- Executive Summary
- Key Findings
- Foreword
- Acknowledgments
- List of Tables
- List of Figures
- Introduction
- Violent Deaths
- Nonfatal Student and Teacher Victimization
- School Environment
- Fights, Weapons, and Illegal Substances
- Fear and Avoidance
- Discipline, Safety, and Security Measures
- References
- Appendix A: Technical Notes
- General Information
- Sources of Data
- Accuracy of Estimates
- Statistical Procedures

- Appendix B: Glossary of Terms
- PDF & Related Info
- Contact

The comparisons in the text have been tested for statistical significance to ensure
that the differences are larger than might be expected due to sampling variation.
Unless otherwise noted, all statements cited in the report are statistically significant
at the .05 level. Several test procedures were used, depending upon the type of
data being analyzed and the nature of the statement being tested. The primary test
procedure used in this report was Student's *t* statistic, which tests
the difference between two sample estimates. The *t* test formula was not
adjusted for multiple comparisons. The formula used to compute the *t* statistic
is as follows:

where *E** _{1}* and

where *r* is the correlation coefficient. Once the *t* value was computed,
it was compared to the published tables of values at certain critical levels, called
alpha levels. For this report, an alpha value of .05 was used, which has a *t
* value of 1.96. If the *t* value was larger than 1.96, then the difference
between the two estimates is statistically significant at the 95 percent level.

A linear trend test was used when differences among percentages were examined relative
to ordered categories of a variable, rather than the differences between two discrete
categories. This test allows one to examine whether, for example, the percentage
of students using drugs increased (or decreased) over time or whether the percentage
of students who reported being physically attacked in school increased (or decreased)
with their age. Based on a regression with, for example, student's age as
the independent variable and whether a student was physically attacked as the dependent
variable, the test involves computing the regression coefficient (*b* and
its corresponding standard error *se*). The ratio of these two (*b/se*)
is the test statistic *t.* If *t* is greater than 1.96, the critical
value for one comparison at the .05 alpha level, the hypothesis that there is no
linear relationship between student's age and being physically attacked is
rejected.

Some comparisons among categories of an ordered variable with three or more levels
involved a test for a linear trend across all categories, rather than a series of
tests between pairs of categories. In this report, when differences among percentages
were examined relative to a variable with ordered categories, analysis of variance
(ANOVA) was used to test for a linear relationship between the two variables. To
do this, ANOVA models included orthogonal linear contrasts corresponding to successive
levels of the independent variable. The squares of the Taylorized standard errors
(that is, standard errors that were calculated by the Taylor series method), the
variance between the means, and the unweighted sample sizes were used to partition
the total sum of squares into within- and between-group sums of squares. These were
used to create mean squares for the within- and between group variance components
and their corresponding *F* statistics, which were then compared to published
values of *F* for a significance level of .05. Significant values of both
the overall *F* and the *F* associated with the linear contrast term
were required as evidence of a linear relationship between the two variables.

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