Question

It is well established that both nature (genetics) and nurture (environment) play a role in who we are and how we behave as humans. One way to examine the effect of nature vs. nurture is to study children who have been adopted at birth. These children are unique in that they received genes from their birth parents and have environmental influence from their adoptive parents. For example, a research study can be conducted to see if the Body Mass Index (BMI) is more correlated with the BMI of his/her birth parent or adoptive parent. If the BMI of the child is more correlated with the birth parent’s BMI, it means that the weight might be genetically determined to a larger extent compared to environmental influence. If it’s more correlated with the adoptive parent’s BMI, then it means that the weight might be influenced by the behavior of the adoptive parent to a larger extent.

Use the following dataset to answer the questions below:

	BMI
Subject ID #	Child	Child’s Birth Parent	Child’s Adoptive Parent
1	22	26	20
2	21	17	22
3	25	23	22
4	19	25	21
5	20	19	25
6	17	19	17
7	25	21	27
8	18	19	17
9	20	28	23
10	19	23	21

Questions:

1. Calculate the mean and standard deviation for the adoptive parents’ BMI. (2 points total: 1 for mean and 1 for SD- deduct .5 if the process is correct but result is wrong)

2. Calculate the Z scores for all the data points for the adoptive parents. (1 point for calculating adoptive parents’ Z scores. Deduct .5 for each error in calculation)

3. Calculate the Pearson’s correlation coefficient r between children’s BMI and their adoptive parents’ BMI. Note that the children’s Z scores have been calculated in Part 1 of this scenario. (2 points total: 1 for work, 1 for r value)

4. Explain the direction and strength of the relationship based on the r. (2 points total: 1 for direction, 1 for strength)

5. What is the proportion of shared variance between children’s BMI and their adoptive parents’ BMI? That is, how much of the variance in the children’s BMI can be predicted from their adoptive parents’ BMI? (2 points total: 1 for work, 1 for result)

6. Based on the two r statistics, what would be the answer to the research question of whether children’s BMI is influenced more by nature or nurture? (1 point)

Answer 1

Note : Allowed to solve 4 sub part for one question

Calculate the mean and standard deviation for the adoptive parents’ BMI. (2 points total: 1 for mean and 1 for SD- deduct .5 if the process is correct but result is wrong)

Calculate the Z scores for all the data points for the adoptive parents. (1 point for calculating adoptive parents’ Z scores. Deduct .5 for each error in the calculation)

Calculate the Pearson’s correlation coefficient r between children’s BMI and their adoptive parents’ BMI. Note that the children’s Z scores have been calculated in Part 1 of this scenario. (2 points total: 1 for work, 1 for r value)

Explain the direction and strength of the relationship based on the r. (2 points total: 1 for direction, 1 for strength)

Direction is positive : As one variable increases, the other variables also increase

Strength: It is a weak correlation. A correlation has a value between -1 and 1. The absolute value ranges from 0 to 1, higher the value stronger is the relationship.