What are the elements that make up a good school?

Ask children, parents or educators, and they'll list a host of factors: teachers and administrators who care about their students; children and parents who take pride in the community; high quality instruction and an array of extracurricular activities. Don't forget the cafeteria food.

When parents research the best schools for their children, though, that isn't the sort of information they usually get. Instead, they'll see what proportion of students were judged proficient on various state tests, or how many graduated high school in four years, or whether the school has made "adequate yearly progress."

Those are very important things to know, but they're not the whole picture.

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The New York School Quality Index — exclusive to the USA Today Network — attempts to capture measures of a school's environment that don't necessarily show up in test scores or graduation rates. The best schools, by this measure, are not those with the highest passage rates on standardized tests, but those that both children and adults find to be pleasant places to spend their weekdays.

There's no easy way to measure that, but putting together some of the data collected by the New York State Education Department makes a good approximation. Are there many fights or other disruptive incidents — and when they do occur, are teachers and administrators able to address them without resorting to harsh discipline? That's reflected in the suspension rate.

Research has shown the benefits of small class sizes; of having both novice and experienced teachers; and of a diverse mix of races and ethnicities. The state collects data on all of those indicators, as well.

The New York School Quality Index combines those considerations for all 4,742 public and charter schools in New York state and assigns each one a score, from 0 to 100. The median score is 77.5; schools in the 90th percentile got a score of 88.7 or higher, while the bottom 10 percent of schools are at 58.2 or lower.

Eight schools in the state, all of them in New York City, rated a perfect 100 in 2015-16, the most recent data available. The school with the worst rating is also in New York City — Research and Service High School, which enrolls high school students off track for graduation, earned only 13.5 points.

Any attempt to encapsulate a school in a single number will inevitably miss a lot of detail, and the New York School Quality Index is no different. There are several factors — parental involvement, for instance, or teacher turnover, or how much homework kids get — that aren't available statewide, and the state data is not universally reliable to begin with.

"All ratings are subject to criticism, but you’re creating a perspective, not an exact science," said Steve Uebbing, a professor at the University of Rochester's Warner School of Education. "The fallacy is thinking there's one right way to look at schools."

It wouldn't be advisable to pick a school without some knowledge of its academic performance. Judgments on schools based solely on academics, though, are incomplete as well. Until now, though, there's been no easy way to look at 'the other stuff.'

A quick glance at the New York School Quality Index's top schools and school districts in any given region will likely be jarring to those accustomed to seeing rankings by test score and graduation rate. Some of the top-achieving academic districts are in the middle of the pack, while some low-scoring schools are at the top here.

Across New York, there is a fairly strong correlation between academic rankings and poverty levels — the wealthier a school is, the better its students do on tests and graduation rates.

The New York School Quality Index, though, is designed to reflect school quality in a way that doesn't dovetail with wealth. It has a much weaker correlation with student poverty, and also with the percentage of black students, or those who have disabilities or don't speak English well.

The ratings in every district, county or region contain interesting stories, but a few statewide trends emerge.

Elementary schools do better than secondary schools. That makes sense, as older students tend to have worse attendance and higher suspension rates than younger children. The average score for primary schools is 78.7, compared to 66.7 for high schools.

That makes sense, as older students tend to have worse attendance and higher suspension rates than younger children. The average score for primary schools is 78.7, compared to 66.7 for high schools. Urban schools are best — and worst. Collectively, schools in New York's largest cities have a bad reputation, but that masks some bright spots. The New York School Quality Index shows that the best schools in Erie, Monroe and Onondaga counties are in the cities of Buffalo, Rochester and Syracuse, respectively, with both district and charter schools scoring very high. On the flip side, the worst schools in those counties are traditional and charter schools in the cities as well.

Collectively, schools in New York's largest cities have a bad reputation, but that masks some bright spots. The New York School Quality Index shows that the best schools in Erie, Monroe and Onondaga counties are in the cities of Buffalo, Rochester and Syracuse, respectively, with both district and charter schools scoring very high. On the flip side, the worst schools in those counties are traditional and charter schools in the cities as well. New York City has the top schools. The same divide in upstate schools is also true in New York — some are very good, and some are very bad. Overall, however, of the 70 schools that scored 95 or higher, 57 are in New York City, and another 10 are on Long Island or in the Hudson Valley.

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MORE: Monroe County's best school? It's in the city, our exclusive Quality Index shows

You can search for one school or filter by district, county or grade level. You can also change the relative importance of the various measures that make up the New York School Quality Index to create custom rankings based on your own values.

JMURPHY7@Gannett.com

The New York School Quality Index — USA Today Network

The New York School Quality Index is based on the most recent data (2015-16) from the New York State Education Department's Report Card Database. Schools are assigned a score of 1-10 on each of five factors, and an overall score out of 100 is generated from those.

Attendance: Research shows that 95 percent average daily attendance is a meaningful threshold for school quality. Schools get a perfect 10 points if attendance is 95 percent or higher, and lose one point for each percentage point beneath that.

Suspensions: A high suspension rate means students are missing class time, and it may also point to the staff struggling to control students. A suspension rate of zero gets a perfect score; schools lose half a point for each point above that.

The attendance and suspension sub-indices are weighed somewhat more heavily than the other three categories. They tend to disadvantage secondary schools compared to elementary schools.

Class size: There are two ways of measuring class size from state data, neither of them perfect. The state provides class sizes for some levels, but it doesn't cover all schools, and they don't always seem accurate. Separately, one can divide the number of students by the number of teachers.

This measure combines those two methods — for each school, the quotient of (students/teachers) is multiplied by half the median difference between the two measures on a statewide level.

Some research on the benefits of small class sizes sets 17 students as the upper bound of the definition. A ratio of 17 students per teacher or lower gets a perfect score, with one point deducted for every student above that.

Teacher experience: Ideally, a school will have both a solid core of veteran teachers as well as a steady stream of new teachers, balancing energy and experience. A school gets a perfect score if between 10 and 25 percent of its teachers have less than three years' experience in the field.

One point is deducted for every percentage point above 25 percent or below 10 percent. The lower bound for a school with exclusively veteran teachers is a score of 5 points.

Diversity: State data shows how many students fall into six demographic categories: American Indian, Asian, black, Hispanic, multiracial and white (Middle Eastern students are counted as white). This index is based on how predominant the largest racial or ethnic group is in each school.

If the largest group is below 50 percent, the school gets a perfect score; that means at least 50 percent of students are something other than the predominant race or ethnicity. One quarter point is deducted for every point above 50 percent. This means that a school with 90 percent students of any one race will receive a score of 0 for diversity.

Database: See how your school ranks | See the criteria for the rankings

MORE: Monroe County's best school? It's in the city, our exclusive Quality Index shows