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Innocent Statistics

Once upon a time, there were some little kids from Nowhere, Planet Earth, who hung out at the local roller skating rink. There were numbers from 1 to 6 around the rink and once a session, there was a game. When the music stopped, we had to skate to a number and then someone tossed a huge die. If you were at that number, you were out, and the game continued until only one of us, the winner, was left. After each roll, when the music again stopped, we ran to the last number that had been on the die. Why? Well, of course, the same number wasn’t likely to come up again!

And, of course, the die had to know this! Any grownup who might have told us that there was the same chance of two “sixes” in a row as the chance of a “six” followed by a “three” had to be stupid. This wasn’t likely to happen anyway because grownups were busy “knocking on wood,” after admitting their families were enjoying good health for a second whole year. So they enjoyed a third year of good health because they “knocked” – unlike the Jones family, where Aunt Pitiful had a recurrence of cancer diagnosed the previous year and Grandpa Tycoon had a heart attack for the second year in a row.

To celebrate her family’s good health (“knock on wood”), Mama Patsy went to Las Vegas, where she knew enough to stick to betting “red” or “black” at roulette. How could she lose? She watched the table and whenever one color came up three times in a row, she bet on the other color! After all, surely the wheel knew it couldn’t pick the same color four times in a row. What was wrong? We observed previous events and used our observations to infer future events.

First, our observations were biased because there were, for example, fewer number repetitions than non-repetitions (after all, there only are six ways that the same number can come up twice in two rolls of the die). Second, unexpected events are more noticeable. For example, two people who live together may have been going to the movies once a week for years. Usually, they looked at newspaper listings and made a choice. Last night, Bella told Bert she had been thinking about seeing “Little Buggers” all day. Bingo! “You must be clairvoyant,” Bert said, “I’ve been thinking the same thing. ”

Third: Mathematical and scientific principles are smarter than people. If a person had been picking the numbers on the die or colors on the roulette wheel, they’d want to have a random ordering – but they don’t know what random means. Had a person been in charge, a strategy of sticking with “three” or switching colors after two repetitions probably would have been a better one than using actual random selection, and a person probably would not have been influenced by the troublesome information that someone in poor health would have a higher probability of continued poor health than a person in good health.

But now I’m out of Nowhere, Planet Earth, in the outside world, in college, where the gentlepeople and scholars know more than the slobs from No-where – right? Wrong. Now here are the winners of the Golden Bleep awards. The “Send in the Clowns Award” (Sondheim, 1973). In a moment of madness, I skimmed Vohs and Schooner (2008) pontificating that the result of an increased belief in determinism may be raising “the ominous possibility . . . [of] an increase in [student] cheating” (p. 53) and “insulating the public against this danger [would become] imperative” (p.

54). I’ll gladly let these fruitcakes insulate me – if they stop falsifying the data they use in their statistical tests (see, please see, pp. 51-53). Most astutely (! ), they randomly assigned participants to one of 5 conditions, all of which required solving 15 questions from the Graduate Record Examination. In one group, participants solved the problems and the experimenter paid them $1 for each correct answer and in a second group, before participants began, they read 15 statements justifying determinism.

In the three other groups, the experimenter first answered her cell phone, and cleverly pretended she had to go to a meeting, so they should grade and pay themselves $1 for each correct answer. Before leaving, the experimenter had these groups read either15 deterministic statements, 15 statements supporting free will, or 15 neutral statements. She then gave them free will, determinism, and mood scales. In these three conditions, the participants shredded their answer sheets – and there were no records of how much money they paid themselves.

Do you believe that this procedure “was crucial to establishing the anonymity necessary to measure active cheating” (p. 53)? In the several million or so other studies published yearly, did participants doubt their anonymity would be preserved? Did they really believe they solved the problem by dividing the total money taken by participants in each of the three groups by the number of group participants, and using these group averages “as a proxy for each participant’s number of correct answers” (p.

51), i. e. , each participant in a group was given the same score, the mean? Dear Vohs and Schooler (2008): You may (or may not) remember that in calculating t, F, and r statistics, you divide the top, the numerator, by the bottom, the denominator. Let’s use the t test since it’s the simplest example. Your numerator is fine – it’s the mean difference between 2 groups. The denominator, however, is a measure of differences in scores within the 2 groups.

By falsely using the group mean for all participants in two of the subgroups in Group 1 (the mean combined over 4 groups) and for all participants in the determinism group, the denominator is smaller than it would have been if individual scores had been used. Thus the ratio of between-group variability to within-group variability – your t value – is inaccurately increased (i. e. , dividing by a smaller than accurate number). Indeed, you acknowledge the possibility “that only 1 or 2 participants . . . cheated and that the remainder took their fair share (or less)” (p. 53).

Unfortunately, you then say “the average take-home pay was far greater [actually, about $2. 25] for participants in the determinism condition” (p. 53). Think: If all but one participant in the determinism condition had scores similar to participants in the other conditions, what should you conclude? You should conclude that the probability of an exceptionally greedy participant being assigned to the determinism condition by chance was high – and that your t value would be smaller and not reach statistical significance. Reviewing an introductory statistics book might be useful (e.

g. , Aron, Aron, & Coups, 2007). The “Joe McCarthy, Have You No Shame Award? ” (Welch, 1954, as cited in Kopel, 1996). Prior to publication of his nasty little book (Simonton, Creighton, & Matthews-Simonton, 1978), Simonton, a radiological oncologist, had already became wealthy treating the similarly wealthy people with cancer who came to his clinic and on his retreats. No, the clinic did not provide chemotherapy or radiation – instead, in the most luxurious of surroundings, people learned that they could recover by means such as guided imagery and – talking to their cancer cells.

By buying his book, everyone, not just the wealthy, could learn Simonton’s techniques. Many editions of this and other books later, Simonton had become a master of the Web, using it to peddle his junk (sorry, “resources and aids,” such as a $75. “Patient Package,” containing 2 books and 3 CDs, Simonton Cancer Center, 2008). He reported and continues to report that those using his methods have “doubled their life expectancy compared to those who received only medical treatment” (Linn, 1998, p. 1).

He’s simply reporting descriptive statistics – with inferences about cause and generalization so obvious they don’t need to be stated. Guess what, doc? Those with high socioeconomic status have equally long survival rates – even when they don’t talk to their cancer cells. They have access to better medical care, better nutrition, etc. You might wonder why someone doesn’t do a study to assess the influence of Simonton’s and others’ “complementary alternative treatments. ” There have been many such studies, all reporting there is no evidence that these treatments affect survival rates (Vickers, 2004).

The Federal Drug Administration places only one restriction on sales of these “complementary alternative treatments” – that they may not be described as “cures” – raising insinuation “to an art form of doublespeak” (Angell & Kassirer, 1999, p. 840). Why do people continue to have faith in all sorts of “complementary alternative treatments? ” People have a long history of believing, indeed perceiving, what they want to believe – you’ll meet only a rare person who reports he or she isn’t above average on just about any desirable trait (Alicke, 1985).

Besides, Doc Simonton might point out that he provides companionship – their cancer cells – to otherwise lonely people, and at least his products don’t give cancer to people. That’s the truth, doc, but you didn’t get the How Low Can You Go Award? High schools like to tell us about the cigarette industry. Early reports that smokers were more likely to have died of cancer than others elicited the response that correlation cannot be interpreted as causation – smokers might have differed from nonsmokers in other ways, ways that might have caused cancer.

Well, rats (who like college sophomores have been promoted from “subjects” to “participants,” American Psychological Association, 2003), who had been randomly assigned to receive what smokers receive from cigarettes, were more likely to die of cancer than other rats. So what! You can’t generalize from rats to people. Besides, teenagers are even more inflicted than others to the It Can’t Happen to Me Disease. Conclusion Why do people behave as described above? I’ll tell you in my next paper. I have to go buy a $14,615. comfy Range of Motion (ROM) chair (advertised in Discover, 2008, p. 9).

If I use my ROM for 4 minutes a day, I’ll remain as healthy as jerks who actually exercise. “Too good to be true? ” (p. 9). Not being a fool, I require evidence. “The best proof for us [the manufacturers] is that 97% of rentals become sales” (p. 9). If it didn’t work, why else would people keep their ROMs? If roulette wheels didn’t know they had to switch colors, why else would we bet on “black” after 3 repetitions of “red”?

References

Alicke, M. D. (1985). Global self-evaluations as determined by the desirability and controllability of trait adjectives. Journal of Personality and Social Psychology, 49, 1621-1650.American Psychological Association (2003). Publication Manual. Washington, D. C. : American Psychological Association. Angell, M. , & Kassirer, J. P. (1999). Alternative medicine – the risks of untested and unregulated remedies. The New England Journal of Medicine, 339, 839-841. Aron, A. , Aron, E. , & Coups, E. (2007). Statistics for the behavioral and social sciences (4th ed. ). Upper Saddle River, NJ: Prentice-Hall. Discover (February 2008). Exercise in exactly 4 minutes per day (ad), p. 9. Kopel, D. (1996). Scoundrel time is back. Denver Post. Retrieved March 1, 2008, from www. davekopel. com/2A/OpEds/ScoundrelTimeIsBack. html.

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