Voluntary Exercise 2 - due in the next class Loneliness of Mothers and Daughters
ID: 1147991 • Letter: V
Question
Voluntary Exercise 2 - due in the next class Loneliness of Mothers and Daughters (Each correct answer is worth 1 CA point, but the maximum is capped at 2 CA points) Parental Variable Loneliness Depression Self-esteem Assertiveness Number of friends Correlation with Daughter's Loneliness .26 19 14 .05 .21 Quality of friendships Source: Journal of Marriage and the Family (August 1986), sample size = 130 Q1. Can we conclude that mother and daughter loneliness scores were positively correlated at 1% significance level? Q2. Can we conclude that there exists a causal relationship for Q1? Why? Q3. Can we conclude those variables with non-significant correlations are unrelated?Explanation / Answer
Q1. Since the correlation coefficient is given to conclude whether the correlation between mother and daughter loneliness scores are positively correlated at 1% significance level, we need to calculate the appropriate t value to test the significance of the correlation coefficient.
Given r = 0.26, Coefficient of determination = r^2 = 0.26 * 0.26 = 0.0676
Is this relationship significant? r = 0.26, N = 130 = sample size (given)
Level of significance asked = 1% = 0.01
Determine one - or - two - tailed test ( am for one - tailed)
t = r sqrt[(n-2)/(1 - r^2)] = 0.26 * sqrt [ ( 130 - 2) / ( 1 - 0.26^2)]
t = 0.26 * sqrt [ 128 / 0.9324] = 0.26 * 11.7166 = 3.046
t = 3.046
If you refer to the t - table then critical value of t = 2.3 (approximately)
Since our t - value = 3.046 is above the critical value we reject the null hypothesis that the mother and daughter loneliness scores are not positively correlated at 1% significance level. Hence we conclude that the mother and daughter loneliness scores are positively correlated at 1% significance level.
Q2. A single statistical test cannot estabilish a causal relationship. Looking at the correlation alone we cannot find causality. To determine causation you need to take test subjects from your sample and test each group statistically and find whether the groups are statistically different from each other or not.
Q3. We cannot conclude those variables with non- significant correlations are unrelated since correlations between two variables does not mean one is directly causing the other, there could be other factors involved in the cause and effect. There could be a relationship between the two or there could not be.
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