Question

For each item below, address the following: (a) specify and interpret the direction of the relationship between the variables; (b) indicate the magnitude/strength of the relationship between the variables; and (c) calculate the shares variance between the variables.

(a) There is a significant correlation between infants’ lengths of hospitalization in the NICU and their parents’ levels of anxiety (r= 0.74, p<0.05). (b) There is a significant correlation between parents’ attendance at PTA meetings and their children’s year in school (r= -0.41, p<0.05). (c). There is a significant correlation between family composition (0=Non-Single parents, 1=Single Parents) and levels of family-related stress (r=0.53, p<0.05).

Answer 1

a) It is given that the the measure of the correlation r = 0.74. So there is positive correlation between infant lengths of hospitalization in the NICU and their parents’ levels of anxiety because the correlation coefficient is positive. As the value is quite high so we can conclude that there is a quite strong positive correlation exists. The shared variance is the covariance between them. It can be obtained by multiplying the correlation coefficient r by square roots of variances of the variables.

b) It is given that the the measure of the correlation r = -0.41.So there is negative correlation between parents’ attendance at PTA meetings and their children’s year in school because the correlation coefficient is negative.As the value is significantly less than zero so we can conclude that there is a moderately strong negative correlation exists. The shared variance is the covariance between them. It can be obtained by multiplying the correlation coefficient r by square roots of variances of the variables.

c) It is given that the the measure of the correlation r = 0.53. So there is positive correlation between family composition and levels of family-related stress because the correlation coefficient is positive. As the value is significantly greater than zero so we can conclude that there is a moderately strong positive correlation exists. The shared variance is the covariance between them. It can be obtained by multiplying the correlation coefficient r by square roots of variances of the variables.

In each case if the there is data available then we will conduct simple linear regression analysis. The null hypothesis will be regressor coefficient equal to zero and the alternative will be either greater or less than zero depending on the situation, If we want to check there is positive relationship between two variables exists or not we will take alternative as regressor coefficient greater than 0. Each case the response and independent variables have to choosen correctly. Based on the p-value we can conclude that at alpha level of significance if there exists any linear relationship or not.