is unbiased and honest. If a milk-distributor advertises, "Ours is the best milk sold in town," or a politician says, "Vote for my friend Mayor Bains; he's a capable administrator," the statement of neither is considered highly reliable; for each is biased. Although evidence is sometimes unreliable, systematic and representative instances and statistics are a solid foundation for sound reasoning.
  3. FALSE ANALOGY: If we say, "We traveled the 1721 miles from our home in Nebraska to Jacksonville, Florida, in forty-three hours of driving time; therefore we shall cover the 1635 miles from our home to Seattle, Washington, in forty-one hours," we are drawing a false analogy. We have not taken into consideration the fact that much of the driving to Seattle must be done over mountainous terrain, against prevailing westerly winds, and for a relatively longer period each day against the glare of the sun than when one is traveling southeastward. Likewise a prospective purchaser is reasoning from a false analogy when he says, "Fifteen hundred dollars is too much for this new car; I bought one of the same make and body style for nine hundred and fifty dollars in 1939." An analogy, then is false if the things compared differ in even one important respect or it the comparison is based upon conditions that have changed. There are times when an appropriate analogy may be helpful in arriving at and supporting sound reasoning.
  4. INVALID EXTENSION OF AN ANALOGY: This happens when one assumes that some analogy holds true in all aspects. For example, "Learning mathematics is like learning to ride a bicycle. Once you've master it you don't lose it." Even if the conclusion about riding a bicycle were true, it may not have anything to do with how we learn mathematics. The false argument by analogy is very prevalent in political and social argument where a model that explains macro-economic systems is applied to explain micro-personal behavior.
  5. MISTAKING THE CAUSE: Assigning a wrong cause is a frequent error in reasoning back from a known result or effect to a probable cause. Thus, a student mistakes the cause (and incidentally indulges in rationalizing) when he says, "I'm going out to the movies every night before a term examination hereafter. I attended a late movie before my big science test, and I got a higher grade on it than on any of the tests the following day." Common superstitions often arise from mistaking the cause. "Beans planted when the east wind blows will never sprout," say a superstitious farmer. Sometimes the beans do not sprout, but the east win did not kill them. It may, however, have brought on a prolonged period of cold, rainy weather that made the seeds rot in the ground. The scientific method is based on a constant dialectic between positing appropriate cause and effect and mistaking the cause.
  6. BEGGING THE QUESTION: We beg the question when we assume without proof that something is true or false. Suppose a man said, "This unfair system of estimating taxes should be abolished!" He would be begging the question; for he must first state that the system of taxation is unfair. In a second step, he may go on to prove that the system of taxation is unfair. Finally, he may prove that because of its unfairness it should be abolished. We also beg the question when we reason in a circle, thus: "installment buying should be prohibited because it is economically unwise; we know that it is economically unwise because it should be prohibited."
  7. IGNORING THE QUESTION: We ignore the question when we do not meet the real issues or issues of an argument, coming to an irrelevant conclusion or arriving at a conclusion by illogical reasoning. We appeal to the prejudice, selfish desires, or other emotions of our hearers or readers; we try to over awe our opponent by quoting from authorities that are not pertinent or by bluster and impressive manner; or we invoke out worm tradition or custom.

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Copyright © 2016 by Peter T. Klassen, Ph.D. Principal,
11 June, 2016