Statistical Infrequency Research Articles

Uncommon Yet Consequential Online Harms

A consistent finding from recent research on harmful online behaviors is that they tend to be concentrated among a small number of individuals. Whether examining misinformation (Grinberg et al. 2019; Guess, Nagler, and Tucker 2019; Allen et al. 2020), radicalizing or partisan content (Hosseinmardi et al. 2021; Muise et al. 2022), or hate speech (Zannettou et al. 2020), a small number of individuals typically accounts for the vast majority of the behavior. Despite this statistical infrequency, the social consequences of such behaviors can be substantial, especially for people targeted by, or within the social networks of, the individuals perpetuating them.

Scrutinizing the basis of originality in divergent thinking tests: On the measurement precision of response propensity estimates.

The originality of divergent thinking (DT) production is one of the most critical indicators of creative potential. It is commonly scored using the statistical infrequency of responses relative to all responses provided in a given sample. Response frequency estimates vary in terms of measurement precision. This issue has been widely overlooked and is addressed in the current study. Secondary data analysis of 202 participants was performed. A total of 900 uniquely identified responses were generated on three DT tasks and subjected to a 1-parameter logistic model with a response as the unit of measurement which allowed for the calculation of response-level conditional reliability (and marginal reliability as an overall summary of measurement precision). Marginal reliability of response propensity estimates ranged from .62 to .67 across the DT tasks. Unique responses in the sample (the basis for the classic uniqueness scoring) displayed the lowest conditional reliability (across tasks: ≈.50). Reliability increased nonlinearly as a function of both the frequency of occurrence predicted by the model (conditional reliability) and sample size (conditional and marginal reliability). This study indicates that the common practice of frequency-based originality scoring with typical sample sizes (e.g., N=100 to N=200) yields unacceptable levels of measurement precision (i.e., in particular for highly original responses). We further offer recommendations to mitigate the lack of measurement precision of frequency-based originality scores for DT research.

Disabling Consent, or Reconstructing Sexual Autonomy

C. Sexual Autonomy [not equal to] Consent Despite Rubenfeld's and Spindelman's otherwise contrary critiques of sexual autonomy--overreaching and under-protective, respectively--both authors equate sexual autonomy with consent. If sexual assault law is premised on consent, warns Rubenfeld, we are obliged to send teenagers to prison for lying about their age in order to have sex. (67) If sexual assault law is premised on consent, warns Spindelman, gay men can infect one another with HIV with impunity, and there is no actionable harm. (68) But what if sexual autonomy denotes something other than, or something more than, first person present active (or passive) consent? Before elaborating that something--that is, before retrieving and then defending a reconstructed, relational, and feminist sexual autonomy--we revisit Rubenfeld's and Spindelman's cases of sexual autonomy gone wild. What inklings are there, in these authors' own examples, of sexual autonomy theorized otherwise? D. Three Seventeen-Year-Olds In his gauntlet-thrown offensive, as well as in the reply to his critics, (69) Rubenfeld repeatedly circles back to teenagers and teenage sex, and specifically to sex with and between seventeen-year-olds. (70) The seventeen-year-old, on the eroticized precipice of majority, (71) is the character that dramatizes the deficiencies of sexual autonomy. But each of his three teen sex scenarios could and should be spun differently, shoring up the possibilities, rather than the pitfalls, of sexual autonomy. We briefly summarize each of his scenarios and amend them with a few provocations--provocations to be fleshed out in Parts II and IV. 1. Seventeen-Year-Old #1 If sexual autonomy is equivalent to consent, then sex-by-deception--any deception--is, concludes Rubenfeld, equivalent to sexual assault. If a seventeen-year-old lies to have sex with an older partner, consent is thereby compromised, the teen therefore assaultive. Rubenfeld appeals to a liberal-leaning, feminist-friendly audience. Are we prepared to incarcerate a seventeen-year-old girl for lying about her age to have sex with an older man? (72) If not, there is but one plausible option: junk nonconsent and reinstate force requirements. (73) First, we should recognize the statistical infrequency of this teen lie, or mootness of the lie (if the lie is told to convince an otherwise law-abiding but libidinal citizen). Rubenfeld mistakenly (or misleadingly) presupposes that the age of consent for sexual conduct is eighteen, a commonly held misperception. But in nearly all states the age of consent is sixteen; (74) so too, nearly all states include age-span provisions in their sexual assault codes. (75) In many states, for example, it is legal for anyone of any age to have sex with a sixteen-year-old, but only those seventeen and under are permitted to have sexual relations with fourteen-year-olds. (76) To the extent that this lie occurs, and occurs to convince a suitor of the ensuing sex's legality, the more likely scenario would be the following: a fourteen-year-old lies about her age to have sex with someone eighteen or nineteen. (77) To compete on Rubenfeld's rhetorical plane: a high school freshman lies about her age to have sex with a college freshman or college sophomore. In this circumstance, we may more justifiably conclude that the high school freshman is not accountable for sexual assault, but because she is not accountable to sex. In other words, we do not hold her criminally accountable for the lie for the same reason the law proscribes sex with her: she is not as capable a decision maker--on account of experiential, educational, and developmental differences--as an older teenager or adult. This legal fiction--an incompetent and thus innocent fourteen-year-old--is more palatable to liberals and sex progressives than the fiction of the incompetent and thus innocent seventeen-year-old. (78) This observation about the extant age of sexual consent law segues to the second and more important criticism of the lying teenager hypothetical. …

Do We Relatively or Absolutely Overestimate Rare Events?

How good are we at estimating the frequency of rare events? Previous evidence has been mixed: While some studies report well-calibrated frequency judgments, others found rare events to be overestimated. We examined whether the distinctiveness of a rare event fosters overestimation. Distinctiveness may result from exceptional valence, statistical infrequency, or the joint occurrence of two distinct features. Such paired distinctiveness has been found to be particularly salient. We conducted two experiments to investigate the impact of paired distinctiveness and valence on frequency estimations of rare events by combining two paradigms from the decision-making literature and the social psychology literature on stereotypes. The results indicate that rarity alone does not necessarily result in overestimation; rather, the combination of statistical infrequency and small sample sizes (i.e., paired distinctiveness) led participants to overestimate the frequency of a rare event. We were able to rule out alternative explanations such as regression to the mean, but the exact role of outcome valence needs further investigation.

Pathology Versus Statistical Infrequency: Potential Sources of Gender Bias in Personality Disorder Criteria

The antisocial, narcissistic, dependent, histrionic, and borderline personality disorders often obtain differential sex prevalence rates. One explanation has been that the diagnostic criteria for these personality disorders have different gender implications for maladaptivity (e.g., perhaps the dependent personality disorder diagnostic criteria are considered by clinicians to be more pathological for women than for men). This hypothesis was explored in two studies that obtained judgments by professional clinicians of the maladaptivity and statistical infrequency of personality disorder diagnostic criteria. Significant differences across gender were obtained for the frequency of diagnostic criteria but not for their maladaptivity. The personality disorder diagnostic criteria appear to be gender neutral with respect to their implications for maladaptivity.

Reply to Cohen

1 In certain ordinary zoological contexts, we know we see a zebra. If closure is right, then in those contexts, we know we do not see a cleverly disguised Cohen's diagnosis: In those contexts, Our reason for denying we see a cleverly-disguised mule, e.g., the infrequency of such deceptions, is sufficient for us to know we do not see a cleverly-disguised mule. Here's another case. I know I'll never have enough money to buy ten Rolls Royces. If closure is right then in those contexts 'know' truly qualifies 'I will never win first prize in a lottery' (even if I have a lottery ticket at home). We can now reapply Cohen's diagnosis: In those contexts, our reasons for denying that we will win first prize in a lottery, namely the statistical infrequency of winning tickets, is sufficient for us to know that we we will never win a lottery. Isn't this bad? You don't have to shift context to realize that you don't know whether or not a lottery ticket is a winner.

The assessment, treatment and community outcome of insanity acquittees: Forensic history and response to treatment

The rather startling similarities in the controversies surrounding the insanity defense over several centuries (Golding & Roesch, 1987; Hans, 1986; Hermann, 1983a; Shah, 1986) underscore the transhistorical and deeply rooted problems involved in the development of a rational and coherent policy for adjudicating criminal non-responsibility on grounds of mental disorder. The importance of developing a clear and coherent set of social, legislative and clinical policies with respect to insanity acquittees, regardless of the statistical infrequency of the insanity verdict (Pasewark & McGinley, 1985), is made patently clear by the continuing legal, public, and scholarly controversy which surrounds the defense. Modern sentiments following John Hinckley’s acquittal by reason of insanity differ little from those of Queen Victoria, “We have seen the trials of Oxford and MacNaughten conducted by the ablest lawyers of the dayand they allow and advise the Jury to pronounce the verdict of not guilty on account of insanity, whilst everybody is morally convinced that both malefactors were perfectly conscious and aware of what they did” (cited in Walker, 1968, p. 168). It is quite clear that the bundle of problems surrounding the insanity defense and the disposition of insanity acquittees will remain a focal problem, whether or not one abolishes or modifies the plea.’ Until both social science researchers and political decision-makers, as well as the lay public, have available a longitu-

Illusory correlation in the perception of group attitudes.

126 undergraduates with pro- or anti-attitudes toward nuclear power and 15 local members of a campaign for nuclear disarmament viewed opinion statements supposedly made by residents of 2 towns. One town was larger and statements from it occurred frequently, the other was small and statements from it were infrequent. Statements expressed either pro- or anti-attitudes to the building of a nuclear power station, in which one position was in a majority over the other. Despite the fact that the proportion of pro- and anti-statements was the same for both towns, it was predicted that the most statistically infrequent category, minority position/small town, would appear most distinctive and receive greatest encoding, leading Ss to overrepresent this category. It was also hypothesized that attitude-congruent positions would appear more salient than others because of their self-relevance, resulting in enhanced illusory correlation for minority-congruent attitude holders (distinctiveness plus salience). Futhermore, it was predicted that salience and therefore illusory correlation would increase as a function of attitude extremity for these Ss. All 3 predictions were supported, replicating the findings of D. L. Hamilton and R. K. Gifford (1976) that distinctiveness, operationalized as statistical infrequency, mediated an illusory correlation effect.

THE EFFECTIVENESS OF REINFORCEMENT AND PRACTICE FOR ENHANCING THE CREATIVE WRITING OF ELEMENTARY SCHOOL CHILDREN1

Reinforcement (team points) and practice were applied to the written work of 16 fifth graders on three operationally defined components of creative writing, fluency, flexibility, and originality.4 These three components were assessed via five response measures. Fluency was defined as the number of different ideas each student listed in an idea list prepared prior to writing an essay. Flexibility was measured in two ways, idea list flexibility and story flexibility. Idea list flexibility was defined as the number of different kinds of ideas which appeared in each day's list whereas story flexibility was defined as the number of different approaches to the topic that the child used in the story itself. Originality was also measured in two ways, idea list originality and story originality. Idea list originality was defined by the statistical infrequency of ideas in the children's lists of ideas. Story originality was determined by blind, subjective ratings of stories conducted by independent raters. All of the measures of creative responding were demonstrated to be under experimental control. The procedures also raised students' scores on Torrance's Tests of Thinking Creatively With Words on three variables, fluency, flexibility, and originality. Adoption for classroom use seems straightforward.

A Comparison of Statistical Infrequency and Subjective Judgment as Criteria in the Measurement of Originality

The Alternate Uses test was administered to a sample of 60 college students. Three different criteria of originality were used in scoring: subjective judgment, statistical infrequency, and random numbers. Correlations among the three methods exceeded .67 (p < .01). The explanation for this finding is that the originality scores are strongly influenced by the number of responses (i.e., ideational fluency). Because the total originality score is based on a sum of the originality weightings for each response, individuals who give many responses are more likely to get high originality scores. Further analysis demonstrated that the subjective and statistical infrequency scoring techniques are not correlated when ideational fluency is controlled. Implications for the measurement of originality are discussed.

Procedures to increase some aspects of creativity.

Instructions reinforcement (team points), and practice were applied to four behaviorally defined creative behaviors of eight fourth- and fifth-grade students. All four aspects (number of different responses, fluency; number of verb forms, flexibility; number of words per response, elaboration; and statistical infrequency of response forms, originality) were demonstrated to be under experimental control. The procedures also raised students' scores on Torrance's tests of creativity. Application of the experimental procedures may well be practical for classroom teachers.

Breaking Away from Perceptual Set and Statistical Infrequency in Production of Original Verbal Images

Breaking Away from Perceptual Set and Statistical Infrequency in Production of Original Verbal Images

Impact of instruction on development of deaf children's originality of thinking.

Presently there are four different methods (Kohl, 1966) employed in the instruction of deaf children: (a) the pure oral method, (b) the oral method, (c) the natural language method, and (d) the Rochester or combined system method Conflicting views exist about the relative usefulness of these methods or their combinations. However, the originality scores obtained on Torrance's Thinking Creatively With Picrures Test might favor deaf children taught under the natural language method as opposed to those taught under the combined system method. The 35 second grade deaf boys and girls came from a School for the Deaf located in the Southeastern United States and were of different ages, mental, and hearing abilities. These Ss were divided at the beginning of the year into four classes, each one being taught by a different teacher. Three classes (N = 27) were taught by teachers who employed the combined-system method while the fourth class (N = 8) was taught by a teacher who used the natural language method. In the first task of the creativity tesr, Thinking Creatively With Pictures, Form A (Torrance, 1966), Ss are asked to draw a picture in which a piece of colored paper shaped like a pear with adhesive backing is an integral part. In the second task, Ss draw pictures by adding lines to 10 incomplete figures. In the third task, pictures using 30 pairs of parallel lines are drawn. In each task, Ss are instructed to produce pictures which are both unusually original and extremely elaborate. These tasks involve acquisition of information from relationships among stimuli which are seen repeatedly and perceiving stimuli in different ways. After the imposed time on each task was over, a teacher for the deaf helped Ss record their titles individually. Each task was scored for originality by the writer according to the standard scoring directions. This score is determined for each response separately and is based on the weight given each response. Responses showing statistical infrequency were assigned scoring weights of two points; obvious, irrelevant, and incomprehensible responses were assigned weights of zero. The means (and standard deviations) for groups with the natural language method and the combined-system method were 26 (4.3) and 22.7 (6.8) respectively (t = 1.66; F = 2.45, df = 1, 0 > .Or). These Ss constitute two independent groups and the measure of originality constitutes an ordinal scale. The results obtained by applying the MannWhitney U test indicate that the quality and quantity of creative originality scores of these two groups of deaf children is not a sufficient basis for concluding that either method of instruction is superior.