Question

Say I wanted to research the relationship between parental criminal activity and offspring misbehavior. I go to a prison and survey the inmates on the number of crimes they’ve committed and how often their child gets in trouble in school. I find no correlation (r = 0) between parent criminal behavior and child misbehavior. Why might this correlation be misleading?

Answer 1

let x and y are two variable and they are linearly depended ; we can calculate the pearson's correlation coefficient for this . because pearson's correlation coefficient are valid only for those random variables which are linearly depended , if there is any non linear dependencies between two random variables, pearson's correlation coefficient ( r) might gives the value 0 whereas those random variables are strongly dependent to each other (non linearly).

here research was conducted to show the relationship between parental criminality and offspring misbehavior and no correlation found between them , i.e: r=0

now it is may be cause of

a. parental criminal activity and offspring misbehavior are may be totally independent to each other

or,

b. there is a non linear dependencies between criminal activities of parents and offspring misbehavior.

now , r=0 does not imply the non dependencies of two variable because the correlation may be 0 when there is a strong dependencies between two variables.

here it is a fact that the crimes and behavior of parents gives impact on child's behavior as they got the lesson  from their parents .

so , there may be some non linear dependencies between parental criminal activity and offspring misbehavior and as a result r gives the value 0. (Ans)