08 Normal Distribution: Linear Hypothesis Testing

Question 1

How do you go about linear hypothesis testing for the mean of linear combinations (what is H₀) ?

Answer 1

H₀: Aμ - b = 0
… A is any q x p data matrix
… and b is any q x 1 vector

Question 2

What is H₀ for a regression model in linear hypothesis testing?

Answer 2

H₀: Aβ - b = 0

Question 3

What is the idea behind linear hypothesis testing for the mean of linear combinations?

Answer 3

Idea: Are some βs linear combinations of each other? Is the observed data significantly different from the mean?

Question 4

What three tests can be done in Profile Analysis?

Answer 4

1. Similarity of Profiles (= Parallel Profiles)
2. Equality of two levels
3. Treatment effects ( = Horizontality of Profiles)

Question 5

What is profile analysis concerned with?

Answer 5

• Comparison study - repeated p measurements applied to two independent groups
• > How are the profiles of the two groups?

Question 6

What do you test with the “similarity of profiles” in profile analysis?

Answer 6

whether there are differences in the means between treatment and other group.

These studies attempt to differentiate between individuals or groups by patterns of test scores. In another type of problem, two or more profiles for the same person are compared. The person is assessed more than once on the same set of variables, and the consistency of the profiles is measured.

Question 7

What is the null hypothesis in “equality of 2 levels” (profile analysis)?

Answer 7

that the sum of the differences in means is 0.
More formally:
1ₚᵀ(μ₁ - μ₂) = 0

Question 8

What is the null hypothesis in “treatment effect” (= horizontality of profiles) in profile analysis?

Answer 8

H₀: C (μ₁ + μ₂) = 0