The data above is from the US Census Bureau. From just the graph, we can appropriately conclude:
A. Median home prices in the United States more than tripled between March 2009 and January 2011.
B. The increase in home price between March 2009 and January 2011 was roughly linear.
A study is done on 250 people, where each person tries to predict whether a particular card from a shuffled deck is red or black before it is revealed. (The deck contains an equal number of each.)
Each participant makes 8 predictions. One participant gets all 8 predictions correct. The researcher claims that this person has exhibited psychic abilities.
Based on just the way the experiment is designed, is the researcher's claim a viable hypothesis? (Note we're not judging the plausibility of psychic ability in itself, just this particular experiment's design.)
Deception in statistics can be quite intentional; the original median home graph's choice of what months to display clearly did not happen by accident. It can also be unintentional; the researcher examining psychic phenomena may be earnest about their hypothesis, but they still interpreted the results of their experiment poorly.
Alternatively, sometimes the statistics themselves can deceive, as the questions that follow will demonstrate.
The data below was collected by hospitals in Ontario, Canada between 2002 and 2014; they indicate the severity of off-road vehicle accidents that resulted in hospital visits. The left column is the data from people who were wearing a helmet during the accident. The right column is the data from people who were not wearing a helmet.
|Arrived in ambulance||19%||9%|
Based on the data from the chart, what seems to be true?
A. People who were wearing helmets during the off-road vehicle accidents that brought them to a hospital are more than twice as likely to arrive in an ambulance, compared to the helmetless victims.
B. People who wear helmets when riding off-road vehicles are more likely to need a hospital visit, compared to people who do not wear helmets.
(Data source: Journal of Internal Medicine.)
Not everyone who gets in an accident goes to the hospital!
The data from the previous question only considers data collected by hospitals. Which quadrant of the data most likely has the largest part missing (that is, the number is smaller than the count of all accidents, not just those seen by hospitals)?
The data from the previous two questions demonstrates what's known as Berkson's bias or Berkson's paradox. In taking what appears to be a representative sample, a specific group may still be excluded (for example, hospitals won't see those who are healthy enough to not need to go to a hospital).
Looking at the data from a different perspective may help. What percentage of people observed by the hospital were wearing a helmet?
Note that in Ontario, motorcycle riders must wear helmets by law! There are definitely helmeted riders not included in the data.
Statistics cannot be done in a mathematical vacuum. As it usually involves real-life reference, knowledge about the circumstances can be as important as any sort of calculation. This course will contain some questions that may seem not to be "purely" math - this is quite intentional, as context is often required for a valid analysis.
It may seem, at this point, that statistics can only serve to confound. However, statistics can be used to pierce deception rather than just create it, as you'll see in the next quiz.