Question

A recent study1 examined the impact of a mother’s voice on stress levels in young girls. The study included 68 girls ages 7 to 12 who reported good relationships with their mothers. Each girl gave a speech and then solved mental arithmetic problems in front of strangers. Cortisol levels in saliva were measured for all girls and were high, indicating that the girls felt a high level of stress from these activities. (Cortisol is a stress hormone and higher levels indicate greater stress.) After the stress-inducing activities, the girls were randomly divided into four equal-sized groups: one group talked to their mothers in person, one group talked to their mothers on the phone, one group sent and received text messages with their mothers, and one group had no contact with their mothers. Cortisol levels were measured before and after the interaction with mothers and the change in the cortisol level was recorded for each girl. The researchers are testing to see if there is a difference in the change in cortisol level depending on the type of interaction with mom.

Determine:
(a) Is this an experiment or an observational study?
(b) What is the total degrees of freedom? The degrees of freedom for groups? The degree of freedom for error?
(c) The results of the study show that hearing mother’s voice was important in reducing stress levels. Girls who talk to their mother in person or on the phone show decreases in cortisol significantly greater, at the 5% level than girls who text with their mothers or have no contact with their mothers. There was not a difference between in-person and on the phone and there was not a difference between texting and no contact. Was the p-value of the original ANOVA test above or below 0.05?

Answer 1

Explanation:

a. The study is an experiment because it assigns people or things to groups and aims to notice if there is a difference in the change in cortisol level depending on the type of interaction with mom. This also occurs where researchers introduce an intervention and then study the effects of such intervention

In an observational study, measurement or members of a sample are surveyed of a sample without trying to affect them. this also occurs where researchers observe the effect of a risk factor or other intervention without trying to change who is or isn’t exposed to it.

b. The total degree of freedom is calculated using the formula N - 1 where N is the total number of girls (68). Thus, we have N - 1 = 68 - 1 = 67.

The degree of freedom for groups is k - 1 where k is the number of girls in each equal-sized group (which is 68/4 groups = 17 girls in each group). Thus, we have k - 1 = 17 - 1 = 16

The error degree of freedom is calculated using the formula N - k where N is the total number of girls (68) and k is the number of groups (4 equal sized groups) in the sample. Thus, we have N - k = 68 - 4 = 64.

c. Was the p-value of the original ANOVA test above or below 0.05?

The p-value of the original ANOVA test was below 0.05 because there was a highly significant level of cortisol observed after the activities.