Generalizing and Describing

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					           Generalizing and Describing
• A generalization, as a term used in critical
  thinking, is a statement that attributes some
  characteristic to all, most, or some members of a
  given set. For example:
   – Many students work full time.
   – Twenty-five percent of Americans believe in astrology.
• A generalized description is a blanket statement
  based on information about every member of a
  group. We say.
   – “All my compact discs are from the ‟90‟s,” or
   – Every women I know is good at math.
• We feel safe in making these broad statements
  because they cover every person and thing we‟ve
  mentioned.
          Inductive Generalization
• An inductive generalization is an argument in
  which a generalization is claimed to be probably
  true on the basis of information about a particular
  class. Here are three examples:
   – Six months ago I met a rancher from Montana, and she
     was friendly.
   – Two months ago I met a waiter from Montana, and he
     was friendly.
   – One week ago I met a student from Montana, and she
     was friendly.
   – I guess most people from Montana are friendly.
        Inductive Generalization II
• Another example:
   – All dinosaur bones so far discovered have been more than 65
     million years old.
   – Therefore, probably all dinosaur bones are more than 65 million
     years old.
• Finally,
   – Most Republicans I know are conservative.
   – Therefore, most Republicans are conservative.
                  Generalizing
• A number of claims we make are generalizations
  that we think hold true. For instance, we see one
  cat, then another, and we recognize features they
  share in common. When we have seen enough of
  them we realize they belong together. We reach
  the conclusion that “All creatures called „cats‟ are
  four-legged, carnivorous, furry mammals, usually
  domesticated, standing about 1 foot tall,” and so
  forth.
• Having abstracted the characteristics they have in
  common, we form a generalization that holds true
  for all cats.
     Generalizing- from M&P
• What do these statements have in common?
• “I avoid philosophy courses. They are too abstract
  for me.”
• “5% of American males at age 20 are taller than
  6‟3”.”
• They are both GENERAL statements, statements
  about an entire group or “population” of things.
• One is a general statement about philosophy
  classes: “They” are too difficult for me.
• The other is a general statement about American
  males at age 20: 5% of them are taller than 6‟3‟‟.
• How, logically, does one support a general
  statement?
• Through GENERALIZING!
• “Generalizing” = arriving at a conclusion about an
  entire group
  by considering a finite subset of that group.
• It isn‟t practical to measure the height of every
  male.
• So we generalize from a subset or “SAMPLE”: a
  sample of males; a sample consisting of the
  philosophy courses I have taken.
• Scientific sampling: a branch of statistics.
• Scientific sampling: a branch of statistics.
• Much scientific knowledge requires scientific
  sampling.
• How do we know if a vaccine works?
• Can we try it on everyone? How do we go about
  determining if it is relatively safe?
• Note: the fallacy of hasty generalization
• Do you remember what this was from the fallacy
  section?
• In this case, it is overestimating the strength of an
  argument based on a small sample. You may have
  too high of a confidence level regarding your
  sample.
• Fallacy of anecdotal evidence- my grandpa drank
  scotch everyday and he lived to be 90 years old.
• Fallacy of biased generalizing – Fox news polls,
  Lou Dobbs polls, and so forth.
• Scientific sampling lets us know about large
  populations
• Health statistics
• Public opinion
• Marketing research/product preferences
• Quality control in manufacturing
• Climate research, e.g., global warming
• Some terms you need to know:
• Sample
• Target Population
• The Feature
• The finite subset of the group is called the
  “SAMPLE”; the entire group is the “TARGET
  POPULATION” (or just “target” or sometimes
  just “the population.”)
• Again, GENERALIZING is arriving at a
  conclusion about an entire group or “population”
  by considering a finite subset of that group.
• Which would you rather be?
• Rich and stupid
• Poor and smart
• Poor and smart? Or rich and stupid?
• Let us generalize…
• Can we take the answers in this class and make a
  generalization about IPFW in general?
• Why or why not?
• The feature refers to x % of this class prefers to
  be fill in the blank. The fill in the blank is „the
  feature.‟
          More ch. 10 M& P
• We want the sample to have the same RELATED
  VARIABLES as the target population, and in the
  same proportion.
• A sample that has a RELATED VARIABLE in a
  proportion not found in the target population is
  ATYPICAL or “BIASED.”
• Do we have a fair proportion of freshmen,
  sophomores, grad students, and so forth?
• Do we have the right mix of business majors and
  liberal arts majors?
                Generalizing II
• Isn‟t generalizing the same thing as stereotyping?
  Only if each member is treated as typical and
  assumed to possess all the group‟s features. Each
  person should be treated as an individual even
  though he or she will probably exhibit some
  characteristics of the group.
• Can we generalize from one instance? That
  depends on the case. From touching a rose‟s
  thorn, we can determine that thorns on a rose are
  sharp. From dropping a pencil to the ground, we
  can determine that gravity always pulls objects
  downward.
                Generalizing III
• Generalizing is unavoidable. To say, You can‟t
  generalize,” is to make a generalization.
• Hegel wrote, “An idea is always a generalization,
  and generalization is a property of thinking. To
  generalize means to think.”
• Samuel Butler wrote, “Life is the art of drawing
  sufficient conclusions from insufficient premises.”
• We generalize through the lessons we draw from
  experience. Since we must generalize the trick is to
  do it well.
• The main problem in generalizing is to figure out
  how to achieve reliability. What percentage of a
  group must be examined for us to feel secure about a
  generalization in our argument? Which members
  should we use as a representative cross section?
              Using a fair sample
• Size. The number of cases we examine should be
  large enough to represent the whole. One way to
  judge how many that should be is to look at what
  we are generalizing about. For some things we
  will need a large sample, for others we will only
  need a few cases.
• Example 1:
   – The coffee in that pot is lousy-I just had a cup.
• There is a high probability that you will not like a
  second cup of coffee from the same pot.
          Using a fair sample II
• Example 2:
• Cocker spaniels are nice dogs, but they eat like
  pigs. When I was a kid, we had this little cocker
  that ate more than a big collie we had.
• One cocker is not enough to base a generalization
  about a whole breed of dogs.
• If we are talking about the taste of pepper, a few
  grains would be sufficient for reaching a general
  conclusion.
• If we want to generalize about the amount of
  pepper used in the average American household,
  we would have to conduct a large survey all across
  America.
             Fair Sample III
• If we want to generalize in an argument we need a
  large enough sample on which to base it. To
  determine whether the sample is sufficiently large
  we need to see what the generalization is about.
• We may not always know the subject well enough
  to determine in advance whether a large or small
  sample is needed. We may know that a
  generalization about the hardness of diamonds
  calls for just a few cases and the use of pepper
  may require a large sample, but when it comes to
  birds, vertebrates and beetles we may not be so
  sure.
             Fair Sample IV
• We may not know that there are 14,000 varieties
  of birds, 40,000 kinds of vertebrates, and 180,000
  species of beetles and that the sample size would
  have to be huge.
• In these cases we may be able to use another
  method to determine the ideal size of the sample.
  We can increase the sample size until the results
  begin to repeat themselves. Then we can stop,
  knowing we have examined enough cases.
               Fair Sample V
• The traditional example of this is the marble
  experiment. Suppose that we want to know the
  percentage of red, black, and clear marbles in a
  jar. We would first reach inside for a handful of
  the marbles and, let‟s say, come up with 30
  percent red, 40 percent black, and 30 percent
  clear. We then put the marbles back in the jar and
  shake it up really well. Maybe this time we count
  40 percent red, 50 percent black, and 10 percent
  clear. We keep putting the marbles back in the jar
  and shaking it very well until the same
  percentages keep showing up. When this happens
  we know we have gone far enough. We have
  probably eliminated the errors in our sample and
  are getting accurate results.
                  Fair Sample VI
• This method is the most reliable for determining whether
  our generalization is based on an adequate sample size.
  Rather than speculating on the proper size based on the
  nature of the subject, we should use this method whenever
  possible.
               Simpson’s Paradox
• Moore and Parker: There are many ways that
  statistical reports can be misleading. The
  following illustrates one of the stranger ways,
  known to statisticians as “Simpson‟s Paradox”:
• Let‟s say you need a fairly complicated but still
  routine operation and you have to pick one of the
  two local hospitals, Mercy or Saint Simpson‟s, for
  the surgery. You decide to pick the safer of the
  two, based on their records for patient survival
  during surgery. You get the numbers: Mercy has
  2,100 surgery patients die in a year, of which 63
  die-a 3 percent death rate. Saint Simpson‟s has
  800 surgery patients, of whom 16 die- a 2 percent
  death rate. You decide it‟s safer to have your
  operation done at Saint Simpson‟s.
             Simpson’s Paradox II
• The fact is, you could be actually more likely to
  die at Saint Simpson‟s than at Mercy Hospital,
  despite the former hospital‟s lower death rate for
  surgery patients. But you would have no way of
  knowing this without learning some more
  information. In particular, you need to know how
  the total figures break down into smaller, highly
  significant categories.
• Consider the categories of high-risk patients (older
  patients, victims of trauma) and low-risk patients
  (e.g., those who arrive in good condition for
  elective surgery). Saint Simpson‟s may have the
  better looking overall record, not because it
  performs better, but because Saint Simpson’s gets
  a higher proportion of low-risk patients than does
  Mercy.
              Simpson’s Paradox III
• Let‟s say Mercy had a death rate of 3.8 percent
  among 1,500 high-risk patients, whereas Saint
  Simpson‟s, with 200 high-risk patients, had a
  death rate of 4 percent. Mercy and Saint
  Simpson‟s each had 600 low-risk patients, with a
  1 percent death rate at Mercy and a 1.3 percent
  rate at Saint Simpson‟s.
• So, as it turns out, it‟s a safer bet going to Mercy
  Hospital whether you‟re high risk or low, even
  though Saint Simpson‟s has the lower overall
  death rate.
• The moral of the story is to be cautious about
  accepting the interpretation that is attached to a set
  of figures, especially if they lump together several
  categories of the thing being studied.
                  Randomness
• In addition to making sure we have a large enough
  sample size, we must also make sure we have
  enough randomness. In other words, we must
  make sure that the sample studied represents the
  whole and does not bias our conclusion. We want
  to avoid “loading” the sample in favor of a
  particular result but five every member of the class
  an equal chance of being chosen.
• For example, to avoid bias in a generalization
  about how the public feels about legalizing
  marijuana, we should not just sample college
  students because they may be more pro-
  legalization and not represent the majority of the
  public.
                Randomness II
• We can be biased because of the prejudices we
  bring to our investigation, but also because of
  more subtle psychological factors. If we buy a
  blue Blazer we are amazed at all of the blue
  Blazer‟s that are out on the road.
• However, we know that we are just all at once
  noticing other blue Blazer‟s.
• To combat this tendency, we should be alert to
  counter examples, picking out the number of
  Silverado‟s or Ranger‟s on the road, or taking a
  sample of ten cars at a time to see the proportion
  of each brand. Then we will avoid the trap of
  seeing only what we are looking for and
  confirming what we already believe.
              Error margin
• “ERROR MARGIN” expresses the range of
  random variation from sample to sample.
• Look at table on page 360
• Note that the larger the random sample size (the
  larger n is), the smaller the error margin.
• CONFIDENCE LEVEL: expresses the probability
  that samples of a given size will have values
  within that error margin.
                  Stratification
• For stratification we want to include all strata or
  classes that could have an important effect on our
  generalization. Every relevant group must be
  taken into account. For example, if we wanted to
  include in our argument about alcohol
  consumption in the United States, we should be
  sure that the sample includes the Northeast, the
  South, the West and the Midwest. We would want
  to include teenagers and senior citizens, rich and
  poor, different racial and ethnic groups, and so
  forth. If we left a segment of the class out our
  results would not be reliable.
     Loaded/slanted questions
• Please see pages 368-369
                  Summary
1. Check for adequate size in terms of the nature of
   the subject matter. In an experimental situation,
   take repeated samples until the results begin to
   repeat themselves.
2. Be sure the generalization is random and free of
   bias in the sampling, so that each of the relevant
   elements has an equal chance of being chosen.
3. Make certain the sample is stratified, which
   means that all relevant categories are included
   and none is excluded that would significantly
   affect the generalization.
        The explanatory hypothesis

• A hypothesis can be defined as an explanatory principle
  accounting for known facts. In hypothetical thinking we
  want to know why something is true, and we reason
  backward to find some explanation for the facts, one that
  makes sense of them. We use our imagination to find
  some reason why things are the way they are.
      The explanatory hypothesis II
• Trial lawyers employ hypothesis in trying to
  construct a plausible account of a crime.
• The prosecuting attorney might argue that because
  the accused man was apprehended in the vicinity
  of the jewelry store with the stolen diamonds in
  his pocket and has a history of arrests for larceny,
  he must have committed the crime.
• The defense attorney, on the other hand, might
  construct a scenario that the accused was walking
  to a nearby shop to buy a cigar and found the
  diamonds on the ground just as the police car
  drove up; the real thief must have dropped them
  while he was running from the scene of the crime.
     The explanatory hypothesis III
• Some hypothesis, of course, bear little relation to
   reality. For example, rain dances will cause it to
   rain or sacrificing virgins will appease the gods.
• What separates a reliable hypothesis from an
   unreliable one?
1. Consistency with other hypothesis we accept. A
   new hypothesis should be consistent with the bulk
   of hypothesis that we believe to be true. Of
   course, sometimes a new hypothesis will put us
   into a whole other paradigm. For example,
   Copernicus revolutionized astronomy by
   proposing that the Sun, not the Earth, is the center
   of the solar system.
     The explanatory hypothesis IV
2. Plausibility. Since we have explanations for a
  great deal of occurrences in the natural world, any
  new hypothesis must be plausible according to
  common sense and tradition explanations.
  Plausibility is a rough assessment of how credible
  a claim seems to us. For example, “McDonalds
  has sold more hamburgers than any other fast food
  chain” seems plausible. However, the claim
  “Charlie‟s 87 year old grandmother swam across
  lake Michigan in the middle of winter” seems less
  plausible because of the obvious way it conflicts
  with what we know about 87 year old bodies,
  about lake Michigan, about swimming in cold
  water, and so forth. We would want to see it
  before we believed it.
       The explanatory hypothesis V
• Comprehensiveness. Any hypothesis that we present
  should be the most complete explanation that we can find.
• Suppose we are writing an English paper on Huckleberry
  Finn by Mark Twain. We could claim that the book
  presents a portrait of life on the Mississippi river before the
  Civil War, or that it is a classic adventure tale. Or that
  Twain‟s purposes was to write a work of irony showing
  how expressive American speech could be. However, a
  more comprehensive interpretation that could incorporate
  these elements might be that the book is about Huck Finn‟s
  desire for freedom, honesty, and justice set against the
  cruelty and prejudices of the a complacent society. This is
  manifested especially through his flight from home and his
  friendship with Jim, which requires him to break the moral
  rules and the law itself.
      The explanatory hypothesis VI

• Simplicity. This principle is attributed to the fourteenth-
  century theologian/philosopher William of Ockham, and it
  is also known as Ockham‟s Razor. It states that “entities
  should not be multiplied beyond what is required,” that is
  keep it simple whenever it is possible.
     The explanatory hypothesis VII

• Predictability. If our hypotheses is sound, we should be
  able to predict events based on that assumption. That is,
  given the conditions described in our hypothesis, we can
  expect certain results to follow.

				
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