Wading Through the Data Swamp:
Program Evaluation 201

Module 1: Descriptive Statistics in Evaluation - Page 16 of 21

Standard Deviation for Alcohol Use
alcohol Icon

You can do these same steps with the kids' responses to the alcohol use question, to see if their alcohol use varies as much as their marijuana use.

  1. Take each score and subtract the mean (for example, for student #1, subtract 1.64 from 2 = 0.36).
  2. Square that number (for example, for student #1, square 0.36 = .1296).
  3. Add the results for each student (all 50 students' results added together = 41.52).
  4. Divide the total by the number of scores minus one (for Jack's group, 41.52/49 = 0.8304).
  5. Take the square root of the result of step 4 (square root of 0.8304 = 0.91).

Here are the results:

Standard Deviation for Alcohol Use

Picture of a scroll Scrolling Table! You can use the table below to scroll through the data.

Kid # Days
Used(x)
(Days Used-Mean)
(x-M)
(Days
Used-Mean)2

(x-M)2
1 2 0.36 0.1296
2 1 -0.64 0.4096
3 2 0.36 0.1296
4 2 0.36 0.1296
5 2 0.36 0.1296
6 1 -0.64 0.4096
7 2 0.36 0.1296
8 0 -1.64 2.6896
9 4 2.36 5.5696
10 1 -0.64 0.4096
11 2 0.36 0.1296
12 2 0.36 0.1296
13 2 0.36 0.1296
14 1 -0.64 0.4096
15 2 0.36 0.1296
16 1 -0.64 0.4096
17 2 0.36 0.1296
18 5 3.36 11.2896
19 1 -0.64 0.4096
20 2 0.36 0.1296
21 2 0.36 0.1296
22 2 0.36 0.1296
23 0 -1.64 2.6896
24 2 0.36 0.1296
25 1 -0.64 0.4096
26 2 0.36 0.1296
27 2 0.36 0.1296
28 1 -0.64 0.4096
29 2 0.36 0.1296
30 2 0.36 0.1296
31 0 -1.64 2.6896
32 2 0.36 0.1296
33 1 -0.64 0.4096
34 0 -1.64 2.6896
35 2 0.36 0.1296
36 2 0.36 0.1296
37 1 -0.64 0.4096
38 2 0.36 0.1296
39 1 -0.64 0.4096
40 2 0.36 0.1296
41 0 -1.64 2.6896
42 2 0.36 0.1296
43 2 0.36 0.1296
44 1 -0.64 0.4096
45 2 0.36 0.1296
46 2 0.36 0.1296
47 2 0.36 0.1296
48 1 -0.64 0.4096
49 2 0.36 0.1296
50 2 0.36 0.1296
 
 

Mean = 82/50 = 1.64

Standard deviation = The square root of : The sum of (each score - mean)2/(number of scores - 1)

square root of

41.52/(50-1) = square root of0.8304 = 0.91

We can see that the standard deviation of marijuana use (2.67) is much higher than the standard deviation for alcohol use (.91). This tells us that the group score varied greatly for marijuana but only slightly for alcohol. In other words, most participants used alcohol about the same number of times per month. The same is not so for marijuana use. Some kids never used, some used moderately, and others used very frequently.