Cortisol is a hormone that plays an important role in mediating stress. There is
ID: 3319762 • Letter: C
Question
Cortisol is a hormone that plays an important role in mediating stress. There is growing awareness that exposure of outdoor workers to pollutants may impact cortisol levels. The article “Plasma Cortisol Concentration and Lifestyle in a Population of Outdoor Workers” (Intl. J. of Envir. Health Res., 2011: 62–71) reported on a study involving three groups of police officers: (1) traffic police (TP), (2) drivers (D), and (3) other duties (O). Here is summary data on cortisol concentration (ng/ml) for a subset of the officers who neither drank nor smoked.
Group Sample Size Mean SD
TP 47 174.7 50.9
D 36 160.2 37.2
O 50 153.5 45.9
Assuming that the standard assumptions for one-way ANOVA are satisfied, carry out a test at significance level .05 to decide whether true average cortisol concentration is different for the three groups. [Note: The investigators used more sophisticated statistical methodology (multiple regression) to assess the impact of age, length of employment, and drinking and smoking status on cortisol concentration; taking these factors into account, concentration appeared to be significantly higher in the TP group than in the other two groups.]
Explanation / Answer
The Hypothesis:
H0: There is no difference between the average cortisol concentration in the three groups.
Ha: There is a difference between the average cortisol concentration for at least 1 of the three groups.
The ANOVA table is as below. the p value is calculated for F = 2.69 for df1 = 2 and df2 = 130
The Fcritical is calculated at = 0.05 for df1 = 2 and df2 = 130
The Decision Rule:
If Ftest is > F critical, Then Reject H0.
Also if p-value is < , Then reject H0.
The Decision:
Since Ftest (2.69) is < F critical (3.065), We Fail to Reject H0.
Also since p-value (0.0714) is > (0.05), We Fail to Reject H0.
The Conclusion: There is insufficient evidence at the 95% level of significance to conclude that there is a difference between the average cortisol concentration for at least 1 of the three groups.
Source Sum of sq DF Mean Square F Fcv p Between 11223.53 2 5611.76 2.69 3.065 0.0714 Within 270845.35 130 2083.43 Total 282068.88 132