### Linear Statistical Models: Regression

### Raw Scores, Deviation Scores & Standard Scores

**Raw Scores**

The observations in a data set. Usually denoted in upper case letters; X, Y, etc.

**Sample Mean**

**Deviation Scores**

Deviation scores are raw scores with the sample mean subtracted from them.
Deviation scores are usually denoted with a lower case letter; x, y, etc. The mean of
deviation scores is always zero.

**Standard Scores**

Standard scores, also called z-scores, are deviation scores divided by the standard
deviation. Standard scores are usually denoted as z. The mean of standard scores is always zero
and the standard deviation is always one.

**Comparing Raw Scores, Deviation Scores & Standard Scores**

Type Score | Mean | Standard Deviation |

Raw | m | sd |

Deviation | 0 | sd |

Standard | 0 | 1 |
---|

**Example:**

**input X
96
87
89
79
92
91
end
summarize X**
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
X | 6 89 5.761944 79 96
**return list**
scalars:
r(N) = 6
r(sum_w) = 6
r(mean) = 89
r(Var) = 33.2
r(sd) = 5.761944116355173
r(min) = 79
r(max) = 96
r(sum) = 534
**generate x = X - r(mean)
generate z = x/r(sd)
format X x z %4.2f
list**
X x z
1. 96.00 7.00 1.21
2. 87.00 -2.00 -0.35
3. 89.00 0.00 0.00
4. 79.00 -10.00 -1.74
5. 92.00 3.00 0.52
6. 91.00 2.00 0.35
**summarize, format**
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
X | 6 89.00 5.76 79.00 96.00
x | 6 0.00 5.76 -10.00 7.00
z | 6 0.00 1.00 -1.74 1.21

Linear Statistical Models Course

Phil Ender, 5Jan98