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based on the
Bullying Survey for Christian Schools (2016)
Analysis of Data (2022) by Precision Consulting
Research Hypotheses
The following null and alternative hypotheses were addressed in this study:
- H01: There is no statistically significant relationship between gender and the type of bullying reported.
- Ha1: There is a statistically significant relationship between gender and the type of bullying reported.
- H02: There is no statistically significant relationship between gender and the location of bullying.
- Ha2: There is a statistically significant relationship between gender and the location of bullying.
- H03: There is no statistically significant relationship between gender and whether bullying was reported.
- Ha3: There is a statistically significant relationship between gender and whether bullying was reported.
- H04: There is no statistically significant relationship between grade and the type of bullying reported.
- Ha4: There is a statistically significant relationship between grade and the type of bullying reported.
- H05: There is no statistically significant relationship between grade and the location of bullying.
- Ha5: There is a statistically significant relationship between grade and the location of bullying.
H06: There is no statistically significant relationship between grade and whether bullying was reported.
Ha6: There is a statistically significant relationship between grade and whether bullying was reported.
H07: There is no statistically significant relationship between years attending a Christian school and the type of bullying reported.
Ha7: There is a statistically significant relationship between years attending a Christian school and the type of bullying reported.
H08: There is no statistically significant relationship between years attending a Christian school and the location of bullying.
Ha8: There is a statistically significant relationship between years attending a Christian school and the location of bullying.
H09: There is no statistically significant relationship between years attending a Christian school and whether bullying was reported.
Ha9: There is a statistically significant relationship between years attending a Christian school and whether bullying was reported.
H010: There is no statistically significant relationship between school size and the type of bullying reported.
Ha10: There is a statistically significant relationship between school size and the type of bullying reported.
H011: There is no statistically significant relationship between school size and the location of bullying.
Ha11: There is a statistically significant relationship between school size and the location of bullying.
H012: There is no statistically significant relationship between school size and whether bullying was reported.
Ha12: There is a statistically significant relationship between school size and whether bullying was reported.
Descriptive Statistics
Table 1 reports the results of the frequency analyses for gender, grade, division, and race. Of the 2016 students included in the sample, 48.8% were male and 51.2% were female. Regarding Race, nearly eight in ten (77.3%) were White, 11.8% were Black, 4.2% were Asian, 3.8% were from multiple races, 1.3% were Hispanic, 1.0% were Amber Indian, 0.6% were Native Hawaiian, and 0.1% reported either Hispanic or Latin American. In addition, 32.7% were in grades 3 through 5, 35.9% were in grades 6 through 8, and 31.3% were in grades 9 through 12. Moreover, 33.3% reported their grade division as elementary school, 35.8% indicated middle or junior high school, and 31.0% stated high school.
Table 1 Results of the Frequency Analyses for Demographic Characteristics of the Sample
| Demographic Characteristics | Frequency | Percent | |
|---|---|---|---|
| Gender | Male | 984 | 48.8 |
| Female | 1032 | 51.2 | |
| Grade | 3 | 205 | 10.2 |
| 4 | 225 | 11.2 | |
| 5 | 228 | 11.3 | |
| 6 | 198 | 9.8 | |
| 7 | 240 | 11.9 | |
| 8 | 287 | 14.2 | |
| 9 | 167 | 8.3 | |
| 10 | 154 | 7.6 |
| 11 | 150 | 7.4 | |
|---|---|---|---|
| 12 | 162 | 8.0 | |
| Race | White | 1558 | 77.3 |
| Asian | 84 | 4.2 | |
| Black | 237 | 11.8 | |
| Multiple | 76 | 3.8 | |
| Amer Indian | 20 | 1.0 | |
| Native Hawaiian | 12 | 0.6 | |
| Hispanic | 27 | 1.3 | |
| Hispanic or Latin American | 2 | 0.1 | |
| Grade Division | Elementary School | 671 | 33.3 |
| Middle or Junior High School | 721 | 35.8 | |
| High School | 624 | 31.0 |
Evaluating Research Hypotheses
Twelve research hypotheses were addressed in this study. Pearson Chi-square test was utilized to evaluate Hypotheses 1-3 and 10-12, independent samples t-test was employed to evaluate Hypotheses 4 -6, and ANCOVA was utilized to examine Hypotheses 7-9. Due to the multiple tests being conducted to address most of these hypotheses, there was the risk of increasing Type I error probability when interpreting the results of the statistical tests. The Bonferroni correction method was utilized to avoid this issue. Following this approach, the significance level for each hypothesis is determined by dividing the number of tests being conducted by the original significance level of .05 (Sedgwick, 2012). Furthermore, for each Chisquare test, Cramer’s V value was reported to assess the magnitude of the association between the categorical variables under study when a significant association is identified. Values less than .20 were considered indicative of weak associations, .20-.40 as moderate, .40-.60 as relatively strong, and above .60 as strong associations. In addition, Cohen’s d values were calculated for each of the independent samples t-tests as a measure of the magnitude of the mean differences between the two groups under comparison. This measure was calculated by dividing
the mean of the differences by the pool standard deviation of the differences between the two groups. Values around .20 were regarded as indicative of small effects, around .50 as moderate effects, and around .80 as large effects (Cohen, 2013).
Hypothesis 1
Null Hypothesis 1 is that there is no statistically significant relationship between gender and the type of bullying reported. To address this hypothesis, three Pearson Chi-squared tests were conducted to determine whether there were significant associations between gender and each of the dummy variables representing seeing bullying, perpetrator of bullying, and victim of bullying. By applying a Bonferroni correction, the significance level for these tests was determined at α = .017. The results of these analyses are summarized in Table 2.
It was found that only the dummy variable representing seeing bullying was significantly associated with gender (p < .017). These results suggested that females were more likely to state that they had witnessed an act of bullying than males. The Cramer’s V value indicated that the magnitude of this association was weak. On the other hand, there were no significant associations between gender and other types of bullying (p > .017). Overall, these results provided support to reject Null Hypothesis 1 that there is no statistically significant relationship between gender and the type of bullying reported.
Table 2 Results of Examining the Associations Between Gender and Different Types of Bullying
| Bullying Type | 2 χ | df | p-value | Cramer’s V |
|---|---|---|---|---|
| Seeing Bullying | 14.154 | 1 | <.001 | .084 |
| Perpetrator | 0.451 | 1 | .462 | .016 |
| Victim | 3.266 | 1 | .071 | .040 |
In addition to the Chi-squared tests, a series of independent samples t-tests were performed to examine whether there were significant differences in physical, verbal, and social bullying by gender. These analyses were conducted based on the number of times students had seen, been victimized by, and been perpetrators of physical, verbal, and social bullying. Hence, a total of nine tests were needed to be conducted. Using a Bonferroni correction method, the significance level for these tests was set at α = .050/9 = .006.
The results of the independent samples t-tests are summarized in Table 3. From these results, it can be seen that there were statistically significant differences in the number of times students had seen verbal and social bullying, and the number of times students had been victimized by social bullying between male and female students. The effect size values for these variables indicated that the magnitudes of all these mean differences were very large. It can be concluded from these results that, on average, female students witnessed significantly more instances of both verbal and social bullying. In addition, the average number of times being socially bullied by other students was significantly higher for females than males. In terms of these three types of bullying, no further significant differences were identified by gender.
Table 3 Comparing Physical, Verbal, and Social Bullying by Gender
| Variable | Equal Variances | T | df | p value | Mean Difference | Std Error Difference | Effect Size |
|---|---|---|---|---|---|---|---|
| Seeing Physical | Assumed | -1.338 | 2014 | .181 | -0.090 | 0.067 | -1.343 |
| Seeing Verbal | Not Assumed | -3.821 | 2013.849 | <.001 | -0.304 | 0.080 | -3.800 |
| Seeing Social | Not Assumed | -4.428 | 2011.26 | <.001 | -0.360 | 0.081 | -4.444 |
| Victim of Physical | Assumed | -0.111 | 2014 | .912 | -0.007 | 0.059 | -0.119 |
| Victim of Verbal | Assumed | -1.094 | 2014 | .274 | -0.068 | 0.062 | -1.097 |
| Victim of Social | Not Assumed | -3.321 | 1995.405 | .001 | -0.219 | 0.066 | -3.318 |
| Perpetrator of Physical | Not Assumed | 1.148 | 1960.054 | .251 | 0.039 | 0.034 | 1.147 |
| Perpetrator of Verbal | Not Assumed | 1.595 | 1904.629 | .111 | 0.057 | 0.036 | 1.583 |
| Perpetrator of Social | Assumed | 0.125 | 2014 | .900 | 0.004 | 0.036 | 0.111 |
Hypothesis 2
Null Hypothesis 2 is that there is no statistically significant relationship between gender and the location of bullying. To address this hypothesis, a series of Pearson Chi-squared tests were conducted to determine whether there were significant associations between gender and each of the 15 dummy variables representing location of bullying for those who had witnessed bullying, perpetrators of bullying, and victims of bullying. This means that a total of 45 Chisquared tests were needed to be conducted. By applying a Bonferroni correction, the significance level for these tests was determined at α = .050/45 = .001.
The first series of Chi-square tests were performed to examine the associations between gender and the dummy variables representing location of bullying for seeing bullying. These analyses were performed based on the data collected from the students who reported seeing bullying. As displayed in Table 4, it was found that there was a significant association between the dummy variable representing hallways and gender (p < .001). The Cramer’s V value suggested that the magnitude of this association was weak. These results indicated that females were more likely than males to see an act of bullying in the hallways than males. No further significant associations were identified between gender and the dummy variable for bullying location (p > .001).
Table 4 Results of Examining the Associations Between Gender and Different Bullying Locations for Those Who Had Witnessed an Act of Bullying
| Bullying Location | 2 χ | df | p-value | Cramer’s V |
|---|---|---|---|---|
| Class-Teacher Present | 4.352 | 1 | .037 | .068 |
| Class- Teacher not Present | 1.244 | 1 | .265 | .036 |
| Playground | 7.784 | 1 | .005 | .090 |
| Gym | .037 | 1 | .847 | .006 |
| Hallways | 18.568 | 1 | <.001 | .140 |
|---|---|---|---|---|
| Restroom | 2.001 | 1 | .157 | .046 |
| Cafeteria | 5.102 | 1 | .024 | .073 |
| Walk To or From School | 1.640 | 1 | .200 | .041 |
| Bus | .156 | 1 | .693 | .013 |
| Online | 1.563 | 1 | .211 | .040 |
| Phone | 8.185 | 1 | .004 | .093 |
| After School Events | 2.042 | 1 | .153 | .046 |
| Home | 2.051 | 1 | .152 | .046 |
| Church | 4.124 | 1 | .042 | .066 |
| Other Places | 0.000 | 1 | .994 | .000 |
The second series of Chi-square tests were performed to examine the associations between gender and the dummy variables representing location of bullying for perpetrators. These analyses were conducted based on the data collected from those who reported being perpetrators. As reported in Table 5, there were no significant associations observed between gender and any of the dummy variables representing bullying location (p > .001).
Table 5 Results of Examining the Associations Between Gender and Different Bullying Locations for Perpetrators of Bullying
| Bullying Location | 2 χ | Df | p-value | Cramer’s V |
|---|---|---|---|---|
| Class-Teacher Present | 0.319 | 1 | .572 | .037 |
| Class- Teacher not Present | 3.948 | 1 | .047 | .130 |
| Playground | 0.035 | 1 | .852 | .012 |
| Gym | 0.092 | 1 | .762 | .020 |
| Hallways | 1.126 | 1 | .289 | 069 |
| Restroom | 0.063 | 1 | .802 | .016 |
| Cafeteria | 0.856 | 1 | .355 | .060 |
| Walk To or From School | 0.043 | 1 | .836 | .013 |
| Bus | 1.561 | 1 | .212 | .082 |
| Online | 0.056 | 1 | .813 | .015 |
| Phone | 0.016 | 1 | .899 | .008 |
| After School Events | 0.204 | 1 | .652 | .029 |
| Home | 0.104 | 1 | .747 | .021 |
| Church | 0.296 | 1 | .586 .035 | |
|---|---|---|---|---|
| Other Places | 0.004 | 1 | .951 .004 |
The third series of Chi-square tests were performed to examine the associations between gender and the dummy variables representing location of bullying for victims of bullying. These analyses were conducted based on the data obtained from those who reported being victimized by bullies. Table 6 shows that there were no significant associations between gender and any of the dummy variables representing bullying location (p > .001).
Table 6 Results of Examining the Associations Between Gender and Different Bullying Locations for Victims of Bullying
| Bullying Location | 2 χ | Df | p-value | Cramer’s V |
|---|---|---|---|---|
| Class-Teacher Present | 3.434 | 1 | .064 | .076 |
| Class- Teacher not Present | 0.532 | 1 | .466 | .030 |
| Playground | 0.630 | 1 | .427 | .033 |
| Gym | 0.024 | 1 | .876 | .006 |
| Hallways | 1.397 | 1 | .237 | .049 |
| Restroom | 0.100 | 1 | .752 | .013 |
| Cafeteria | 0.031 | 1 | .859 | .007 |
| Walk To or From School | 1.178 | 1 | .278 | .045 |
| Bus | 1.416 | 1 | .234 | .049 |
| Online | 0.133 | 1 | .715 | .015 |
| Phone | 5.069 | 1 | .024 | .093 |
| After School Events | 0.355 | 1 | .551 | .024 |
| Home | 3.568 | 1 | .059 | .078 |
| Church | 0.210 | 1 | .647 | .019 |
| Other Places | 0.070 | 1 | .791 | .011 |
In summary, the results of the Pearson Chi-squared tests determined that some indicators of bullying location were significantly associated with gender. Hence, these results provided support to reject Null Hypothesis 2 that there is no statistically significant relationship between gender and the location of bullying.
Hypothesis 3
Null Hypothesis 3 is that there is no statistically significant relationship between gender and whether bullying was reported. To address this hypothesis, a Pearson Chi-squared test was conducted to examine the association between gender and whether bullying was reported. Only the data for those who reported being victims of bullying were included in this analysis. The results of this analysis are reported in Table 7. It was found that a significant association existed between gender and whether bullying was reported (p < .05). The Cramer’s V value indicated that the strength of this association was weak. These results suggested that females were significantly more likely to report being victimized by bullies than males. Therefore, these results provided support to reject Null Hypothesis 3.
Table 7 Results of Examining the Associations Between Gender and Whether Bulling Was Reported for Victims of Bullying
| 2 χ | Df | p-value | Cramer’s V | |
|---|---|---|---|---|
| Bullying Being Reported | 6.121 | 1 | .013 | .103 |
Hypothesis 4
Null Hypothesis 4 is that there is no statistically significant relationship between grade and the type of bullying reported. To address this hypothesis, three independent samples t-tests were conducted to examine whether there were significant differences in the mean of grade by the dummy variables representing seeing bullying, being a perpetrator of bullying, and being a victim of bullying. By applying a Bonferroni correction, the significance level for these tests was determined at α = .050/3 = .017.
As displayed in Table 8, the results of the independent samples t-tests revealed that the mean of grade level significantly varied by all three different types of bullying (p < .017). The effect size values for these grouping variables suggested that the magnitudes of all these differences were very large. These results indicated that the mean of grade was significantly lower for those who had seen bullying, perpetrators of bullying, and victims of bullying compared to the other groups. It can be concluded from these findings that students in lower grades were significantly more likely to have witnessed bullying, be perpetrators of bullying, and be victims of bullying compared to students in higher grades. Overall, these results provided support to reject Null Hypothesis 4 that there is no statistically significant relationship between grade and the type of bullying reported.
Table 8
Results of Comparing Grade Level by Different Types of Bullying
| Grouping Variable | Equal Variances | t | Df | p -value | Mean Difference | Std Error Difference | Effect Size |
|---|---|---|---|---|---|---|---|
| Seeing Bullying | Not assumed | -3.238 | 2012.910 | .001 | -0.393 | 0.121 | -3.248 |
| Perpetrator | Not assumed | -2.546 | 314.350 | .011 | -0.448 | 0.176 | -2.545 |
| Victim | Assumed | -9.327 | 2014 | < .001 | -1.225 | 0.131 | -9.351 |
In addition to the independent samples t-tests, a series of Pearson correlation analyses were conducted to examine whether there were significant associations between physical, verbal, and social bullying and grade. A total of nine tests were needed to be conducted. Hence, using a Bonferroni correction method, the significance level for these tests was set at $\alpha = .050/9 = .006$ .
As reported in Table 9, the results of the Pearson correlation analyses indicated that significant negative associations existed between grade and the variables of the number of times students had seen physical bullying, had been physically, verbally, and socially bullied by other students, and had physically bullied other students. On the other hand, grade was significantly
positively correlated with the number of times students had witnessed verbal bullying. No further significant associations were identified.
Table 9 Examining the Correlations Between Grade and Physical, Verbal, and Social Bullying
| Variable | Df | Pearson Correlation | p-value | Strength of the Association |
|---|---|---|---|---|
| Seeing Physical | 2014 | 117 | < .001 | Small |
| Seeing Verbal | 2014 | .069 | .002 | Very Small |
| Seeing Social | 2014 | 002 | .935 | Very Small |
| Victim of Physical | 2014 | 200 | < .001 | Medium |
| Victim of Verbal | 2014 | 072 | .001 | Very Small |
| Victim of Social | 2014 | 124 | < .001 | Small |
| Perpetrator of Physical | 2014 | 066 | .003 | Very Small |
| Perpetrator of Verbal | 2014 | .015 | .506 | Very Small |
| Perpetrator of Social | 2014 | 034 | .129 | Very Small |
Hypothesis 5
Null Hypothesis 5 is that there is no statistically significant relationship between grade and the location of bullying. To address this hypothesis, a series of independent samples t-tests were conducted to determine whether there were significant differences in the mean of grade by each of the 15 dummy variables representing location of bullying for those who had witnessed bullying, perpetrators of bullying, and victims of bullying. Thus, a total of 45 t-tests tests were needed to be conducted. By applying a Bonferroni correction, the significance level for these tests was determined at α = .050/45 = .001.
The first series of t-tests were performed to examine whether there were significant differences in the mean of grade by each of the dummy variables representing location of bullying for seeing bullying. These analyses were performed based on the data collected from the students who reported seeing bullying. The results of these t-tests indicated that there were
statistically significant differences in the mean of grade level by the dummy variables representing classroom with the teacher present, playground, gym, hallways, online, phone, and after school even. The effect size values for these grouping variables indicated that the magnitudes of all these associations were very large. Furthermore, these results suggested that students in higher grades were significantly more likely to see bullying in the classroom with the teacher present, in the hallways, online, by phone, and after school events compared to students in lower grades. On the other hand, students in lower grades were significantly more likely to witness bullying on the playground and in the gym. No other significant differences were observed.
Table 10 Results of Comparing Grade Level by Different Locations of Bullying for Those Who Had Witnessed an Act of Bullying
| Equal | p | Mean | Std Error | Effect | |||
|---|---|---|---|---|---|---|---|
| Grouping Variable | Variances | T | Df | value | Difference | Difference | Size |
| Class-Teacher Present | Assumed | -6.068 | 951 | <.001 | -1.028 | 0.169 | -6.083 |
| Class- Teacher not | Not assumed | -3.024 | 943.727 | .003 | -0.507 | 0.168 | -3.018 |
| Present | |||||||
| Playground | Not assumed | 15.561 | 751.458 | <.001 | 2.383 | 0.153 | 15.575 |
| Gym | Not assumed | 3.580 | 825.886 | <.001 | 0.596 | 0.166 | 3.590 |
| Hallways | Assumed | -9.976 | 951 | <.001 | -1.611 | 0.162 | -9.944 |
| Restroom | Assumed | 2.610 | 951 | .009 | 0.565 | 0.217 | 2.604 |
| Cafeteria | Not assumed | -2.317 | 950.351 | .021 | -0.390 | 0.168 | -2.321 |
| Walk To or From | Assumed | 0.150 | 951 | .881 | 0.047 | 0.314 | 0.150 |
| School | |||||||
| Bus | Assumed | 1.870 | 951 | .062 | 0.554 | 0.296 | 1.872 |
| Online | Not assumed | -5.607 | 231.765 | <.001 | -1.212 | 0.216 | -5.611 |
| Phone | Not assumed | -5.836 | 228.521 | <.001 | -1.224 | 0.210 | -5.829 |
| After School Events | Assumed | -3.503 | 951 | <.001 | -0.685 | 0.196 | -3.495 |
| Home | Not assumed | 1.173 | 110.765 | .243 | 0.376 | 0.321 | 1.171 |
| Church | Not assumed | -0.025 | 41.471 | .980 | -0.012 | 0.493 | -0.024 |
| Other Places | Not assumed | -0.189 | 39.600 | .851 | -0.067 | 0.355 | -0.189 |
The second series of t-tests were performed to examine whether there were significant differences in the mean of grade by each of the dummy variables representing location of bullying for perpetrators. These analyses were conducted based on the data collected from those who reported being perpetrators. As displayed in Table 11, it was found that there was a significant difference in the mean of grade level by the dummy variable representing playground (p < .001). The value of the effect size suggested that the magnitude of this difference was very large. These results indicated that students in lower grades were significantly more likely to be perpetrators of bullying on the playground than students in higher grades. No further significant differences were observed (p > .001).
Table 11Results of Comparing Grade Level by Different Locations of Bullying for Perpetrators of Bullying
| Cassain a Variable | Equal | J.C | Mean | Std Error | Effect | ||
|---|---|---|---|---|---|---|---|
| Grouping Variable | Variances | t | df | p -value | Difference | Difference | Size |
| Class-Teacher Present | Assumed | -1.321 | 233 | .188 | -0.447 | 0.339 | -1.319 |
| Class- Teacher not | Assumed | -1.084 | 233 | .280 | -0.376 | 0.347 | -1.084 |
| Present | Assumed | -1.064 | 233 | .200 | -0.370 | 0.347 | -1.064 |
| Playground | Assumed | 5.075 | 233 | <.001 | 1.829 | 0.361 | 5.066 |
| Gym | Assumed | -0.663 | 233 | .508 | -0.263 | 0.397 | -0.662 |
| Hallways | Not assumed | -2.98 | 175.079 | .003 | -0.971 | 0.326 | -2.979 |
| Restroom | Not assumed | -0.383 | 48.757 | .703 | -0.153 | 0.398 | -0.384 |
| Cafeteria | Not assumed | -1.595 | 145.326 | .113 | -0.545 | 0.342 | -1.594 |
| Walk To or From School | Assumed | -0.22 | 233 | .826 | -0.157 | 0.716 | -0.219 |
| Bus | Assumed | 1.239 | 233 | .217 | 0.827 | 0.668 | 1.238 |
| Online | Assumed | -1.543 | 233 | .124 | -1.19 | 0.772 | -1.541 |
| Phone | Assumed | -1.624 | 233 | .106 | -0.927 | 0.571 | -1.623 |
| After School Events | Not assumed | -1.468 | 46.117 | .149 | -0.594 | 0.405 | -1.467 |
| Home | Assumed | 1.797 | 233 | .074 | 0.917 | 0.51 | 1.798 |
| Church | Assumed | 0.77 | 233 | .442 | 1.122 | 1.457 | 0.770 |
| Other Places | Assumed | 0.315 | 233 | .753 | 0.284 | 0.903 | 0.315 |
The third series of t-tests were conducted to examine whether there were significant differences in the mean of grade by each of the dummy variables representing location of bullying for victims of bullying. These analyses were conducted based on the data obtained from those who reported being victimized by bullies. The results of the mean comparisons using the t-tests indicated that there were significant differences in the mean of grade level by the dummy variables for classroom with the teacher present, playground, hallways, cafeteria, online, and phone. The effect size values indicated that the magnitudes of all these mean differences were very large. These results suggested that students in higher grades were significantly more likely to be bullied in the classroom with the teacher present, in the hallways, in the cafeteria, online, and by phone. On the contrary, students in lower grades were significantly more likely to be bullied on the playground. No further significant differences were observed.
Table 12
Results of Comparing Grade Level by Different Locations of Bullying for Victims of Bullying
| Equal | 1.0 | 1 | Mean | Std Error | Effect | ||
|---|---|---|---|---|---|---|---|
| Grouping Variable | Variances | t | df | p -value | Difference | Difference | Size |
| Class-Teacher Present | Assumed | -5.613 | 589 | <.001 | -1.203 | 0.214 | -5.621 |
| Class- Teacher not Present | Assumed | -2.19 | 589 | .029 | -0.478 | 0.218 | -2.193 |
| Playground | Not assumed | 13.364 | 537.325 | <.001 | 2.449 | 0.183 | 13.383 |
| Gym | Not assumed | 0.549 | 383.65 | .584 | 0.120 | 0.219 | 0.548 |
| Hallways | Assumed | -6.359 | 589 | <.001 | -1.344 | 0.211 | -6.370 |
| Restroom | Assumed | 0.956 | 589 | .340 | 0.304 | 0.318 | 0.956 |
| Cafeteria | Assumed | -3.547 | 589 | <.001 | -0.784 | 0.221 | -3.548 |
| Walk To or From | A gayma a d | -1.082 | 590 | 200 | 0.542 | 0.502 | 1 002 |
| School | Assumed | -1.082 | 589 | .280 | -0.543 | 0.302 | -1.082 |
| Bus | Assumed | 0.595 | 589 | .552 | 0.265 | 0.446 | 0.594 |
| Online | Assumed | -3.924 | 589 | <.001 | -1.271 | 0.324 | -3.923 |
| Phone | Assumed | -5.284 | 589 | <.001 | -1.636 | 0.31 | -5.277 |
| After School Events | Assumed | -2.376 | 589 | .018 | -0.650 | 0.274 | -2.372 |
| Home | Not assumed | -0.105 | 85.501 | .916 | -0.038 | 0.361 | -0.105 |
| Church | Assumed | -0.696 | 589 | .487 | -0.392 | 0.563 | -0.696 |
| Other Places | Assumed | -0.786 | 589 | .432 | -0.381 | 0.486 | -0.784 |
To sum it up, the results of the independent samples t-tests determined there were statistically significant differences in the mean of grade by several indicators of bullying location. Hence, these results provided support to reject Null Hypothesis 5 that there is no statistically significant relationship between grade and the location of bullying.
Hypothesis 6
Null Hypothesis 6 is that there is no statistically significant relationship between grade and whether bullying was reported. To address this hypothesis, an independent samples t-test was performed to test whether there was a significant difference in the mean of grade by whether bullying was reported. Only the data for those who reported being victims of bullying were included in this analysis.
The results showed that there was a statistically significant difference in the mean of grade level by whether bullying was reported. The effect size value determined that the magnitude of this difference was very large. These results indicated that students in lower grades were significantly more likely to report that they were bullied than students in higher grades. Thus, these results provided evidence to reject Null Hypothesis 6 that there is no statistically significant relationship between grade and whether bullying was reported.
Table 13
Results of Comparing Grade Level by Whether Bullying Was Reported for Victims of Bullying
| Grouping Variable | Equal | T | Df | p -value | Mean | Std Error | Effect |
|---|---|---|---|---|---|---|---|
| Grouping variable | Variances | 1 | Dj | Difference | Difference | Size | |
| Bullying Being Reported | Not assumed | -3.717 | 523.946 | <.001 | -0.792 | 0.213 | -3.718 |
Hypothesis 7
Null Hypothesis 7 is that there is no statistically significant relationship between years attending a Christian school and the type of bullying reported. To evaluate this hypothesis, three
ANCOVAs were performed to determine whether there were significant differences in the mean of number of years attending a Christian school by the dummy variables representing seeing bullying, being a perpetrator of bullying, and being a victim of bullying after controlling for grade. By applying a Bonferroni correction, the significance level for these tests was determined at α = .050/3 = .017.
As shown in Table 14, the results of these analyses indicated that there was a statistically significant difference in the mean of number of years attending a Christian school by being a perpetrator of bullying (p < .017). The effect size for this grouping variable indicated that the magnitude of this difference was small. It can be concluded from these results that after accounting for grade, students attending a Christian school for more years were significantly more likely than those attending for fewer years to be perpetrators of bullying. No further significant differences were observed (p > .017). Overall, these results provided support to reject Null Hypothesis 7 that there is no statistically significant relationship between years attending a Christian school and the type of bullying reported.
Table 14 Results of Comparing Years at a Christian School by Different Types of Bullying After Controlling for Grade
| Grouping Variable | df1 | df2 | F | p-value | Effect Size |
|---|---|---|---|---|---|
| Seeing Bullying | 1 | 2013 | 0.026 | .871 | <.001 |
| Perpetrator | 1 | 2013 | 9.986 | .002 | .005 |
| Victim | 1 | 2013 | 2.080 | .149 | .001 |
Hypothesis 8
Null Hypothesis 8 is that there is no statistically significant relationship between years attending a Christian school and the location of bullying. To evaluate this hypothesis, a series of ANCOVAs were conducted to determine whether, after controlling for grade, there were
significant differences in the mean of number of years attending a Christian school by each of the 15 dummy variables representing location of bullying for those who had witnessed bullying, perpetrators of bullying, and victims of bullying. Hence, a total of 45 ANCOVAs tests were needed to be conducted. Using the Bonferroni correction approach, the significance level for these tests was determined at α = .050/45 = .001.
The first series of the ANCOVAs were performed to examine whether there were significant differences in the mean of number of years attending a Christian school by each of the dummy variables representing location of bullying for seeing bullying. These analyses were performed based on the data collected from the students who reported seeing bullying. As displayed in Table 15, after controlling for grade, no significant differences were identified in in the mean of number of years attending a Christian school by any of the dummy variables representing location of bullying for seeing bullying (p > .001).
Table 15 Results of Comparing Years at a Christian School by Different Locations of Bullying for Those Who Had Witnessed an Act of Bullying After Controlling for Grade
| df1 | df2 | F | p-value | Effect Size |
|---|---|---|---|---|
| .001 | ||||
| .005 | ||||
| 1 | 950 | 0.056 | .813 | .000 |
| 1 | 950 | 0.004 | .950 | .000 |
| .001 | ||||
| .003 | ||||
| .000 | ||||
| .001 | ||||
| .004 | ||||
| .000 | ||||
| .004 | ||||
| .001 | ||||
| .000 | ||||
| 1 | 950 | 1.798 | .180 | .002 |
| 1 1 1 1 1 1 1 1 1 1 1 | 950 950 950 950 950 950 950 950 950 950 950 | 1.241 4.360 1.364 2.859 0.261 0.803 4.162 0.391 3.754 0.545 0.243 | .265 .037 .243 .091 .609 .371 .042 .532 .053 .460 .622 |
Other Places 1 950 0.630 .427 .001
The second series of ANCOVAs were conducted to determine whether there were significant differences in the mean of number of years attending a Christian school by each of the dummy variables representing location of bullying for perpetrators. These analyses were conducted based on the data collected from those who reported being perpetrators. As reported in Table 16, after controlling for grade, no statistically significant differences were observed in the mean of number of years attending a Christian school by any of the dummy variables representing the location of bullying for perpetrators (p > .001).
Table 16 Results of Comparing Years at a Christian School by Different Locations of Bullying for Perpetrators of Bullying After Controlling for Grade
| Grouping Variable | df1 | df2 | F | p-value | Effect |
|---|---|---|---|---|---|
| Size | |||||
| Class-Teacher Present | 1 | 232 | 0.198 | .657 | .001 |
| Class- Teacher not | 1 | 232 | 0.209 | .648 | .001 |
| Present | |||||
| Playground | 1 | 232 | 0.098 | .754 | .000 |
| Gym | 1 | 232 | 0.010 | .921 | .000 |
| Hallways | 1 | 232 | 0.821 | .366 | .004 |
| Restroom | 1 | 232 | 0.212 | .646 | .001 |
| Cafeteria | 1 | 232 | 2.160 | .143 | .009 |
| Walk To or From School | 1 | 232 | 0.117 | .733 | .001 |
| Bus | 1 | 232 | 0.000 | .999 | .000 |
| Online | 1 | 232 | 0.399 | .528 | .002 |
| Phone | 1 | 232 | 1.540 | .216 | .007 |
| After School Events | 1 | 232 | 0.367 | .545 | .002 |
| Home | 1 | 232 | 1.906 | .169 | .008 |
| Church | 1 | 232 | 6.118 | .014 | .026 |
| Other Places | 1 | 232 | 4.515 | .035 | .019 |
The third series of the ANOVAs were conducted to examine whether there were significant differences in the mean number of years attending a Christian school by each of the dummy variables representing location of bullying for victims of bullying. These analyses were conducted based on the data obtained from those who reported being victimized by bullies. As reported in Table 17, it was found that after controlling for grade, no statistically significant differences were observed in the mean of number of years attending a Christian school by any of the dummy variables representing the location of bullying for victims of bullying (p > .001).
Table 17 Results of Comparing Years at a Christian School by Different Locations of Bullying for Victims of Bullying After Controlling for Grade
| Grouping Variable | df1 | df2 | F | p-value | Effect Size |
|---|---|---|---|---|---|
| Class-Teacher Present | 1 | 588 | 0.069 | .794 | .000 |
| Class- Teacher not | 1 | 588 | 3.822 | .051 | .006 |
| Present | |||||
| Playground | 1 | 588 | 0.421 | .517 | .001 |
| Gym | 1 | 588 | 0.282 | .595 | .000 |
| Hallways | 1 | 588 | 0.429 | .513 | .001 |
| Restroom | 1 | 588 | 0.662 | .416 | .001 |
| Cafeteria | 1 | 588 | 2.471 | .117 | .004 |
| Walk To or From School | 1 | 588 | 0.632 | .427 | .001 |
| Bus | 1 | 588 | 1.345 | .247 | .002 |
| Online | 1 | 588 | 3.575 | .059 | .006 |
| Phone | 1 | 588 | 4.495 | .034 | .008 |
| After School Events | 1 | 588 | 1.021 | .313 | .002 |
| Home | 1 | 588 | 0.316 | .574 | .001 |
| Church | 1 | 588 | 0.003 | .954 | .000 |
| Other Places | 1 | 588 | 0.097 | .756 | .000 |
In summary, the results of the ANCOVAs failed to provide support to reject Null Hypothesis 8 that there is no statistically significant relationship between years attending a Christian school and the location of bullying.
Hypothesis 9
Null Hypothesis 9 is that there is no statistically significant relationship between years attending a Christian school and whether bullying was reported. To evaluate this hypothesis, an ANCOVA was performed to determine whether there was a significant difference in the mean of number of years attending a Christian school by whether bullying was reported after controlling for grade. Only the data for those who reported being victims of bullying were included in this analysis. As reported in Table 18, it was observed that after controlling for grade, there was no significant difference in the mean of number of years attending a Christian school by whether bullying was reported, F(1,577) = 0.635, p = .426. Hence, these results failed to provided evidence to reject Null Hypothesis 9 that there is no statistically significant relationship between years attending a Christian school and whether bullying was reported.
Table 18 Results of Comparing Years at a Christian School by Whether Bullying Was Reported for Victims of Bullying After Controlling for Grade
| Grouping Variable | df1 | df2 | F | p-value | Effect Size | |
|---|---|---|---|---|---|---|
| Bullying Being Reported | 1 | 577 | 0.635 | .426 | .001 |
Hypothesis 10
Null Hypothesis 10 is that there is no statistically significant relationship between school size and the type of bullying reported. To address this hypothesis, three Pearson Chi-squared tests were conducted to test whether there were significant associations between school size and each of the dummy variables representing seeing bullying, perpetrator of bullying, and victim of bullying. Three chi-square tests were conducted to evaluate this hypothesis.
By performing a Bonferroni correction, the significance level for these tests was determined at α = .017.
As can be seen from Table 19, the results of the Chi-squared tests revealed that there were significant associations between school size and all dummy variables representing different types of bullying (p < .017). The Cramer’s V values indicated that the magnitudes of these
associations were weak. These results indicated that the students in the schools that fell into the category of medium were more likely to see bullying, commit bullying, and be bullied than students in small and large schools. In addition, students in small schools were more likely to witness bullying, commit bullying, and be bullied than students in large schools. Hence, these results provided evidence to reject Null Hypothesis 10 that there is no statistically significant relationship between school size and the type of bullying reported.
Table 19 Results of Examining the Associations Between School Size and Different Types of Bullying
| Bullying Type | 2 χ | Df | p-value | Cramer’s V |
|---|---|---|---|---|
| Seeing Bullying | 50.908 | 2 | <.001 | .159 |
| Perpetrator | 19.754 | 2 | <.001 | .099 |
| Victim | 27.548 | 2 | <.001 | .117 |
In addition to the Chi-squared tests, a series of one-way ANOVAs were performed to examine whether there were significant differences in physical, verbal, and social bullying by school size. These analyses were conducted based on the number of times students had seen, been victimized by, and been perpetrators of physical, verbal, and social bullying. Hence, a total of nine tests were needed to be conducted. Using a Bonferroni correction method, the significance level for these tests was set at α = .050/9 = .006.
The results of the one-way ANOVAs comparing physical, verbal, and social bullying by school size are reported in Table 20. There were statistically significant differences in the number of times students had seen physical, verbal, and physical bullying, the number of times students had been physically and socially bullied, and the number of times they had physically, verbally, and socially bullied other students by school size. The magnitudes of these differences can be seen in Table 20. Tukey’s procedure was utilized for post hoc analysis in order to
determine where these differences had occurred. The results of the post hoc analysis showed that the average number of times students had seen physical bullying was significantly higher (p < .001) in medium schools (M = 1.44, SD = 1.73) than in large schools (M = 0.83, SD = 1.32). The average number of times students had witnessed verbal bullying was significantly higher (p = .003) in small schools (M = 1.55, SD = 1.99) than in large schools (M = 1.16, SD = 1.75). The average number of times students had seen social bullying was significantly higher (p < .001) in medium schools (M = 1.69, SD = 1.91) than in large schools (M = 1.19, SD = 1.75). Moreover, the average number of times students had been physically bullied was significantly higher (p < .001) in medium schools (M = 0.91, SD = 1.56) than in large schools (M = 0.51, SD = 1.14). The average number of times students had been socially bullied was significantly higher (p < .001) in medium schools (M = 0.94, SD = 1.60) than in large schools (M = 0.66, SD = 1.38). Furthermore, the average number of times students had physically bullied other students was significantly higher (p < .001) in medium schools (M = 0.34, SD = 0.96) than in large schools (M = 0.14, SD = 0.52). The average number of times students had socially bullied other students was significantly higher (p = .001) in medium schools (M = 0.33, SD = 0.93) than in large schools (M = 0.18, SD = 0.68). No further significant differences were identified.
Table 20 Comparing Physical, Verbal, and Social Bullying by School Size
| Variable | df1 | df2 | F | p-value | Effect Size | Magnitude of the Difference |
|---|---|---|---|---|---|---|
| Seeing Physical | 2 | 2013 | 33.937 | < .001 | .033 | Medium |
| Seeing Verbal | 2 | 2013 | 7.939 | < .001 | .008 | Small |
| Seeing Social | 2 | 2013 | 15.898 | < .001 | .016 | Medium |
| Victim of Physical | 2 | 2013 | 19.260 | < .001 | .019 | Medium |
| Victim of Verbal | 2 | 2013 | 3.331 | .036 | .003 | Small |
| Victim of Social | 2 | 2013 | 7.733 | < .001 | .008 | Small |
| Perpetrator of Physical | 2 | 2013 | 16.094 | < .001 | .016 | Medium |
|---|---|---|---|---|---|---|
| Perpetrator of Verbal | 2 | 2013 | 5.242 | .005 | .005 | Small |
| Perpetrator of Social | 2 | 2013 | 7.074 | .001 | .007 | Small |
Hypothesis 11
Null Hypothesis 11 is that there is no statistically significant relationship between school size and the location of bullying. To evaluate this hypothesis, a series of Pearson Chi-squared tests were conducted to determine whether there were significant associations between school size and each of the 15 dummy variables representing location of bullying for those who had witnessed bullying, perpetrators of bullying, and victims of bullying. Thus, a total of 45 Chisquared tests were needed to be conducted. Using the Bonferroni correction method, the significance level for these tests was set at α = .050/45 = .001.
The first series of Chi-square tests were performed to examine the associations between school size and the dummy variables representing location of bullying for seeing bullying. These analyses were conducted based on the data obtained from the students who reported seeing bullying. As reported in Table 21, the results of these tests showed that there were significant associations between school size and the dummy variables representing classroom without the teacher present, playground, bus, and phone (p < .001). The Cramer’s V value indicated school size was weakly associated with classroom without the teacher present and moderately associated with playground. These results showed that regarding school size, students in small schools were most likely to see bullying in the classroom without the teacher present, while students in large schools were least likely. In addition, students in medium schools were most likely to see bullying on the playground while students in large schools were least likely. Moreover, students in small schools were most likely to witness bullying on the bus whereas
students in large schools were least likely. Lastly, students in large schools were most likely to witness bullying by phone whereas students in small schools were least likely. No other significant associations were found.
Table 21 Results of Examining the Associations Between School Size and Different Bullying Locations for Those Who Had Witnessed Bullying
| Bullying Location | 2 χ | df | p-value | Cramer’s V |
|---|---|---|---|---|
| Class-Teacher Present | 1.074 | 2 | .584 | .034 |
| Class- Teacher not Present | 26.170 | 2 | <.001 | .166 |
| Playground | 53.596 | 2 | <.001 | .237 |
| Gym | 1.689 | 2 | .430 | .042 |
| Hallways | 8.246 | 2 | .016 | .093 |
| Restroom | 6.926 | 2 | .031 | .085 |
| Cafeteria | 6.071 | 2 | .084 | .080 |
| Walk To or From School | 8.689 | 2 | .013 | .095 |
| Bus | 27.876 | 2 | <.001 | .171 |
| Online | 8.119 | 2 | .017 | .092 |
| Phone | 16.635 | 2 | <.001 | .132 |
| After School Events | 3.374 | 2 | .185 | .060 |
| Home | 6.999 | 2 | .030 | .086 |
| Church | 4.257 | 2 | .119 | .067 |
| Other Places | 0.818 | 2 | .664 | .029 |
The second series of Chi-square tests were performed to evaluate the relationships between school size and the dummy variables representing location of bullying for perpetrators of bullying. These tests were conducted based on the data collected from those who reported being perpetrators. As shown in Table 22, these results revealed that there were significant associations between school size and the dummy variables representing classroom without the teacher present, and playground (p < .001). The Cramer’s V value indicated that the magnitude of both these associations was weak.
These results revealed students in small schools were most likely to be perpetrators of bullying in the classroom without the teacher present, while students in large schools were least likely. Furthermore, students in medium schools were most likely to be perpetrators of bullying on the playground while students in large schools were least likely. No further significant relationships were observed (p > .001).
Table 22 Results of Examining the Associations Between School Size and Different Bullying Locations for Perpetrators of Bullying
| Bullying Location | 2 χ | df | p-value | Cramer’s V |
|---|---|---|---|---|
| Class-Teacher Present | 6.647 | 2 | .036 | .168 |
| Class- Teacher not Present | 18.628 | 2 | <.001 | .282 |
| Playground | 18.957 | 2 | <.001 | .284 |
| Gym | 2.160 | 2 | .340 | .096 |
| Hallways | .064 | 2 | .968 | .017 |
| Restroom | 6.322 | 2 | .042 | .164 |
| Cafeteria | 4.665 | 2 | .097 | .141 |
| Walk To or From School | 9.601 | 2 | .008 | .202 |
| Bus | 1.348 | 2 | .510 | .076 |
| Online | 0.885 | 2 | .642 | .061 |
| Phone | 0.134 | 2 | .935 | .024 |
| After School Events | 0.436 | 2 | .804 | .043 |
| Home | 2.824 | 2 | .244 | .110 |
| Church | 2.247 | 2 | .325 | .098 |
| Other Places | 1.150 | 2 | .470 | .080 |
The third series of Chi-square tests were performed to examine the associations between school size and the dummy variables representing location of bullying for victims of bullying. These tests were performed based on the data obtained from those who reported being victimized by bullies. The results of these tests are provided in Table 23. It was found that there were statistically significant associations between school size and the dummy variables indicating playground, and walk to or from school (p < .001). The Cramer’s V values indicated that school
size was moderately associated with playground and weakly associated with walk to or from school. These results indicated that students in medium schools were most likely to be victimized by bullies on the playground whereas students in large schools were least likely. Furthermore, students in medium schools were most likely to be bullied when walking to or from school while students in small schools were least likely. No other significant associations were identified (p > .001).
Table 23 Results of Examining the Associations Between School Size and Different Bullying Locations for Victims of Bullying
| Bullying Location | 2 χ | Df | p-value | Cramer’s V |
|---|---|---|---|---|
| Class-Teacher Present | 1.209 | 2 | .546 | .045 |
| Class- Teacher not Present | 9.265 | 2 | .010 | .125 |
| Playground | 24.978 | 2 | <.001 | .206 |
| Gym | 1.313 | 2 | .519 | .047 |
| Hallways | 12.334 | 2 | .002 | .144 |
| Restroom | 1.584 | 2 | .453 | .052 |
| Cafeteria | 2.755 | 2 | .252 | .068 |
| Walk To or From School | 15.615 | 2 | <.001 | .163 |
| Bus | 10.004 | 2 | .007 | .130 |
| Online | 2.045 | 2 | .360 | .059 |
| Phone | 3.864 | 2 | .145 | .081 |
| After School Events | 7.225 | 2 | .027 | .111 |
| Home | 13.233 | 2 | .001 | .150 |
| Church | 2.272 | 2 | .321 | .062 |
| Other Places | 3.541 | 2 | .170 | .077 |
To sum it up, the results of the Pearson Chi-squared tests determined that some indicators of bullying location were significantly associated with school size. Therefore, these results provided support to reject Null Hypothesis 11 that there is no statistically significant relationship between school size and the location of bullying.
Hypothesis 12
Null Hypothesis 12 is that there is no statistically significant relationship between school size and whether bullying was reported. To evaluate this hypothesis, a Pearson Chi-squared test was conducted to examine the association between school size and whether bullying was reported. Only the data for those who reported being victims of bullying were included in this analysis. As shown in Table 24, the results of this test indicated that there was no significant association between bullying being reported and school size (p > .05). Thus, Null Hypothesis 12 was not rejected.
Table 24 Results of Examining the Associations Between School Size and Whether Bullying Was Reported for Victims of Bullying
| 2 χ | Df | p-value | Cramer’s V | |
|---|---|---|---|---|
| Bullying Being Reported | 4.321 | 2 | .115 | .086 |
References
Sedgwick, P. (2012). Multiple significance tests: the Bonferroni correction. Bmj, 344. Cohen, J. (2013). Statistical power analysis for the behavioral sciences. Routledge.