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1963 andrew gelman stats-2013-07-31-Response by Jessica Tracy and Alec Beall to my critique of the methods in their paper, “Women Are More Likely to Wear Red or Pink at Peak Fertility”


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Introduction: Last week I published in Slate a critique of a paper that appeared in the journal Psychological Science. That paper, by Alec Beall and Jessica Tracy, found that women who were at peak fertility were three times more likely to wear red or pink shirts, compared to women at other points in their menstrual cycles. The study was based an 100 participants on the internet and 24 college students. In my critique, I argued that we had no reason to believe the results generalized to the larger population, because (1) the samples were not representative, (2) the measurements were noisy, (3) the researchers did not use the correct dates of peak fertility, and (4) there were many different comparisons that could have been reported in the data, so there was nothing special about a particular comparison being statistically significant. I likened their paper to other work which I considered flawed for multiple comparisons (too many researcher degrees of freedom), including a claimed relation bet


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1 That paper, by Alec Beall and Jessica Tracy, found that women who were at peak fertility were three times more likely to wear red or pink shirts, compared to women at other points in their menstrual cycles. [sent-2, score-1.074]

2 a) Gelman suggests that we might have benefited from researcher degrees of freedom by asking participants to report the color of each item of clothing they wore, then choosing to report results for shirt color only. [sent-17, score-0.639]

3 b) We categorized shirts that were red and pink together because pink is a shade of red; it is light red. [sent-19, score-0.661]

4 The theory we were testing is based on the idea that red and shades of red (such as the pinkish swellings seen in ovulating chimpanzees, or the pinkish skin tone observed in attractive and healthy human faces) are associated with sexual interest and attractiveness (e. [sent-20, score-0.512]

5 Thus, our decision to combine red and pink in our analyses was a theoretical one. [sent-27, score-0.424]

6 If any of these analyses other than those of pink and red had produced significant differences, we would have failed to support our hypothesis. [sent-40, score-0.499]

7 We conducted these studies with the sole purpose of testing one specific hypothesis: that conception risk would increase women’s tendency to dress in red or pink. [sent-43, score-0.519]

8 Gelman is right that there is a good deal of debate about which days best reflect a high conception risk period, and this is a legitimate criticism of all research that assesses fertility without directly measuring hormone levels. [sent-49, score-0.568]

9 We adopted the Day 6-14 categorization period after finding that this is the categorization used by a large body of previously published, well-run studies on conception risk (e. [sent-51, score-0.492]

10 Rather, we adopted it a priori and used it and only it in analyzing our data; no researcher degrees of freedom came into play. [sent-58, score-0.477]

11 e) In any study that assesses conception risk using a self-report measure, certain women must be excluded to ensure that those for whom risk was not accurately captured do not erroneously influence results. [sent-59, score-0.601]

12 The decision of whether to exclude women on the basis of these gray-area criteria does lead to the possibility of researcher degrees of freedom. [sent-64, score-0.555]

13 First, like any published set of empirical studies, our article should not be viewed as the ultimate conclusion on the question of whether women are more likely to wear red or pink when at high risk for conception. [sent-73, score-0.877]

14 Indeed, a statistician like Gelman could go well beyond simply mentioning possible places where additional degrees of freedom might have come into play and then making assumptions about the validity of our findings on that basis. [sent-82, score-0.496]

15 He could, and should, instead find out exactly the places where researcher degrees of freedom did come into play, then calculate the precise likelihood that they would have resulted in the two significant effects that emerged in our studies if these effects were not in fact true. [sent-83, score-0.681]

16 In other words, additional researcher degrees of freedom increase the chance that we will find a significant effect where none exists. [sent-84, score-0.62]

17 How many researcher degrees of freedom would it take for this to become a figure that would reasonably allow Gelman to suggest that our effect is most likely a false positive? [sent-89, score-0.589]

18 Researchers do have certain responsibilities—such as avoiding, to whatever extent possible, taking advantage of researcher degrees of freedom and being honest about it when they do– but critics of research have certain responsibilities too. [sent-92, score-0.666]

19 Tracy and Beall write, “If any of these analyses other than those of pink and red had produced significant differences, we would have failed to support our hypothesis. [sent-108, score-0.499]

20 The point is that there are many degrees of freedom available, even if with the particular data that happened to occur , the researchers did only one particular analysis. [sent-113, score-0.421]


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