What predicts a school's ties to outside organizations

Results

Schools differ in how many, not in which

Schools differ mainly in how many of the seven they work with. Which ones they pick is close to unpredictable, and knowing the count barely narrows them down.

Count how much schools differ from one another, and compare it with how much they would differ if every school decided each of the seven separately. The spread is 2.74 times what independence allows. That holds inside every kind of school: 2.72 in primary schools, 2.66 in high schools, 2.75 in cities, 2.67 in towns. Not one of the 21 pairs of organizations is negatively related, so no two are treated as alternatives.

Table 13. Spread against independence, mean pair correlation and negative pairs, within each kind of school

Note: The first column is the variance of the count divided by what it would be if every school decided each of the seven separately, so a value above one means schools differ more than independence allows. Survey-weighted, on all school-years including those working with all seven or with none, because the restriction used elsewhere removes exactly the tails whose spread this measures.

A model of the whole network says the same. Fitted to the 2015-16 wave, the term for how unevenly ties are spread across schools comes out at -1.096, and the minus sign means some schools hold far more ties than chance would give them.

The same model carries the study's other result inside it. Put the crime reading in on its own and it predicts the ties, at +0.040. Add what the school runs for itself and the crime coefficient falls to +0.023 and stops separating from zero, while security staffing comes in at +0.278. What the principal sees in the neighborhood works partly through what the school has built.

Table 11. Bipartite exponential random graph model of schools and the seven organizations, 2015-16 wave

Note: A coefficient is the change in the log odds of a school working with a given organization. Column 1 puts the neighborhood in on its own; column 2 adds what the school runs for itself, which here is security staffing and recorded incidents, because the formal parent-consultation process is a parent measure and this variant excludes it. The neighborhood coefficient falls from +0.040* to +0.023, which is the direct-and-indirect result inside the model. Unweighted, since exponential random graph models do not take survey weights. ***p < 0.001, **p < 0.01, *p < 0.05.

One faint pattern does survive. Among the seven, three pairs turn up together slightly more often than chance: social services with mental-health providers, juvenile justice with the police, and civic groups with businesses. Against 300 reshuffles that hold every school's number of ties and every organization's popularity exactly fixed, the within-side z runs from 12.5 to 18.6 across the six surveys. It is small, and it sorts the organizations rather than the schools, so the finding that schools have no types still stands.

Table 12. Co-occurrence of organizations on the same side, against randomizations holding the margins fixed, by survey

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 and 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 community side has three members here rather than four, because parents' groups was a community tie and this variant excludes it, which is why there are nine within-side pairs rather than twelve. The structure is present in every wave, with the within-side z running from 12.5 to 18.6. Randomization seed 7, matching the published table.

How many organizations a school works with

A school works with 3.40 of the seven on average. The police are the commonest partner, held by 84% of schools, then social services at 68% and mental-health providers at 66%. Churches are the rarest at 22%.

The number rises with the crime a principal reports. Schools in the areas principals call low-crime work with 3.34 of the seven. In the areas they call moderate, 3.55. In the areas they call high, 3.62.

Table 2. The crime level the principal reports as a predictor of the number of organizations, by survey

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 and urbanicity, and wave in the pooled row. Standard errors clustered on the sampling stratum within wave. ***p < 0.001, **p < 0.01, *p < 0.05.

What the school runs for itself

Schools with more security staff and more security equipment work with more outside organizations, at +0.232 per standard deviation on its own and +0.225 with the crime reading also in the model.

This comes out weaker than the companion study reports, for a reason. That version puts a third item in the same index, a formal process for consulting parents, and gets +0.48. Half of what "what the school runs" was measuring there is a parent arrangement. Take it out and what remains, the security side of the house, predicts about half as much.

Table 1. What a school runs for itself, and the crime level its principal reports, as predictors of how many of the seven external organizations it works with

Note: n = 12,691. Survey-weighted, standard errors clustered on the sampling stratum within wave, in brackets. All predictors standardized. What the school runs is security staffing (harmonized to any-versus-none across a wording change in 2015-16) and security equipment, each standardized, averaged, and the average restandardized. The published analysis puts a third item in that index, a formal process for consulting parents; it is a parent measure and this variant excludes it, which is most of why the coefficient here is smaller. The last three rows test whether advantage builds reach. ***p < 0.001, **p < 0.01, *p < 0.05.

The crime level the principal reports

The crime reading predicts the count at +0.109 per standard deviation on its own, and +0.094 once what the school runs is in the model too.

The survey asks the question twice, once about the area where the school is and once about the areas where its students live. The second predicts better than the first, +0.156 against +0.109.

Does the principal's answer mean anything?

The crime level here is not a police statistic. It is one thing a principal typed into a form. So we checked it against two things this study never uses it to predict.

Schools whose principals report more crime have more crimes actually recorded against them that year, at +0.112. Staff at those schools report more bullying, harassment and verbal abuse, at +0.179.

The companion study has a third check here, how many parents turn up to school events. It is a parent measure, so it is not in this version.

Table 9. The crime level the principal reports against things this variant never uses it to predict, and each tie with the regression turned around

Note: The top panel asks whether the principal's reading tracks anything beyond the ties it is used to predict. The published analysis has a third row there, how many parents turn up to school events; it is a parent measure and this variant excludes it. 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. ***p < 0.001, **p < 0.01, *p < 0.05.

Which of the seven schools in rougher areas add

Both sides of the field rise. The three community organizations rise by +0.061 per standard deviation, the four government ones by +0.048, and the balance between them stays flat, at -0.014.

Table 7. The crime level against the count of community organizations, the count of government organizations, and the balance between them

Note: The sides are uneven here, three community organizations against four government ones, because parents' groups was a community tie and this variant excludes it. Per standard deviation of the reported crime level, survey-weighted, clustered on the sampling stratum within wave, same controls throughout. ***p < 0.001, **p < 0.01, *p < 0.05.

Taken one at a time, churches rise most and the police do not rise at all.

Table 3. Each of the seven organizations against the crime level the principal reports

Note: One model per organization, per standard deviation of the reported crime level, controlling for size, grade level, urbanicity and wave, 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. ***p < 0.001, **p < 0.01, *p < 0.05.

The police are the one partner schools do not add

Of the seven, the police are the one a school in a high-crime area does not add. Three checks say so, and none of them depends on the others.

The first takes the police out of the count of organizations, so the outcome becomes the other six. If the real story were that rougher areas simply get more police into schools, then counting only those six should make the pattern weaker. It makes it stronger: +0.129 per standard deviation, against +0.109 with the police counted in. Leave juvenile justice agencies out as well and it is +0.116. Count only civic groups, businesses and churches, with no government body among them at all, and it is +0.061.

Table 6. The crime level as a predictor, with the enforcement organizations taken out of the count

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. 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.

The second holds the number of partners still and asks which ones they are. Take two schools that work with the same number of organizations. The one in the area its principal calls rougher is less likely for one of those to be the police, by -0.028 per standard deviation. On the survey's own three-point scale that is about 10 percentage points from a low-crime area to a high-crime one.

That is not an accident of putting young children's schools and high schools in one pot. Look at each kind on its own and the answer is the same in all three: -0.036 in primary schools, -0.015 in middle schools and -0.019 in high schools. Leaving any one of the six surveys out of the pooled estimate leaves it between -0.025 and -0.030.

Table 4. Each of the seven organizations against the crime level, holding the total number constant

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 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. On the survey's own three-point scale rather than in standard deviations the police 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. ***p < 0.001, **p < 0.01, *p < 0.05.

Table 5. The police tie at a fixed number of organizations, within each grade level

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 and the total count of organizations. The association is negative at every grade level. Leaving any single wave out of the pooled estimate gives -0.029***, -0.028***, -0.026***, -0.029***, -0.030***, -0.025***. ***p < 0.001, **p < 0.01, *p < 0.05.

The third check is simply how common the police already are. 84% of schools work with them, more than any of the other six, so there is very little room for that share to go up.

What those schools take instead

Saying the police are the one they do not add leaves a question open. If a school in a rougher area works with more organizations, and the police are not among the extras, then what is?

Take only the schools that work with exactly one of the police and mental-health providers. Every school in that group faces the same either-or and has landed on one side of it. Then ask whether the crime the principal reports predicts which side.

It does. The rougher the principal calls the area, the more likely the one they have is the mental-health provider, at +0.051 per standard deviation on 4,274 schools facing that choice. Social services is the same, at +0.053 on 4,174.

It happens against the community organizations too, more weakly: +0.027 for local businesses, +0.025 for civic groups, +0.023 for churches. Against juvenile justice agencies, the other body with a crime remit, the police barely give way at all, at +0.008.

So the police do not simply thin out. They give way, and they give way to the organizations that look after children rather than to the other one that enforces.

Table 8. Which one a school holds, among the schools holding exactly one of the police and the organization named

Note: n varies by row because each keeps only the school-years holding exactly one of the two ties named, so the comparison is between schools facing the same either-or. A positive coefficient means that as the reported crime level rises, a school facing that choice holds the other organization rather than the police. Not a prevalence artefact: cutting schools by how many organizations they work with, the police coefficient at a fixed count is -0.048*** on 1 or 2 organizations (police share 67%), -0.020** on 3 or 4 organizations (police share 89%), -0.022*** on 5 or 6 organizations (police share 97%). Not selected on the predictor either: whether a school falls in the either-or group at all is unrelated to the crime level its principal reports, at -0.016* for mental-health providers, -0.013* for social services. ***p < 0.001, **p < 0.01, *p < 0.05.

Could it be the other way round?

So far this reads one way. A principal thinks the area is rough, and the school works with more organizations.

But maybe it works the other way. Maybe the school already works with a lot of organizations. They tell the principal the area is rough. And that is why the principal says so.

If partners were doing the telling, it would be the crime ones doing it. So turn the question around. For each of the seven, ask which ones go with a rougher description.

The answer comes out backwards for that story. Schools that work with the police have principals who report less crime, at -0.083. The two tied most closely to a rough description are churches at +0.076 and mental-health providers at +0.075. Count only businesses and churches, which have nothing to do with crime, and it is still there at +0.061.

None of this settles the direction. Every survey is a fresh sample taken at one moment. No school is followed over time.

What changed over the sixteen years

Table 10. Share of schools working with each of the seven organizations, by survey

Note: Survey-weighted shares of the analyzed panel. ***p < 0.001, **p < 0.01, *p < 0.05.