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