Explanation of Misuses
Here's the points I like to make for the different misuses. Most of these points
come from D. Moore's discussion in Concepts and Controversies .
- What comparisons are being made? (Examples 1-3)
- Five milligrams less tar than what?
- Need to know what the ingredients are - turns out both ads are referring to Aspirin.
- Fewer cavities than who? When? How many patients?
- Is the information complete? (Example 4)
- What other cars are in the Lumina's class? Turns out, this
is the only car in it's class
- Are the numbers plausible? (Examples 5-7)
- Arithmetic Errors
This statement assumes a population of 120 million in
the year 2000. We already have a population twice that. The 30 million is correct,
but will only constitute about 10-11% of the population. We need to ask if the
numbers presented are reasonable.
- Nonsensical Values
If there are 20 animals, the percentages must be multiples of 5.
- Exactness
These numbers seem a little too exact for such a long period of time, for an unreliable source, on something so difficult to measure.
- Are the definitions clear? (Example 8)
- How many people know the criterion used to measure the "unemployment rate"?
- Changes in the definition while the study is in progress can cause misleading results
- Ratios vs. Counts (Example 9)
- More elderly people are in accidents because there are more drivers in that
age category
- To properly examine which sport is riskiest by looking at the number of
emergency room visits, need to know the number of participants.
- The US received the most medals but also had the most participants.
- Approximately 6% of SD residents take the exam, where are 60% take
the exam in CA, and over 80% in Connecticut
- What is the source of the information? (Example 10)
- The Investment Company will try to present the information
in the most positive light. Turns out, the payoff from all the stocks would have
been even higher.
- How was the sample selected? (Example 11)
- Need to know whether these 4 respondents were randomly
chosen from the 20 instead of chosen selectively by the interviewer.
- Does the conclusion follow /Are the generalizations valid? (Example 12)
- While the study is valid, it was observational, therefore, a "causal" relationship has not been established.
- Results from a study of Boston college students may not apply to a more
general population.