Critical Analysis Chapter 7: Are there flaws in the statistical reasoning?

For the assigned passage(s), identify the thesis and reasons. Then, identify the flaws in the statistical reasoning. Where averages are mentioned, name the three types of averages we discussed in class and how each would give different results here. Which of the three would be best and why? Please use complete sentences, not simply phrases or single words, in all segments of your answers. Also, avoid quoting full sentences. Paraphrase instead.

Passage 1:
“It just isn’t safe to drive anymore,” my friend lamented, shaking his head as we tooled through Friday afternoon traffic on the freeway. But the fact is, driving in America is safer than it’s been in over 60 years. In 1984, we had 18.4 traffic fatalities per 100,000 population, compared to 25.8 in 1970 and 23.3 in 1950. Today you’re a lot safer on the road in your car than you are at home or at work. Twelve out of 100 Americans are laid up or need medical attention during the year because of household accidents. Five out of 100 get hurt at work. But only 2.2 per 100 are injured in automobile accidents.

Passage 2:
The financial problems of our public schools are highly overrated. In 2001–2002, an average $6,835 was spent on every public school student in the United States. Furthermore, full-time public school teachers make an average $44,367 per year according to the American Federation of Teachers. This salary is not at all bad, compared to the 2001 median household income of $42,000 in the United States. It isn’t insufficient funding or ill-paid teachers that are killing the educational system; it is, instead, the lack of well-trained teachers thanks to grossly lax colleges of education.

Passage 3:
Americans in general are spoiled. Most of us tend to judge the times in relative terms – and we have had rich relatives. Materially, no people on earth have ever been as well off. So, when most of us say “times are bad,” we say it in a comfortable home, with a well stocked electric refrigerator, television, and electric laundry equipment. One in every five households in America in 1980 was affluent (had an income over $25,000). Twenty-five years ago, only one in 33 households was this comfortable. Our personal income, disposable income, and personal savings have all climbed continuously since 1950.True, we still have a vast army of poor in the country. One in every eight Americans is living below the poverty level – one in every four aged 65 or over is poor. But twenty years ago, one in every five citizens was below the poverty line. In seven years, more than 14 million of us have climbed out of the poverty hole. Any country in which, while population increased 56 percent, home ownership increased 100 percent, car ownership 130 percent, personal savings 696 percent, is a long way from hard times. All that happened between 1946 and 1980.

Lecture Summary:

Statistics can be impressive because they are scientific and precise, but they can and do lie. Definition: Statistics are evidence presented as numbers

  1. First, look at how the numbers were created or gathered to make sure the method was reliable.
  2. See if the thesis and the statistics fit together (see example 1 and 2 below)
    a. Ignore the stats; decide what stat is needed to prove point
    b. Ignore the thesis; decide what is proven to you by the stats
    c. See if the thesis says one thing while the stats prove another
  3. See if you have the necessary context to make sense of the numbers
    a. Beware of impressively large or small numbers
    b. Are the percentages misleading? Then look for the absolute amounts. (see example 3 below)
    c. Are the absolute amounts misleading? Then look for the percentages. (see example 1 and 2 below)
    d. What is the total range used to arrive at averages
  4. Watch out for ambiguous averages.

Ambiguous Averages – an average is ambiguous when we don’t know which type the author is using. Types of averages include:
1. Mean: add up all the values and divide by the total of the number of values
2. Median: list all the values from highest to lowest, and then find the number in the middle; half the values will be above the median and half will be below. Also known as the 50th percentile.
3. Mode: the value that appears most frequently

Sometimes the mean (or “common” average) is not the best one to use (see example 5). Sometimes it is (see example 6).

How to calculate the various averages:
Test score results
1. 100
2. 94
3. 94
4. 88
5. 87
6. 84
7. 82
8. 67
9. 66
10. 65
11. 64
12. 62
13. 24

Mean: add all and get 977; divide by 13 and get a mean of 75.15
Median: middle digit of values is 82; only 18 from the top but 58 from lowest value
Mode: 94

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