Matrix Algebra And Introduction

Question 1

Diagonal matrix

Answer 1

Square matrix, with off diagonal elements equal to zero

Question 2

Definition of a symmetric matrix

Answer 2

Square matrix where each element (i,j) is identical to element (j,i)

Question 3

How to check of two matrices are the inverse of each other?

Answer 3

Multiply them, if the outcome is an identity matrix, it is correct.

Question 4

What is an identity matrix?

Answer 4

Diagonal elements are 1, off diagonal elements are 0

Question 5

How to calculate the determinant of a matrix?

Answer 5

(a x d) - (b x c)

Question 6

Definition of type 1 error

Answer 6

The chance that you reject H0 when H0 is actually true. This chance is alpha

Question 7

What is the difference between actual alpha and nominal alpha ?

Answer 7

Nominal alpha is the alpha the researcher chooses. Actual alpha is the actual alpha from the test.
When actual alpha is larger than nominal alpha, the test is too liberal
When actual alpha is smaller than nominal alpha, the test is too conservative

Question 8

Definition of a square matrix

Answer 8

Equal number of rows and columns (d x d)

Question 9

What is power ?

Answer 9

Chance that you reject H0 when H0 is not true.

Question 10

How to increase the power?

Answer 10

Test multivariate in stead of univariate, increase alpha, add an covariate or blocking variable, increase N

Question 11

What is chance capitalization?

Answer 11

When you do multiple analysis, the chance on type 1 error increases