Exploring Bullying Behavior: Correlation, Scatter Plot, and Regression Analysis

Proportion of Males and Females Involved in Bullying

1. What is the proportion of males who bullied others?  What is the proportion of females who bullied others?  Which gender (male or female) possessed a deeper involvement in bullying others?

2. What is the correlation between friends who bully individuals and the number of times the respondent bullied others?  Is this correlation coefficient significant? How do you know?  What is the coefficient of determination between friends who bully individuals and the number of times the respondent bullied others?  Using your own words, interpret the coefficient of determination for these data.   
3. Draw a scatter plot of “number of friends who bully” [x axis] and “number of times respondent bullied others” [y axis].  Based only on the scatter plot, do you believe the correlation between these two variables is positive or negative.  Why?

4. Which variable(s) in the table above cannot be used to calculate a correlation coefficient?  Why did you identify these variables?  From the table above, identify the only variables that could be appropriately used for an Ordinary Least Squares Regression.  Why did you identify these variables?

5. If you were to draw one individual from this sample of 10 individuals, what characteristics do you believe would be the most likely to be drawn (1 = Bully Victim and Bully Offender; 2 = Bully Victim but not Bully Offender; 3 = Bully Offender but not Bully Victim; or 4 = Non Bully Victim and Non Bully Offender)?  Why?

6. If the researcher only had the variable “number of times the respondent bullied others” and you were to randomly select one individual but did not know his/her value on this variable, what would be the value you would guess (you need to provide a number to receive credit)?

7. The table listed below communicates the results of a statistical test exploring the relationship between different types of bully victimizations (cyber, verbal, and physical) and individual reports of mental health (depression and suicide ideation).  The victimization variables are all categorical (yes/no) and the depression and suicide ideation measures are scored on an interval/ratio level such that higher values are indicative of the respondent experiencing higher levels of depression and suicide ideation. Write a paragraph summarizing the relationship between different types of victimizations (cyber, verbal, and physical) and mental health status (depression and suicide ideation).  Pay particular attention to significant and non-significant findings (i.e., *p < .01 indicates that the finding is significant at the .01 level).