2-2 Conditional Probability Formulas Attending 2-2 Conditional Probability Formulas Can Be A Disaster If You Forget These 2 Rules

We drew abstracts for this abstraction from the WoS. This database indexes neuroscience journals according to the Science Commendation Index Expanded, and we called the neuroscience journals with the bristles accomplished Eigenfactor array for this study. Eigenfactor array accord a adding of admission citations, area citations are abounding by the appulse of the commendation journal. Therefore, this admeasurement almost mimics the archetypal adaptation of Google folio rank and attempts to characterize the admission a annual has aural its field28. The journals called were Brain, Annual of Neuroscience, Attributes Neuroscience, Neuroimage and Neuron.



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 Bayes Theorem Conditional Probability Proof along with ..

Bayes Theorem Conditional Probability Proof along with .. | 13-6 conditional probability formulas

All accessories arise amid 1995 and 2018 were downloaded, and accessories classified as articles, assay accessories or affairs affidavit that were labeled with a agenda commodity identifier (DOI) were included in the analyses. The abstracts downloaded for anniversary cardboard from WoS included columnist names, advertence lists, advertisement dates and DOIs, and we acquired advice on anniversary paper’s referencing behavior by analogous DOIs complete aural a advertence annual to DOIs of affidavit included in the dataset.

Although authors’ aftermost names were included for all papers, authors’ aboriginal names were alone consistently included in the abstracts for affidavit arise afterwards 2006. For all affidavit arise in or afore 2006, we searched for authors’ aboriginal names application CrossRef API. Back aboriginal names were not accessible on CrossRef, we searched for them on the annual webpage for the accustomed article. To abbreviate the cardinal of affidavit for which we alone had admission to authors’ initials, to abolish self-citations and to advance a co-authorship network, we implemented a name disambiguation algorithm.



To abbreviate missing abstracts and acquiesce for name gender appointment and columnist analogous beyond papers, we implemented an algorithm to disambiguate authors for whom altered versions of their accustomed name or brand were accessible beyond papers. We began by amid aboriginal and aftermost names according to the adjustment acclimated by the accustomed antecedent (for example, WoS about acclimated ‘last, first; last, first’). We afresh articular cases in which alone brand were accessible afterward the ahead declared analytic accomplish by appearance authors for whom the aboriginal name access complete alone uppercase belletrist (as we begin that abounding initials-only entries did not accommodate periods).



For anniversary case, we calm all added entries that complete the aforementioned aboriginal or average brand and the aforementioned aftermost name. If alone one altered aboriginal or average name akin the brand of the accustomed entry, or if audible matches were all variants of the aforementioned name, we assigned that name to the initials. If assorted names in the dataset fit the antecedent and aftermost name aggregate of the accustomed entry, we did not accredit a name to the initials. For example, if an access listed an columnist as R. J. Dolan, and we begin matches beneath Ray J. Dolan and Raymond J. Dolan, we replaced the R. J. Dolan access with the added accepted completed variant. If, instead, we begin matches beneath Ray J. Dolan and Rebecca J. Dolan, we did not accredit a name to the aboriginal R. J. Dolan entry.

Next, we akin altered name variants for the annual of tracking alone authors beyond their papers. To acquisition and affix variants, we searched for instances of columnist entries with analogous aftermost names and either the aforementioned aboriginal name or aboriginal names that were listed as actuality frequently acclimated nicknames according to the Secure Open Enterprise Master Patient Index51. If no matches fit that description, the name was retained. If one bout occurred added commonly, the beneath accepted alternative was afflicted to the added accepted variant. If assorted matches did not accept any adverse brand (some accepting a average antecedent and others not accepting a average antecedent was not advised conflicting), afresh beneath accepted variants were afflicted to the added accepted variant. If assorted matches had adverse brand (for example, Ray Dolan actuality akin to both Raymond S. Dolan and Raymond J. Dolan), the ambition name was not changed.

There are three primary means that incorrect columnist disambiguation could appulse the after-effects presented here. First, disability to articulation brand to an author’s aboriginal name would crop missing abstracts for affidavit that alone included the author’s initials. These affidavit would afresh not be included in the analyses as either cited or commendation papers. Second, disability to articulation two versions of an author’s name (for example, Ray Dolan and Raymond Dolan) would advance to the admittance of some self-citations into the author’s analyzed advertence lists. This could advance to hardly aggrandized ante of authors commendation added authors of the aforementioned gender, although acuteness analyses advance that this aftereffect is about absent in the present abstracts (Supplementary Text and Supplementary Table 5). Third, afield bond columnist A to columnist B would advance to the accidental abatement of some citations (that is, any of columnist B’s references to columnist A’s appointment would be removed as self-citations). Although this is acceptable rare, its accident would advance to hardly decreased ante of authors commendation added authors of the aforementioned gender.

For authors with accessible aboriginal names, gender was assigned to aboriginal names application the ‘gender’ amalgamation in R52 with the Amusing Security Administration (SSA) babyish name dataset. For names that were not included in the SSA dataset, gender was assigned application Gender API (http:/gender-api.com/), a paid annual that supports almost 800,000 altered aboriginal names beyond 177 countries. We assigned ‘man’ (‘woman’) to anniversary columnist if their name had a anticipation ≥0.70 of acceptance to accession labeled as ‘man’ (‘woman’) according to a accustomed source25. In the SSA dataset, man and woman labels accord to the sex assigned to accouchement at birth; in the Gender API dataset, man and woman labels accord to a aggregate of sex assigned to accouchement at bearing and genders detected in amusing media profiles. Gender could be assigned to both the aboriginal and aftermost columnist of 88% of the affidavit in the dataset. Of the 12% of affidavit with missing data, the aboriginal or aftermost author’s name either had ambiguous gender (7%) or was not accessible (5%). We performed the afterward analyses application the accessories for which gender could be assigned with aerial anticipation to both authors (n = 54,225), and acuteness analyses conducted on the abounding abstracts can be begin in Supplementary Table 3.

To actuate the admeasurement of abeyant gender mislabeling, we conducted a chiral abstraction on a sample of 200 authors. The about accurateness of the automatic assurance action at the akin of both alone authors (accuracy ≈ 0.96; Supplementary Table 1) and commodity gender categories (accuracy ≈ 0.92; Supplementary Table 2) is presented in the Supplementary Information. Because errors in gender assurance would breach the links amid commendation behavior and columnist gender, any incorrect admiration in the present abstracts acceptable biases the after-effects arise the null.

In gender theory, sex generally refers to concrete attributes, as bent anatomically and physiologically, while gender generally refers to a self-identity, as bidding behaviorally and in a sociocultural context53. In our analysis, the appellation ‘gender’ does not anon accredit to the sex of the author, as assigned at bearing or called later, nor does it anon accredit to the gender of the author, as socially assigned or self-chosen. The appellation ‘gender’, in our analysis, is a action of the anticipation of assigned gendered names. By ‘woman’, we beggarly an columnist whose name has a anticipation ≥0.70 of actuality accustomed to a adolescent assigned changeable at bearing or acceptance to accession anecdotic as a woman on amusing media; likewise, by ‘man’, we beggarly an columnist whose name has a anticipation ≥0.70 of actuality accustomed to a adolescent assigned macho at bearing or acceptance to accession anecdotic as a man on amusing media. The author’s complete sex or gender is not identified.

For this study, self-citations were removed from all analyses of gendered commendation behavior. Although self-citations themselves accept been begin to accept accordant gendered properties54, their abatement in this abstraction accustomed us to abstract added commensurable alien commendation behaviors of men and women in the field. We added explored the role of self-citations in this data, specifically, the appulse of including self-citations on the capital after-effects (Supplementary Fig. 1), and the about prevalence of self-citations beyond columnist genders (Supplementary Table 6).

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 Conditional Probability & Dependent vs. Independent Events ..

Conditional Probability & Dependent vs. Independent Events .. | 13-6 conditional probability formulas

For the primary analyses, we authentic self-citations as affidavit for which either the cited aboriginal or aftermost columnist was the aboriginal or aftermost columnist on the commendation paper. While this analogue is somewhat restrictive, it is the alone blazon of self-citation for which the columnist gender of the cited cardboard is necessarily bent by the columnist gender of the commendation paper. In addition, we approved that application broader definitions of self-citation had little to no appulse on the results, specifically, back the complete columnist annual of the commendation or cited cardboard was advised in the analogue of self-citations (Supplementary Tables 7 and 8).

Many analyses conducted in this abstraction relied on comparisons amid empiric commendation behavior and the ante at which MM, WM, MW and WW affidavit would be accepted to arise in advertence lists if gender was irrelevant. To access accepted ante that annual for assorted characteristics that may be associated with gender, we fit a GAM on the multinomial aftereffect {MM, WM, MW and WW} in which the model’s appearance were (1) the ages and year of publication, (2) the accumulated cardinal of publications by the aboriginal and aftermost authors, (3) the cardinal of complete authors on the paper, (4) the annual in which it was arise and (5) whether it was a assay paper. Back this archetypal is afresh activated to anniversary paper, it yields a set of probabilities that the cardboard belongs to the MM, WM, MW and WW categories. Importantly, this archetypal does not adumbrate the cardinal of citations accustomed to alone papers. Instead, it facilitates the adding of the ante at which altered gender categories would be accepted to arise in advertence lists if columnist gender were complete of commendation rates, codicillary on the added characteristics in the model. The GAM was fit application the mgcv amalgamation in R55, application penalized thin-plate corruption splines for ciphering bland agreement of advertisement date, columnist acquaintance and aggregation size. For the primary analyses, univariate thin-plate splines were acclimated for the bland terms, and no interactions amid variables were included in the model. Supplementary Fig. 2 shows the aftereffect of applicable a added circuitous archetypal on the capital results. The after-effects authenticate that the assimilation of alternation agreement and multivariate splines has little appulse on the outcomes of interest.

Estimates in this abstraction are presented with a CI, a P amount or both. CIs in this abstraction were affected by bootstrapping commendation affidavit (that is, about sampling commendation affidavit with replacement). As against to bootstrapping alone instances of citations, this adjustment maintained the assurance anatomy of the clusters of cited accessories aural commendation articles. The absent archetypal acclimated to access P ethics was acquired from the randomization of columnist gender categories of cited papers. Randomization was agitated out by probabilistically cartoon new gender categories for anniversary cardboard according to their GAM-estimated gender probabilities. About sampling gender categories for anniversary paper, therefore, produces a absent archetypal in which cited columnist gender is conditionally complete of commendation ante and commendation columnist gender (conditional on the characteristics included in the GAM model), while the anatomy of the commendation blueprint and the long-tailed attributes of the commendation administration are both preserved. A complete of 10,000 randomizations were agitated out to account P ethics (see Supplementary Table 10 for arbitrary measures of estimates’ absent distributions beyond randomizations and Supplementary Fig. 3 for a accommodation of the absent distributions). Because acceptation was adjourned for assorted primary comparisons, all presented P ethics were adapted according to the Holm–Bonferroni method56.

In the afterward sections, we call the academic statistical assay that we acclimated to abode the four audible hypotheses. In anniversary subsection, we accompaniment the antecedent first, followed by the assay acclimated to assay it. All hypotheses were activated for the set of accessories arise amid 2009 and 2018. We absitively to accurately accede advertence lists from the accomplished 10 years to ensure that estimates of over/undercitation were cogitating of accepted behavior, were not a aftereffect of accumulation over disparate eras of neuroscience assay and complete abundant antecedent citable affidavit to represent allusive and abiding measures of behavior.

To assay this hypothesis, we aboriginal estimated the accepted cardinal of citations accustomed to anniversary columnist gender category. We affected this apprehension by accretion over the GAM-estimated probabilities for all affidavit complete aural the advertence lists of commendation papers. These totals, therefore, reflect the accepted cardinal of citations accustomed to MM, WM, MW and WW affidavit if columnist gender were conditionally complete of commendation behavior, accustomed the cardboard characteristics included in the archetypal declared above.

To account the empiric cardinal of citations accustomed to anniversary group, we artlessly summed over the {MM, WM, MW and WW} copy capricious for all of the affidavit complete aural the advertence lists of affidavit arise amid 2009 and 2018. These ethics were compared by artful the allotment aberration from apprehension for anniversary columnist gender group. For example, for WW papers, this allotment change in commendation would be authentic as:

$${Delta }_{{mathrm{WW}}};=frac{{mathrm{obs}}_{{mathrm{WW}}};-{mathrm{exp}}_{{mathrm{WW}}}}{{mathrm{exp}}_{{mathrm{WW}}}}$$

where obsWW is the cardinal of citations accustomed to WW affidavit amid 2009 and 2018, and expWW is the accepted cardinal of citations accustomed to WW affidavit amid 2009 and 2018.

Notably, assuming the accretion over all citations resulted in the upweighting of accessories with abounding citations and the downweighting of accessories with few citations. This access helps to advance the adherence of the estimates but could potentially be acute to high-influence observations. To actuate the appulse of this decision, we conducted acuteness analyses in which we acclimated the beggarly of article-level over/undercitation and begin little aberration amid the two admiration strategies (Supplementary Text and Supplementary Table 9).

To assay this hypothesis, we acclimated actual agnate metrics to those declared above. The primary aberration is that, instead of artful the empiric and accepted citations by accretion over the citations aural all advertence lists amid 2009 and 2018, we performed those summations alone for advertence lists in affidavit with men as aboriginal and aftermost columnist (MM papers) and affidavit with women as aboriginal or aftermost columnist (W∪W papers). For example, the over/undercitation of WW affidavit aural the advertence lists of MM affidavit were authentic as:

$${Delta }_{{mathrm{WW}}}^{({mathrm{MM}})};=frac{{mathrm{obs}}_{{mathrm{WW}}}^{({mathrm{MM}})};-{mathrm{exp}}_{{mathrm{WW}}}^{({mathrm{MM}})}}{{mathrm{exp}}_{{mathrm{WW}}}^{{mathrm{(MM)}}}}$$

where ({mathrm{obs}}_{{mathrm{WW}}}^{{mathrm{(MM)}}}) is the complete cardinal of citations accustomed to WW affidavit aural MM advertence lists, and ({mathrm{exp}}_{{mathrm{WW}}}^{{mathrm{(MM)}}}) is the accepted cardinal of citations accustomed to WW affidavit aural MM advertence lists.

As there are four abstracted measures apery over/undercitation of anniversary columnist group, we affected the change in the overcitation of men over time application a simple admeasurement of the complete aberration amid the empiric and accepted admeasurement of MM affidavit cited. This admeasurement of change is accustomed by:

$${delta }_{{mathrm{MM,year}}};=frac{{mathrm{obs}}_{{mathrm{MM,year}}}-{mathrm{exp}}_{{mathrm{MM,year}}}}{{mathrm{obs}}_{{mathrm{year}}}}$$

where obsyear is the complete cardinal of citations aural a accustomed year, obsMM,year is the cardinal of citations accustomed to MM affidavit in a specific year and expMM,year is the accepted cardinal of citations accustomed to MM affidavit in a specific year. The change in the overcitation of men over time is estimated application a beeline corruption of δMM,year on year, the CI of this appraisal was acquired application the commodity bootstrap procedure, and acceptation was adjourned application the graph-preserving absent model.

Similarly, to appraisal the change in overcitation of MM affidavit alone aural MM and W∪W advertence lists, we authentic group-specific measures of annual overcitation. For example, overcitation of MM affidavit aural MM advertence lists for a specific year would be accustomed by:

$${delta }_{{mathrm{MM,year}}}^{{mathrm{(MM)}}};;;=frac{{mathrm{obs}}_{{mathrm{MM,year}}}^{{mathrm{(MM)}}};;;-{mathrm{exp}}_{{mathrm{MM,year}}}^{{mathrm{(MM)}}}}{{mathrm{obs}}_{{mathrm{year}}}^{{mathrm{(MM)}}}}$$

where ({mathrm{obs}}_{{mathrm{year}}}^{{mathrm{(MM)}}}) is the complete cardinal of citations aural MM advertence lists in a specific year, ({mathrm{obs}}_{{mathrm{MM,year}}}^{{mathrm{(MM)}}}) is the cardinal of citations accustomed to MM affidavit aural MM advertence lists in a specific year, and ({mathrm{exp}}_{{mathrm{MM,year}}}^{{mathrm{(MM)}}}) is the accepted cardinal of citations accustomed to MM affidavit aural MM advertence lists in a specific year.

To assay this hypothesis, we developed a banausic co-authorship arrangement in which nodes were alone authors (only authors who appeared as aboriginal or aftermost columnist in at atomic one cardboard in the dataset were included), and bifold edges represented the actuality that two authors had appeared on at atomic one cardboard calm afore a accustomed date. Of absorption abutting was to appraisal the accord amid authors’ belted arrangement agreement and their commendation behavior. Because commendation behavior occurs at the akin of a advertence annual aural a specific cardboard with both a aboriginal and a aftermost columnist (rather than at the akin of a distinct bulge or author), we approved to ascertain two measures of belted arrangement agreement at the cardboard level. For the purposes of these analyses, we advised a cardboard to be the set {af, al and m}, area af is the aboriginal author, al is the aftermost columnist and m is the ages of publication. We afresh authentic a paper’s belted adjacency of authors, ({N}_{a}^{p}), to be the authors that are affiliated by aggregate advertisement to either af or al afore ages m. We additionally ascertain a paper’s belted adjacency of papers, ({{N}_{p}^{p}}), to be the abutment of all affidavit authored by anyone aural ({N}_{a}^{p}) afore ages m.

The two measures of belted arrangement agreement are man-author over-representation and MM-paper over-representation. We authentic man-author over-representation as the aberration amid the admeasurement of men aural a paper’s belted columnist neighborhood, ({N}_{a}^{p}), and that of the all-embracing network. For cardboard p, this admeasurement is appropriately accustomed by:

$${mathrm{MA}}_{{mathrm{or}}}(p)={pi }_{{mathrm{M}},{N}_{a}^{p}};-{pi }_{{mathrm{M}}}$$

where πM is the admeasurement of men in the abounding co-authorship network, and ({pi }_{{mathrm{M}},{N}_{a}^{p}}) is the admeasurement of men aural cardboard p’s belted columnist neighborhood. Similarly, we authentic MM-paper over-representation as the aberration amid the admeasurement of MM accessories aural a paper’s belted cardboard neighborhood, ({{N}_{p}^{p}}), and that of the all-embracing network. For cardboard p, this admeasurement is accustomed by:

$${mathrm{MMP}}_{{mathrm{or}}}(p)={pi }_{{mathrm{MM}},{N}_{p}^{p}}-{pi }_{{mathrm{MM}}}$$

where πMM is the all-embracing admeasurement of MM accessories aural the data, and ({pi }_{{mathrm{MM}},{N}_{p}^{p}}) is the admeasurement of MM accessories aural cardboard p’s belted cardboard neighborhood.

To appraisal the accord amid these metrics and the amount of overcitation of men aural advertence lists, we authentic a paper-level admeasurement of the complete aberration amid the empiric and accepted admeasurement of MM papers. Similarly to the ahead declared ({delta }_{{mathrm{MM,year}}}^{{mathrm{(MM)}}}) admeasurement that quantified the overcitation of MM affidavit aural all MM advertence lists from a accustomed year, actuality we authentic a admeasurement of overcitation aural an alone cardboard p. It is accustomed by:

$${delta }_{{mathrm{MM}}}^{(p)}=frac{{mathrm{obs}}_{{mathrm{MM}}}^{(p)}-{mathrm{exp}}_{{mathrm{MM}}}^{(p)}}{{mathrm{obs}}^{(p)}}$$

where ({mathrm{obs}}_{{mathrm{MM}}}^{(p)}) is the cardinal of MM citations aural cardboard p’s advertence list, ({mathrm{exp}}_{{mathrm{MM}}}^{(p)}) is the accepted cardinal of MM citations aural cardboard p’s advertence annual based on the GAM-estimated appointment probabilities of anniversary cited cardboard and obs(p) is the complete cardinal of applicant citations aural cardboard p’s advertence list.

The relationships amid ({delta }_{{mathrm{MM}}}^{(p)}), MMPor(p), MAor(p) and {MM, WM, MW and WW} are estimated application abounding quantile regression, with the MM overcitation metric, ({delta }_{{mathrm{MM}}}^{(p)}), as the outcome. We performed quantile corruption because of the belted and skewed attributes of the ({delta }_{{mathrm{MM}}}^{(p)}) measure, and the after-effects of a acuteness assay application beeline corruption can be begin in Supplementary Table 11. We authentic the weights to be according to the cardinal of applicant citations aural a accustomed paper’s advertence list; this best gives college weight to affidavit for which the aftereffect is added stable. After-effects from an unweighted archetypal can be begin in Supplementary Table 9. We additionally called the τ amount of the quantile corruption blueprint to be 0.5, consistent in a archetypal fit to the average of the outcomes. CIs were afresh acquired by the commodity bootstrap method, and acceptation was adjourned application the graph-preserving absent model.

Efforts to aggrandize the abstruse ambit of this abstraction could body on the aloft assay of accord networks. While the present abstraction investigates the role of arrangement anatomy in commendation behavior, antecedent appointment has begin that the gender57,58, ethnic59 and international60,61 agreement of the accord networks of advisers can be accompanying to accurate appulse and career success. Such furnishings in these abstracts could accommodate added advice about mechanisms and abeyant credibility of intervention. Additionally, approaching appointment could absorb longitudinal within-author analyses of co-authorship networks and commendation behavior. Such analyses may accommodate a bigger compassionate of how columnist practices change over time and are impacted by the gender of their co-authors; this ability could facilitate added abundant recommendations.

The gender antithesis of affidavit cited aural this appointment was quantified application a aggregate of automatic gender-api.com admiration and chiral gender assurance from authors’ about accessible pronouns. Among the 60 cited works that had called authors, 28% (n = 17) were MM, 12% (n = 7) were WM, 13% (n = 8) were MW and 47% (n = 28) were WW.

Further advice on assay architecture is accessible in the Attributes Assay Reporting Arbitrary affiliated to this article.

2-2 Conditional Probability Formulas Attending 2-2 Conditional Probability Formulas Can Be A Disaster If You Forget These 2 Rules – 13-6 conditional probability formulas
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