Psychometric scores for anxiety, depression, negative self, somatization, and hostility were combined into a single Global Severity Index (GSI). GSI was compared for 76 adolescents who were seen in the outpatient clinic for 7 different physical complaints (short stature, obesity, lack of weight gain, breast problems, genital problems, menstrual problems, and hirsutism).
a. Report the explanatory variable and tell whether it is quantitative or categorical.
b. Report the response variable and tell whether it is quantitative or categorical.
c. The null hypothesis states that those variables are not related. Alternatively, it can be written in terms of population means. Write this null hypothesis about means using mathematical notation.
d. Should the alternative state that not all population means are the same, or that all population means are different?
e. How many degrees of freedom does the relevant F statistic have in the numerator and in the denominator?
f. The F statistic is found to be 1.01. Keeping in mind that F distributions are centered near 1, is the P-value small enough to reject the null hypothesis and conclude that GSI is related to type of physical complaint?
g. If psychometric scores differ significantly depending on the particular physical complaint, then clinicians could use that information to make referrals for psychiatric screening of clinic patients. Discuss the consequences of a Type II Error in this situation.