649week04 → Ethical Considerations in InfoViz
Last week, someone in class mentioned that people are more likely to accept nonsensical conclusions if supported by attractive visualizations. In response, I mentioned a book by R”udiger Pohl, Cognitive Illusions, Psychology Press, 2004. I claimed that this was a separate topic from establishing definitions about information graphics. I looked at the book (you can see this part of it as a Google Books preview, and found a complementary case where external cognition (called external representation there) facilitates reasoning. It seems worthwhile to share it.
cover of Pohl, 2004
A famous problem investigated by many researchers (pp. 62-67) is the breast cancer problem. Subjects are told that the probability of breast cancer is 1 percent for women of a certain age who participates in routine screening. If a woman has breast cancer, the probability that she will test positive is 80 percent. If a woman does not have breast cancer, the probability that she will test positive is 9.6 percent. A woman in this age group tested positive in a routine screening. What is the probability that she has breast cancer?
This problem can be solved by Bayes’ theorem, P(H|D) = (P(D|H)P(H))/(P(D|H)P(H)+P(D|H’)P(H’)) = (.8 * .01)/(.8 * .01)+(.096 * .99) = 7.76 percent, a surprising result to most subjects, who frequently give 80 percent as the answer.
By the way, the notation above uses H to mean hypothesis, D to mean datum, ‘ to mean not, P to mean probability, and | to mean given. So in English (with disambiguating parentheses) the equation would read “The probability that the hypothesis of breast cancer is true given the datum of a positive test is equal to the following quantity: (the probability of seeing the datum given that the hypothesis is true times the probability that the hypothesis is true in general) divided by ((the probability of seeing the datum given that the hypothesis is true times the probability that the hypothesis is true in general) plus (the probability of seeing the datum given that the hypothesis is false times the probability that the hypothesis is false in general)).
Pohl Figure 3.1
The application of an external representation, a tree diagram of the information provided above, causes most subjects to answer correctly. The tree diagram starts with 1,000 women at the root and two branches, breast cancer (10) and no breast cancer (990). Each of those has two branches, test positive and test negative. In the case of the 10 who have breast cancer, the size of the two branches is governed by the 80 percent mentioned above, so there are 8 positive and 2 negative. In the case of the 990, the size of the two branches is governed by the 9.6 percent mentioned above, so there are 95 positive and 835 negative. The woman in question must be on one of those two branches, the 8 and the 95, so it’s easy to see that 8/(8 + 95) = 7.76 percent.
The question last week suggested that infoviz could be misused to make people accept false conclusions by showing attractive graphics. Now I have just given you a purely textual description of a graphic. Can you create the corresponding graphic and make it mislead? The easiest way is to plug false data into it. You could do that intentionally or you could try to improve the data because you know it to be old and you have new information indicating that cancer rates in general have changed by some number. You could just make a mistake. What about the external cognition. Note that a correct answer depends on seeing that two branches are related. Could you draw this simple picture so that you obscure that relation or draw attention to something else?
Could you embed this in a larger system, either a system that asks the user to supply raw information and shows a Bayesian interpretation for single events, or a larger system where Bayesian inference is part of a black box of conclusions?
Could you provide the illusion of control through interactions? A chapter in the Pohl book describes numerous experiments on the illusion of control and relates them to real life situations of slot machine gamblers and mothers seeking to quiet infant crying. These studies suggest that both socially beneficial and harmful outcomes can result from providing the illusion of control, sometimes stimulating people to take on challenging tasks but sometimes stimulating self-destructive gambling behavior. It seems likely that the reliance on infoviz could be increased by increasing the illusion of control. But is this always desirable or undesirable?
