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"The Hannah Experiment" (Darley & Gross 1983) is cited as an example of labels biasing evaluation. This is described in "Drunk Tank Pink by Adam Alter" which I've paraphrased below:

Princeton University students decided whether a young fourth-grader named Hannah was performing above, below, or precisely at the level expected of an average student in the fourth grade.

During the first phase of the experiment, the students watched one of two brief videos:

  1. Lucky Hannah is shown to come from a college-educated family and lives in a wealthy neighbourhood.
  2. Unlucky Hannah is shown to come from a family with a high-school education and a poor neighbourhood.

At this point, some of the students watched a second video, in which Hannah was asked to answer a series of twenty-five questions from an achievement test. The questions were designed to assess her mathematical, reading, science, and social science skills. Instead of presenting a clear image of her ability, the video was ambiguous: sometimes she was engaged, answering difficult questions correctly, and sometimes she seemed distracted and struggled with relatively easy questions.

Hannah’s ability was difficult to discern from the video, but some of the students began watching with the labels “wealthy” and “college educated” in mind, whereas the others began watching with the labels “working class” and “high school educated” in mind. These labels functioned as tiebreakers when Hannah’s performance was neither flawless nor disastrous. The students who expected Hannah to succeed saw exactly that pattern of achievement in her responses (ignoring her missteps and distractibility), whereas those who expected less from Hannah saw exactly what the negative labels implied (ignoring her intermittent engagement and mastery of the difficult questions). In the end, the Lucky Hannah was judged to have performed above her fourth-grade level, whereas her Unlucky counterpart seemed to perform below fourth-grade level. The Hannah study showed that people are suggestible, willing to view the world with the guidance of labels when faced with an otherwise unbreakable tie.

Does this bias have a name? Has it been replicated/generalized?

References

Darley, J. M., & Gross, P. H. (1983). A hypothesis-confirming bias in labeling effects. Journal of Personality and Social Psychology, 44(1), 20–33. https://doi.org/10.1037/0022-3514.44.1.20

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This is basically describing stereotyping. (Several biases overlap to form these, depending which theory you prefer the most.)

The most cited paper that cites Darley & Gross seem to be a 1995 review titled "Implicit social cognition: Attitudes, self-esteem, and stereotypes". It cites D & G for implicit stereotyping (research):

Although research on stereotypes has often used direct or explicit measures (see Judd & Park, 1993), there are also substantial research programs on stereotypes that use indirect measures— ones in which a stigmatizing feature with which a stereotype is associated (e.g., weight, race, or gender) is peripheral to the respondent's judgment task (e.g., Darley & Gross, 1983) or in which the purpose of investigation is otherwise disguised (e.g., Hamilton & GifFord, 1976). Crosby, Bromley, and Saxe (1980) were able to locate enough research using indirect measures of prejudicial stereotypes to conclude that "anti-Black sentiments are much more prevalent among White Americans than the survey data [i.e., direct or explicit measures of stereotypes] lead one to expect." Although the use of indirect measures in these studies often reflects the researchers' intent to avoid intrusion of unwanted demand or impression-management artifacts (which would plausibly suppress accurate expressions of conscious stereotypes), some of the research that is summarized just below was designed specifically to investigate unconscious operation of stereotypes. These studies suggest that stereotypes are often expressed implicitly in the behavior of persons who explicitly disavow the stereotype. The next two sections focus attention on race and gender stereotypes because these, having been much more heavily investigated than other stereotypes, have provided the most persuasive evidence for implicit stereotyping.

Wikipedia also has a more specific article on implicit stereotype, although it seems someone was unhappy with it... The wiki article claims:

Implicit stereotype was first defined by psychologists Mahzarin Banaji and Anthony Greenwald in 1995

which is probably referring to the above 1995 review, but I'm not sure how correct is the claim that Banaji & Greenwald were the first to define the notion. (They clearly were not the first to study it.)

Greenwald has actually co-authored a more recent (2019) review titled just "Implicit Social Cognition", which (I guess) could be useful to check for research progress on implicit stereotyping. Most of the later research seems to have involved (the veritable explosion of) IAT studies. Greenwald (2019) summarizes several meta-analyses and does some moderator analysis.

For a broader theoretical perspective (and to clarify what Greenwald and Banaji actually introduced--it's actually the term "implicit cognition", with a specific def), Hahn & Gawronski (2015) write contrasting Greenwald's conception with De Houwer et al.'s:

Drawing on the notion of implicit memory, Greenwald and Banaji (1995) defined implicit cognition as “introspectively unidentified (or inaccurately identified) trace of past experience that mediates responses” (p. 5). Although this definition was meant to imply unawareness of the sources of mental contents, it has often been interpreted to imply unawareness of the mental contents themselves (e.g., unawareness of the source of an attitude vs. unawareness of the attitude itself). However, the latter interpretation conflicts with a considerable body of evidence, suggesting that the psychological constructs captured by nonreactive, computerized measures are consciously accessible and thus not unconscious (e.g., Hahn et al., 2014).

More recently, De Houwer et al. (2009) proposed an alternative conceptualization to overcome the common confusion regarding the meaning of the term implicit. [...] Measurement procedures [...] may be described as direct if their measurement outcomes are based on participants’ self-assessment of the to-be-measured attribute (e.g., when participants’ racial attitudes are inferred from their self-reported liking of Black people). Conversely, measurement procedures may be described as indirect if their outcomes are not based on a self-assessment (e.g., when participants’ racial attitudes are inferred from their reaction times to positive and negative words after being primed with Black faces) or when it is based on a self-assessment of attributes other than the to-be-measured attribute (e.g., when participants’ racial attitudes are inferred from their self-reported liking of a neutral object after being primed with Black faces).

Applying the latter categorization to D & G (1983) study, they clearly used an indirect measure in De Houwer's categorization. Thus from this methodological perspective (after glancing over De Houwer et al.) D & G (1983) is an affect priming study.

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