What predicts a school's ties to outside organizations

Grouped by the question each one answers, and numbered in that order, so Table 1 is the first one down this page and the numbers match the ones cited on the findings page.

How every measure was built, and the survey question behind it

Each organization the survey asks about, the crime questions, the school's own arrangements and the student-body measures, with the wording the questionnaire used.

Table 1. Every measure used, with the survey question and the answers as the questionnaire put themsource table 12

Note: Wording from the 2015-16 codebook, which is the wave the two-mode model uses. The eight tie items and the two crime items are worded the same way in all six waves; the year named in a stem changes with the wave. The crime item on where students live carries a fourth answer that the item on the school's own area does not, which is why the two are not on the same scale and are not treated as though they were. Parents' groups (C0204) is asked with the others but is not one of the seven counted organizations. Read off the codebook by scripts/paper_tables.py, not transcribed.

Schools differ in how many organizations they work with, not in which ones

Whether schools fall into recognizable types, and whether the seven organizations cluster into groups. Schools differ mainly in how many of the seven they work with rather than in which ones.

Table 2. A network model of which schools work with which of the seven organizations, fitted to the 2015-16 survey (n = 1,726 schools)source table 1

Note: A coefficient is the change in the log odds of a school working with a given organization. The first two terms describe the shape of the network. The rest ask whether schools with more of that characteristic hold more ties, which this kind of model calls an activity effect, so columns 1 and 2 speak to how many ties a school holds and not to which. Column 1 puts the neighborhood in on its own; column 2 adds the three things the school runs for itself, and the neighborhood coefficient falls to nothing, which is the paper's direct-and-indirect result inside the model. Column 3 asks the compositional question instead. With every organization given its own baseline, and the degree term already holding how concentrated the ties are, the edge covariate is the police tie's own answer to the neighborhood reading, at -0.335 against a general activity effect of +0.036 in the same model. That is the fixed-count result of Table 18 estimated inside the two-mode model rather than beside it. Checked with an estimator that shares nothing with it: laying the same schools out as 12,082 school-and-organization pairs and giving every school its own intercept, which removes that school's count of partners from the comparison altogether, the crime reading predicts the police cell at -0.046***, against the other cells of the same row. Unweighted, since exponential random graph models do not take survey weights. ***p < 0.001, **p < 0.01, *p < 0.05.

Table 3. How often the seven organizations turn up together, against 300 reshuffles that keep every school's number of organizations and every organization's popularity exactly as observed, by surveysource table 19

Note: Each z compares the observed number of schools holding both ties in a pair (summed over the nine within-side pairs in the first column, single pairs in the others) against 300 curveball randomizations that hold every school's count of ties and every organization's prevalence exactly fixed, so the margins explain none of it. The structure is present in every wave and it is small: the first two eigenvalues of the tetrachoric correlation matrix are 2.4 and 1.5, so the count's dimension is about 1.6 times the size of the sides dimension, and at a fixed count the residual correlations of the three pairs shown are -0.04, +0.06, +0.05 against a compositional baseline of -0.17, the mean over all 21 pairs. A varimax rotation of the two factors reproduces the community and government sides used throughout the paper. Randomization seed 7; reproduce.R rechecks the observed totals exactly and the z-scores with independent draws.

Table 4. How much schools differ in how many organizations they work with, against how much they would differ if each relationship were decided on its own, within each kind of schoolsource table 16

Note: Survey-weighted, on all school-years including those working with all seven organizations or with none, because the restriction used elsewhere removes exactly the tails whose spread the first column measures. The first column compares how much schools' totals actually vary against how much they would vary if every school decided about each organization on its own; a value of 1 would mean the seven are independent. The last two columns describe the relations among the seven. If different kinds of school organized these relationships differently, the rows would not agree. Every row falls between 2.5 and 2.8 on the first column and between 0.25 and 0.30 on the second, and not one of the 21 pairs is negative in any subgroup. This is H2(b).

Security staff, parent processes and equipment predict how many

Security staff, a formal process for consulting parents, and security equipment, as predictors of how many of the seven organizations a school works with. This is the strongest pattern in the data.

Table 5. Security staff, the parent process and equipment as predictors of the number of organizations, by grade levelsource table 2

Note: Survey-weighted least squares within grade level, controlling for size, location, wave and how far inadequate funds limit the school's crime prevention. Standard errors clustered on the sampling stratum within wave. Parent process and security equipment are standardized; the index row enters the three as one standardized index, built within the grade level. The three columns cover 12,164 of the 12,691 school-years; the 527 schools spanning several grade levels are a mixed category and are not shown. ***p < 0.001, **p < 0.01, *p < 0.05.

Table 6. Security staff, the parent process and equipment, and the crime level the principal reports, entered alone and entered togethersource table 17

Note: n = 12,691. Survey-weighted, standard errors clustered on the sampling stratum within wave, in brackets. All predictors standardized, so each coefficient is the difference in the count of organizations between two schools one standard deviation apart. What the school has built is an index of the three standing arrangements the survey carries in every wave: security staffing (harmonized to any-versus-none across a wording change in 2015-16), the formal parent process, and security equipment; each is standardized, the three are averaged, and the average is restandardized. Every model controls for size, grade level, urbanicity, wave and how far inadequate funds limit the school's crime prevention; the within-wave estimates drop the wave. The capacity coefficient carries the scrutiny the environmental one does. Estimated within wave it is 2005-06 +0.343***, 2007-08 +0.396***, 2015-16 +0.350***, 2017-18 +0.350***, 2019-20 +0.428***, 2021-22 +0.374***, significant in all six; leaving any one wave out keeps the pooled estimate between +0.362 and +0.392. It is not an artefact of overlap between the index and the ties (the staffing measure includes sworn officers; one tie is law enforcement): on the six ties excluding the police it is +0.334*** (0.020), the same rate per organization. The index measures how much machinery, not which kind: at a fixed count, security staffing goes with the government side of the field (+0.048**) and the parent process with the community side (-0.034*), while equipment goes with the community side (-0.034*). In the joint rows the two main effects come from the additive model; the product row comes from the model that adds it, whose main effects are +0.379 and +0.066. The interaction implies an environmental slope of +0.094 (0.027)*** at -1, +0.066 (0.023)** at +0, +0.037 (0.028) at +1, +0.009 (0.039) at +2 standard deviations of capacity: the first two separate from zero and the last two do not, so the environmental route is clear at and below average capacity and cannot be distinguished from zero in the sixth of schools more than one standard deviation above it. The last three rows test whether advantage builds reach. Entered alone, the share expected to go to college and the share testing at the bottom carry the wrong sign for a position account; entered together both keep those signs and still separate from zero, at -0.057** and +0.039*, and with the crime reading and all five student-body measures present they are -0.038 and +0.019. Nothing here suggests that advantage builds reach. The funding rows compare schools whose principals say inadequate funds limit their crime prevention a little or a lot with schools saying not at all. Estimated within each crime reading, with the standard controls, they are low crime (9,488 school-years) +0.209*** and +0.101*; moderate crime (2,460 school-years) +0.230* and +0.093; high crime (743 school-years) +0.195 and +0.223. ***p < 0.001, **p < 0.01, *p < 0.05.

The crime level the principal reports predicts how many too

The other predictor of that same count, and what becomes of it as the school's own arrangements and its students' circumstances enter the model.

Table 7. The crime level the principal reports as a predictor of the number of organizations, by surveysource table 3

Note: Per standard deviation of the principal's description of the crime level in the area where the school is located, reversed so that higher means more crime, and standardized. Controlling for size, grade level, urbanicity and how far inadequate funds limit the school's crime prevention, and wave in the pooled row. Standard errors clustered on the sampling stratum within wave. The variation across waves is larger than sampling noise: a joint test of crime by wave interactions gives F = 4.13, p = 0.0012. The pooled estimate does not depend on any single wave. Dropping 2021-22 gives +0.135*** and dropping 2015-16 gives +0.080**. In the two waves carrying the fifty replicate weights, a jackknife standard error on the pooled specification gives 0.021 against 0.024 here. The sample excludes the 2,504 school-years that work with all seven organizations or with none; putting them back gives +0.129*** on 15,195 school-years, and the exclusion rate does not vary with the crime measure (low 16.8%, moderate 16.8%, high 15.1%). ***p < 0.001, **p < 0.01, *p < 0.05.

Table 8. The two crime questions, separately and averaged, as predictors of the number of organizationssource table 5

Note: n = 10,927, the schools answering both readings on a scale. Survey-weighted, standard errors clustered on the sampling stratum within wave, in brackets. Each column is a separate model; the three measures are never entered together except where the note says so. The two readings correlate at 0.79 and the two-item scale has an alpha of 0.88, which is why averaging them is reasonable. Entered together the catchment reading takes the association: +0.141*** against +0.014 for the school's own area. Splitting schools four ways by whether the principal calls each area high or moderate rather than low, and taking schools calling neither as the comparison, gives 2 the school's area only +0.019, 3 the students' areas only +0.261***, 4 both +0.335***. The two do not interact: entered as a product the interaction is -0.001 (p = 0.97). Across single surveys, the combined scale separates from zero in 5 of six and the school's own area in 3. ***p < 0.001, **p < 0.01, *p < 0.05.

Table 9. The crime level the principal reports as a predictor, before and after the school's own staff, parent process and equipment enter the modelsource table 8

Note: n = 12,691. The first three rows are survey-weighted with standard errors clustered on the sampling stratum within wave. The fourth drops the weights, as the exponential random graph model in Table 1 does. These are adjusted estimates in sequence rather than a formal decomposition: the fall from the first row to the third measures what the school's own arrangements account for, not an estimated indirect effect. The last row gives the outcome the sequence presumes, that schools in rougher areas employ more security staff; it is a probability, so it is not on the same scale as the rows above it but is on the same scale as the per-organization ties. ***p < 0.001, **p < 0.01, *p < 0.05.

Table 10. The crime level the principal reports as a predictor, before and after the student-body measures enter the model

Note: Survey-weighted least squares, standard errors clustered on the sampling stratum within wave, in brackets. All predictors standardized, so a coefficient is the change in the count of organizations for a school one standard deviation higher on that measure. Both columns control for size, grade level, urbanicity, wave and how far inadequate funds limit the school's crime prevention. The neighborhood coefficient falls from +0.104 to +0.087 when the student body is added, and only one of the five separates from zero, students who transferred in, and at p < 0.05. This is H4. ***p < 0.001, **p < 0.01, *p < 0.05.

Table 11. The crime level the principal reports, recorded incidents and trouble reported inside the school, as predictors of the number of organizationssource table 13

Note: n = 12,691. Survey-weighted, standard errors clustered on the sampling stratum within wave, in brackets. The outcome is the count of the seven counted organizations except in the last two rows; parents' groups, in the first of those, is a tie outside the count. Reported trouble is how often the principal says bullying, harassment and verbal abuse occur; recorded incidents is the count of crime and violence the school recorded that year. Both describe what the school is dealing with inside. Entered together with the reading of the outside, reported trouble no longer separates from zero. The reading of the outside does. On parents' groups the reading of the school's own area is accounted for by what happens inside, but the reading of the areas where the students live is not: it is -0.016** (0.006) in the same specification. ***p < 0.001, **p < 0.01, *p < 0.05.

Table 12. The crime level the principal reports as a predictor of the number of organizations, within city, suburb, town and rural schoolssource table 7

Note: Per standard deviation of the reported crime level, survey-weighted, standard errors clustered on the sampling stratum within wave, controlling for size, grade level, wave and how far inadequate funds limit the school's crime prevention. The rows compare high-crime with low-crime schools inside the same kind of place, so a difference in how many organizations exist in cities against rural areas cannot produce them. ***p < 0.001, **p < 0.01, *p < 0.05.

Which of the seven organizations schools in higher-crime areas add

When a school in a higher-crime area works with more organizations, which ones it adds: enforcement bodies, or community groups and government agencies alike.

Table 13. Each of the seven organizations against the crime level the principal reportssource table 4

Note: One model per organization, per standard deviation of the reported crime level, controlling for size, grade level, urbanicity, wave and how far inadequate funds limit the school's crime prevention, with standard errors clustered on the sampling stratum within wave. The last column gives the share of schools reporting the tie, which bounds how far a coefficient can go. The police coefficient is the only negative one. Estimated within wave the police coefficient is 2005-06 -0.008, 2007-08 -0.023, 2015-16 -0.017, 2017-18 -0.011, 2019-20 -0.016, 2021-22 -0.043*, negative in every wave, and the pooled estimate stays significant in every sample that leaves one wave out. ***p < 0.001, **p < 0.01, *p < 0.05.

Table 14. Each of the seven organizations against the crime level the principal reports, holding the total number constantsource table 18

Note: Linear probability models, one per organization, per standard deviation of the reported crime level, survey-weighted, standard errors clustered on the sampling stratum within wave, controlling for size, grade level, urbanicity, wave, how far inadequate funds limit the school's crime prevention and the total count of organizations. Because the count is held constant, a coefficient reads as a change in the share of schools holding that tie at a given number of ties: the mix, not the amount. The police carry the only negative coefficient that separates from zero, and it is negative in every wave and significant on every leave-one-out sample. Civic organizations (-0.006) and juvenile justice (-0.004) are also negative and do not separate from zero. The shift does not change the balance between the community and government sides, and it comes on top of the rise in the count, not in place of it. ***p < 0.001, **p < 0.01, *p < 0.05.

Table 15. The crime level the principal reports against the count of community organizations, the count of government organizations, and the balance between themsource table 9

Note: n = 12,691. Per standard deviation of the reported crime level, survey-weighted, with standard errors clustered on the sampling stratum within wave and the same controls throughout, how far inadequate funds limit the school's crime prevention among them. Both sides rise. The balance between them does not change, with or without the number of organizations held constant, which is H5: a rougher area is associated with a school reaching further out rather than with a school reaching in a particular direction. ***p < 0.001, **p < 0.01, *p < 0.05.

What schools in rougher areas take instead of the police

Six of the seven organizations become more common as the reported crime level rises. The police do not. Take a school holding exactly one of the police and mental-health providers: as the reported crime level rises, the one it holds is more likely to be the mental-health providers. The same goes for social services, churches, civic groups, local businesses and juvenile justice.

Table 16. The crime level the principal reports as a predictor, with the police and juvenile justice agencies taken out of the countsource table 6

Note: n = 12,691. Per standard deviation of the reported crime level, survey-weighted, with standard errors clustered on the sampling stratum within wave and the same controls throughout, how far inadequate funds limit the school's crime prevention among them. If the association were police arriving in schools under another name, it should weaken as the enforcement organizations are removed. ***p < 0.001, **p < 0.01, *p < 0.05.

Table 17. Parent turnout against the crime level the principal reports, and the parents' groups tie with parent turnout in the modelsource table 14

Note: The first four rows use n = 8,425: the parent-participation items are carried by 2005-06, 2007-08, 2015-16 and 2017-18 but not by the last two waves. The last two rows use all 12,691. Parents' groups are not one of the seven counted organizations; the tie is measured and analyzed here as a tie outside the count. Parent turnout averages four items, how many parents attend open house, parent-teacher conferences and subject-area events and how many volunteer, each on a four-point scale; schools not offering an event are held out of it. Survey-weighted, standard errors clustered on the sampling stratum within wave. Parents turn up substantially less where the principal reports more crime. On these 8,425 school-years the tie to organized parents does not fall clearly with the reading (-0.010, p = 0.10), and with turnout controlled it is +0.008 (p = 0.22). The last two rows test whether schools reach out to other organizations because parents or police are unavailable: if so, schools lacking those ties would hold more of the rest. They hold fewer. The fourth row adds the count of the seven counted organizations, which does not contain the parents' tie, so it asks whether the tie is held at a given reach. There the estimate is -0.001 (p = 0.84). ***p < 0.001, **p < 0.01, *p < 0.05.

Table 18. The police tie at a fixed number of organizations, within each grade levelsource table 20

Note: Linear probability models, per standard deviation of the reported crime level, survey-weighted, standard errors clustered on the sampling stratum within wave, controlling for size, urbanicity, wave, how far inadequate funds limit the school's crime prevention and the total count of organizations. Holding the count fixed makes this a statement about the mix rather than the amount: at a given number of organizations, a school in an area its principal calls high-crime is less likely to hold the police tie. The association is negative at every grade level and it is not carried by one of them. Within high schools alone it survives leaving any single wave out, at -0.020***, -0.018**, -0.021***, -0.022***, -0.015**, -0.018** for the six leave-one-out samples. Estimated within single waves among high schools it is 2005-06 -0.011, 2007-08 -0.024, 2015-16 -0.008, 2017-18 -0.002, 2019-20 -0.037*, 2021-22 -0.021, negative in all six and significant in one, which is what splitting 4,383 schools six ways gives. On the survey's own three-point scale rather than in standard deviations the estimate is -0.049*** per step, so of two schools working with the same number of organizations, the one whose principal calls the area high-crime is about 10 percentage points less likely to count the police among them than the one whose principal calls it low-crime. The count of all seven includes the police tie itself, so the last row holds fixed the count of the other six organizations instead, which does not contain the outcome; the low-to-high difference there is about 8 percentage points. On all schools, in percentage points from low- to high-crime areas at the same number of organizations, the estimate by survey is 2005-06 -6.6, 2007-08 -10.0*, 2015-16 -12.5**, 2017-18 -7.0, 2019-20 -7.8*, 2021-22 -13.4*, negative in every survey; leaving any one survey out, the pandemic year included, keeps it between -10.3 and -8.7, and each of those six estimates is significant at the 0.001 level. ***p < 0.001, **p < 0.01, *p < 0.05.

Table 19. Which one a school holds, among the schools holding exactly one of the police and the organization namedsource table 21

Note: n varies by row because each keeps only the school-years holding exactly one of the two ties named. Survey-weighted, standard errors clustered on the sampling stratum within wave, controlling for size, grade level, urbanicity, wave and how far inadequate funds limit the school's crime prevention. A positive coefficient means that as the reported crime level rises, a school facing that either-or holds the other organization rather than the police. The police give way to every alternative. The coefficient column is not a ranking of the alternatives. A linear probability model's slope is bounded by how rare its outcome is, and this column follows the share in the column beside it almost exactly, so it orders the alternatives by how often schools hold them rather than by what they are. The last column repeats the same models on a log-odds scale, which carries no such bound. There the six run from +0.207 to +0.362 with standard errors of 0.05 to 0.09, which does not separate them from one another, and juvenile justice sits at +0.247 among the rest rather than below them, so its near-zero linear estimate is the floor of a 3% base rate. The result is not an artefact of the police being the commonest of the seven, which a fixed-count model could mistake for a preference: cutting schools by how many organizations they work with, the police coefficient at a fixed count is -0.040*** on 1 to 3 organizations (police share 74%), -0.023*** on 4 or 5 organizations (police share 94%), -0.008 on 6 organizations (police share 98%), strongest where the police tie is furthest from universal. Whether a school falls in the either-or group at all goes with the crime level its principal reports, at -0.016* for mental-health providers, -0.013* for social services, so rougher-reading schools are less likely to face that either-or, and the comparison is selected on the predictor to that extent. The swap is not a recent politics of school policing. In the two earliest surveys it is mental-health providers 2005-06 +0.035, mental-health providers 2007-08 +0.036, social services 2005-06 +0.062**, social services 2007-08 +0.052*, about a decade before school policing became a national argument. One reading of the swap, that schools are holding on to authority over order inside the building, is not supported by what the survey can say about it. Of the incidents a school records, the weighted share reported to the police is 30% where the principal calls the area low-crime, 29% where the principal calls the area moderate-crime, 27% where the principal calls the area high-crime, but adjusted for size, grade level, urbanicity, wave and how far inadequate funds limit the school's crime prevention that gradient is +0.003 and comparing schools that recorded the same number of incidents it reverses, at +0.012** (n = 11,517 recording at least one). Nor does the swap depend on the school having its own security staff to fall back on: the police coefficient at a fixed count is -0.031** for schools without security staff of their own and -0.029*** for schools with security staff of their own. What a school writes down about the officers in it cannot be used to test the same reading, though the estimates are reported here for completeness. The survey asks whether the policy for sworn officers covers a domain and never what it says in that domain, so a school recording that the officer is kept out of student discipline answers as a school recording that the officer takes part in it. Among the 5,379 schools with sworn officers present, from 2015-16 on, a rougher reading goes with a formalized policy at all at +0.008, one covering student discipline at +0.013, one covering the use of restraints at +0.030**, one covering the use of firearms at +0.015, one covering making arrests at +0.001, one covering the reporting of offences at +0.012, which is uninformative in either direction for that reason. ***p < 0.001, **p < 0.01, *p < 0.05.

What changed between 2005-06 and 2021-22

Work with juvenile justice agencies fell and work with mental-health providers rose across the six surveys, while the number of organizations per school stayed about the same.

Table 20. Share of schools working with juvenile justice agencies and with mental-health providers, by survey and by the crime level the principal reportssource table 11

Note: Survey-weighted shares, n = 12,691. Crime level is the principal's description of the area. The two rows that changed over the period are shown; the other five organizations barely changed. On mental health, high-crime schools led low-crime schools by 16 points in 2005-06 and low-crime schools led by 7 points in 2021-22. Between 106 and 144 schools report a high level of crime in any one wave, so a single cell carries a standard error of roughly four points and the wave-to-wave movement in that row should not be read closely. Interacting the crime measure with time, the association with the count of organizations falls across the six waves by -0.134 (p = 0.013). The fall sits in the pandemic year, not in a gradual narrowing: estimated without 2021-22 it is -0.039 (p = 0.46), and on the four pre-pandemic waves -0.010 (p = 0.85). So the convergence in the levels shown above does not appear as a downward trend in the association before the closures. Taken one organization at a time the trend does not separate from zero either, at p = 0.11 and p = 0.12. ***p < 0.001, **p < 0.01, *p < 0.05.

Could it run the other way? The reverse does not hold

Maybe it works the other way round. Maybe a school works with a lot of organizations, those organizations tell the principal the area is rough, and that is why the principal says it is. If that were what happened, the organizations that deal with crime would be the ones tied to the roughest descriptions. They are not. Schools that work with the police have principals who report less crime, not more, at -0.074. The two tied most closely to a rough description are churches at +0.151 and local businesses at +0.136, and neither of them deals with crime. Counting only those two gives +0.118. The principal's answer also matches things the study never uses it to predict: crimes actually recorded at the school, bullying reported by staff, and how few parents turn up to school events. The last table gives the recorded crime in counts.

Table 21. Three checks on the direction: the crime level the principal reports against things it is not used to predict, the police relationship on every margin the survey records, and each of the seven organizations with the regression turned aroundsource table 15

Note: n = 12,691, except the parent-turnout row, which uses the 8,425 school-years in the four waves carrying those items. Survey-weighted, standard errors clustered on the sampling stratum within wave. The top panel asks whether the principal's reading tracks anything beyond the ties it is used to predict. The bottom panel reverses the regression: if a school came to describe its area as rougher because its partners told it so, the partners with a crime remit would be the ones going with a higher reading. The middle panel gives the police relationship on the margins the survey records beyond the tie itself, carried from 2015-16 on; the agreement rows apply only to schools with officers, and the discipline row only to those with an agreement, which is why their samples shrink. ***p < 0.001, **p < 0.01, *p < 0.05.

Table 22. The crime level the principal reports against what the school itself records

Note: Survey-weighted means per school, and shares, on the analyzed panel. The counts are NCES's own, derived from the incident battery the school completes; the principal's reading is question 50, the crime level in the area where the school is located. Schools whose principals call the area high-crime record 2.1 times as many incidents as those whose principals call it low-crime, and the gradient holds inside every enrollment band. Violent and serious violent incidents are absent from the 2021-22 file and disciplinary actions start in 2007-08, so those columns run on fewer years. As a rank correlation, weighted, the reading goes with incidents recorded at 0.17, with violent incidents at 0.19 and with reported trouble at 0.19: the averages double while most schools in every category record few incidents, so the reading separates groups of schools more sharply than it ranks single ones. All of these come from the school on the same questionnaire; the public files carry no geography that would allow a check against crime recorded outside it.