On testing hypotheses regarding a class of covariance structures

Let x be ap-component random variable having a multivariate normal distribution with covariance matrix . In this paper, we consider the problem of testing hypotheses of the formH ₀: =b ₁₁ + +b _{m m} , whereb _i 's are unknown scalars, and _i 's are a set of known and simultaneously diagonalizable matrices. This problem has both psychometric and statistical interest, and its basic theory is developed here. Besides, the problem of obtaining likelihood-ratio statistic for testingH ₀ is studied, and the statistic obtained in a special case.     

Transitional Adolescents,Anxiety, and Group Counseling

One hundred-eighty college-bound high school seniors were studied to determine whether small group counseling would affect their anxiety level. 60 students comprised the experimental group and 60 students each the 2 control groups. 6 small group counseling sessions were conducted during the spring just prior to high school graduation and 6 more in the fall, following college enrollment. Comparison of anxiety levels was made at the conclusion of each series of counseling sessions. The students of the experimental group showed significantly lower anxiety scores than did those of the control groups, both in the spring and in the fall. The conclusion was drawn that experience in small group counseling was followed by significantly lower levels of anxiety in transitional adolescents.