10. Statistical Arguments
Statistical
reasoning allows us to use specific inductive principles and mathematical
calculations to generate conclusions about events and groups of things.
Although mathematics is a deductive science, it can be used to generate
inductive conclusions, both because of the types of generalizations inferred
from the calculations and the fact that the guiding principles are
fundamentally experiential.
We
use samples (a subset of a population) when we want to know
something about a specific group of things, because we cannot successfully
count each individual member of the target group, or population.
For
example, if we want to know something about “U.S. citizens’ attitudes toward
gender,” we can’t interview each one. What we do instead is identify our
population, which in this case is U.S. citizenry, and determine the representative
sample, that is, the sample that accurately reflects the characteristics of
the population as a whole. Sometimes, the representative sample is created
through random sampling, in which every member of the population
has an equal chance of getting into the sample. Very often, our aim is to find
a statistical average—a numeric version of generalization. There are three
types of statistical average:
1.
Mean:
determined by adding relevant numerical values, then dividing by the number of
objects represented by those values.
2.
Median:
determined by locating the number that divides the numeric data set in half.
3.
Mode:
determined by locating the value in the data set that occurs most.
Standard
deviation measures the amount of diversity in a numeric
data set. This is useful in statistical reasoning for determining diversity
around the mean.
The standard deviation of a numeric
data set is calculated through a series of steps.
Step 1:
Calculate the mean value.
Step 2:
Calculate the difference between each value in the set and the mean value.
Step 3:
Multiply each difference by itself (square each difference).
Step 4:
Add the results of the squaring process in step 3.
Step 5:
Divide the result of step 4 by one fewer than the number of members in the set.
Step 6:
The square root of the total variance is the standard deviation.
Results
can be skewed. Because real-life data does not always fit perfectly bell-shaped
curves, the same basic principles apply in calculating the standard deviation.
The problem lies in interpreting and applying unexpected sets of results. For
example, interpretation and application of complex statistical data can be
influenced by social policy, such as federal funding for Higher Education,
which often depends on the results of statistical studies. While some school
administrators have used statistical data to justify an increase in the amount
of money for colleges, others have used statistical data to justify a decrease
in the amount of money available. They relied on different data, but also on
different interpretations. Statistical inferences can be erroneous. This can be
accidental or intentional, but in either case, it is important never to take
conclusions inferred from statistical evidence at face value. When data is too
precise one could be committing the fallacy of misleading precision (A tour guide at a museum says a dinosaur
skeleton is 100,000,005 years old, because an expert told him that it was 100
million years old when he started working there 5 years ago.)
Another fallacy that
could occur is the Fallacy of
composition. When we assume all journalists are bias because a few are is an
example of this fallacy which I will illustrate bellow.
The
Liberal Media[1]
Is there a liberal bias in the media? A
recent study says there is neither a liberal nor a conservative bias in media
reporting. Although most journalists lean left (nearly 80 percent of the
respondents certainly did), this ideological bias has no statistical effect on
their reporting.
Between May 2017 and July 2017 a team of
four researchers searched for the email addresses of political journalists and
editors after visiting the website or Facebook page of every newspaper in each
state. To test this possibility of strong ideological skew, in the spring of
2018, the team ran a correspondence experiment, sampling around 13,500
journalists[1].
They created fake campaign email address
for a fake candidate running for the state legislature. They asked Journalist
to cover this potential candidate (Its ok, the journalist didn’t know it was a
fake candidate). It’s a journals job to cover campaigns and the people who run
in them. This this kind of request is common.
As the authors state this
“…a story on this topic would not be so
important that it eliminates journalist discretion about whether to cover the
topic depending on the journalist’s perception of the nature of the story, the
presence of other ongoing news stories, and the time required to follow up on
the story. In short, this story appears to be something that is generally
considered newsworthy but is subject to journalist discretion and is exactly
the type of story where gatekeeping biases could be manifest”[2]
The study found no statistical
difference[3] in the probability of a journalist responding to a conservative
or a progressive candidate.[4]
One could argue that these journalists are
simply responding to market demand. They may feel more pressure to cover a
conservative candidate due to conservative subscribers in the media
organization they work for and they don’t want to alienate current and
potential revenue.[5]
In response to this argument the authors
state
“…we find that a journalist working for a
newspaper in a county that voted for Trump is just as likely to respond to a
request for an interview with a progressive candidate as they are to a request
from a conservative candidate..[6]
This is something you can through at
people who use the term “The Liberal Media“.
Although this is only one study.
The Fallacy of composition.
This occurs when one infers that something is true of the whole
from the fact that it is true of some part of the whole. A trivial example
might be: "This sign on the building is made of paint, thus this building
is made of paint.
If everyone has the right business concept, everyone will become a
billionaire.
If a swims faster, he can win the race. Therefore, if all the swimmers swim
faster, they can all win the race.
Another example of this fallacy is when people assume that all protests are
violent because a few are as illustrated in the article below.
The Condorcet paradox, in voting theory, is another example. Because even if all
voters have rational preferences, the collective choice induced by majority rule is not transitive and hence not
rational. The fallacy of composition occurs if from the rationality of the
individuals one infers that society can be equally rational. The principle
generalizes beyond the aggregation via majority rule to any reasonable
aggregation rule, demonstrating that the aggregation of individual preferences
into a social welfare function is fraught with severe difficulties.
The Modo hoc fallacy[i]
is also related. This error occurs when assessing meaning to an existent based on the constituent
properties of its material makeup while omitting the matter's arrangement. A chicken, which is a live a
happy and a chicken which has been chopped into pieces is the same.
Another Fallacy is the Out-group homogeneity effect. This occurs when the perception of out-group members as more similar to one another than are in-group members,
"they are alike; we are diverse".
Another
Fallacy is Overwhelming
exception. This occurs when a generalization that is accurate, becomes less accurate with one or more
qualifications which eliminate so many cases that what remains is much less
impressive than the initial statement might have led one to believe.
Another fallacy is the apples and oranges
fallacy. This fallacy occurs when comparisons are drawn between events or sets
of circumstances that appear to share a commonality but are distinct from one
another. They are distinct due to having occurred during different times in
diverse places, under diverse socio-economic conditions, to dissimilar groups
of people, etc. Assuming these distinct things are the same can lead to the
false assumption that, just because something is true under one set of
circumstances, it will necessarily be true for all circumstances of a similar
sort. This apples and oranges fallacy is a fallacy of false equivalence – which
is committed when one shared trait between two subjects is assumed to show
equivalence, especially in order of magnitude, when equivalence is not necessarily
the logical result.
Apples
and Oranges and Murders
“…
of the 2,491 murders of black people reported in the U.S. in 2013, 2,245
perpetrators (90%) were black and 189 perpetrators (7.6%) were white. Of 3,005
murders of white people, 2,509 perpetrators (83.5%) were white while 409
perpetrators (13.6%) were black.”
You know what this means…
This means that people reporting that
black people kill more white people that white people kill black people need to
learn about statistics.
Because the person that made this graph
assumed that there was about 245 million white people and 42 million black
people living in the US in 2013. Depending on the race of the murderer they
divided these numbers into the four different murder categories by either 245 or
42 to find the ‘per million’ rates they used in the bar graph.
By this logic 0.77 white people out of
every million white people are killed by a black person, while 9.83 black
people out of every million black people are killed by a white person.
Due to the label at the top of the chart
stating per 1,000,000 members of the murderer’s race essentially what is being
standardized by is changed in each of those bar charts. Thus, the numbers are
presented side by side as though directly comparable, but they are not.
There are almost six times more white
people than black people, so these numbers are reported as though the
populations are equal. The numbers don’t support an argument confirming white
genocide, because the numbers are not proportional.
They don’t support an argument against
white privilege either especially when you look at the likelihood of being
killed by someone of the same race or someone of a different race.
According to Reuters:
“If you’re a white person in 2013, based
on the FBI data, your chances of being killed by anyone are roughly 13 in a
million; if you’re a black person in 2013, your chances of being killed by
anyone were 62 in a million, which is almost five times what the odds are for a
white person.”
While data shows more white people killed
in general, by police or whatever, this is mainly because there are more of
them. Almost 200 million. But when we get into likelihood and stuff like that
we see the difference between the population and the likelihood of being
killed.
Anyway comparing these two groups side by
side when the populations vary so widely is called the apples and oranges
fallacy. This occurs when you compare two very different things as though they
are the same.
https://www.reuters.com/article/uk-fact-check-bar-graph-black-white-homi/fact-check-misleading-bar-graph-presents-distorted-interpretation-of-black-and-white-murder-rates-idUSKBN23M2SX
[1]
https://advances.sciencemag.org/content/6/14/eaay9344/tab-pdf
[1]
(pg.3)
[2]
(pg.4)
[3]
“no statistical or substantive difference”
[4]
Comparing the two poles, strong conservative candidates are, on average, a mere
0.4 percentage points less likely to get a response than strong progressive
candidates. This effect is miniscule…(pg. 4)
[5]
(pg. 5)
[6]
(pg. 5)
[i] metaphysical
naturalism states that while matter and motion are all that compose humans, it cannot be assumed that the
characteristics inherent in the elements and physical reactions that make us up
ultimately and solely define our meaning
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