Use of Correlation in Understanding Fathering Behaviors

Statistical Guide

For a correlation coefficient based on data for a sample randomly drawn from a population, the null hypothesis states that the observed value is a chance deviation from a true value of 0.00 in the population (i.e., the observed value of r is not truly different from 0.00). When the probability that the null hypothesis is true equals 5 or less in 100, most researchers reject it and declare the coefficient to be statistically significant (i.e., reliable). The lower the probability, the more significant the relationship.

Excerpt from the Research Article¹

Children were between the ages of 9 and 12, with a mean age of 10.8 years.

Parental involvement:The Parent Involvement Scale consisted of 12 items focusing on different areas of potential parent-child activity, such as “Celebrating holidays with child,” [and] “Attending school or church related functions”….

Parental behavior:The Children’s Report of Parental Behavior [yields scores], with a higher score representing a higher frequency of supportive behaviors and a lower frequency of critical or angry behaviors.

Parenting together:The Parenting Together Scale…consisted of 11 items describing possible aspects of partners’ parenting collaboration (e.g., “Discussing personal problems the child may be experiencing”).

Self-concept:The Self-Concept scale…consists of 15 items related to children’s feelings of self-worth … with a higher score indicating a more positive self-concept.

Psychological problems: Each parent responded to a 19-item psychological and behavioral problem scale…(e.g., “Restless, jumpy, hyperactive,” “Bullying or mean to animals or other children,” “Has trouble sleeping”).

Classroom behavior:The instrument’s total score…represented teachers’ overall impression of adjustment, as reflected in classroom behavior, with a higher score indicating more positiveadjustment.

Peer popularity:[The] Peer Friendship Survey asked all children, anonymously, to indicatewhich classmates, if any, were their best friends.

Correlations of parenting measures with child adjustment measures [for fathers in two-biologicalparent households (n = 79)]

×p< 0.1

*p< 0.05

**p< 0.01

***p< 0.001

Questions

1.     Which two variables have the strongest relationship between them?

2.     The correlation between family income and GPA indicates that those who are lower on income tend to be:

A.     lower on GPA.   B. higher on GPA.

3.     Is the relationship between family income and involvement direct or inverse?

4.     Is the relationship between parenting behavior and psychological problems direct or inverse?

5.     Is the relationship between involvement and psychological problems statistically significant? Explain.

6.     Should the null hypothesis for the relationship referred to in question 5 be rejected?

7.     All the correlations with GPA are significant. Which one is significant at the highest level?

8.     What is the probability that the value of .34 (the r in the upper-left corner of the table) is a random deviation from a true correlation of 0.00?

9.     The value of r for the relationship between peer popularity and parental behavior is .05. Does this mean that the correlation coefficient is statistically significant at the .05 level? Explain.

10.  The value “p < .001” in the footnote to the table indicates that the probability that the null hypothesis is true is less than one in

A.     10

B.     100  

C.    1,000

11.  Write out in words, without using numerals, the meaning of “p < 0.1,” which appears in the footnote to the table.