Descriptive Statistics

1
Chapter 2 Descriptive Statistics
We will be comparing the univariate and matrix
formulae for common statistical quantities.
2
The Sample Mean Vector
Scalar
Matrix
3
Deviation Scores
Scalar
Matrix
4
Sum of Squares Conceptual Formula
Scalar
Matrix
A D?D
5
Sum of Squares Hand Calculator Version
Scalar
Matrix
6
The Variance-Covariance Matrix
Scalar
Matrix
7
The Variance-Covariance Matrix

• Its a key matrix It summarizes the
  relationship between
• each pair of variables.
• Its order is m m (where m is the number of
  vars)
• It has lots of names variance matrix,
  covariance matrix,
• variance-covariance matrix

8
The Variance-Covariance Matrix
Diagonal entries could be called
There are m (m-1) / 2 unique off diagonal
elements. There are m (m1) / 2 unique
elements.
The S matrix is symmetric
9
The Diag() Function
10
The Square Root of a Diagonal Matrix
A unique square root of a diagonal matrix may
exist. For other square or rectangular matrices,
the square root is not unique.
11
Z Scores
Scalar
Matrix
12
The Correlation Matrix