Wading Through the Data Swamp:
Program Evaluation 201

Module 2: Subgroup Analysis - Page 7 of 12

Standard Deviation

After looking at the means from the gender subgroup analysis, Jack decided that he should also take a look at the standard deviations from the subgroup analysis for the boys and girls. Jack learned in Module 1 that if you only look at means you may not see what is really going on with the kids.

Standard Deviations for Boys' Marijuana Use
Boys Icon Marijuana Icon

M = Mean

Pretest

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

Kid # Days
Used (x)		 (x-M) (x-M)2
1 0 -2.21 4.88
2 0 -2.21 4.88
3 7 4.79 22.94
4 0 -2.21 4.88
5 5 2.79 7.78
6 3 0.79 0.62
7 0 -2.21 4.88
8 8 5.79 33.52
9 0 -2.21 4.88
10 0 -2.21 4.88
11 0 -2.21 4.88
12 0 -2.21 4.88
13 0 -2.21 4.88
14 7 4.79 22.94
15 0 -2.21 4.88
16 0 -2.21 4.88
17 5 2.79 7.78
18 7 4.79 22.94
19 0 -2.21 4.88
 
 

Standard deviation = formula for standard deviation

The square root of: The sum of (each score - mean)2 divided by (number of scores - 1)

Remember that the number of scores is 19, because we're missing one score.

square root of

177.08/(19-1) = square root of9.84 = 3.14

Posttest

M = Mean

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

Kid # Days
Used (x)		 (x-M) (x-M)2
1 0 -1.42 2.02
2 0 -1.42 2.02
3 5 3.58 12.82
4 0 -1.42 2.02
5 0 -1.42 2.02
6 0 -1.42 2.02
7 0 -1.42 2.02
8 10 8.58 73.62
9 0 -1.42 2.02
10 3 1.58 2.5
11 0 -1.42 2.02
12 2 0.58 0.336
13 0 -1.42 2.02
14 2 0.58 0.336
15 0 -1.42 2.02
16 3 1.58 2.5
17 2 0.58 0.336
18 0 -1.42 2.02
19 0 -1.42 2.02
 
 

Standard deviation = formula for standard deviation

The square root of: The sum of (each score - mean)2 divided by (number of scores - 1)

Remember that the number of scores is 19, because weíre missing one score.

square root of

116.688/(19-1) = square root of6.48 = 2.55

Standard Deviations for Girls' Marijuana Use
Girls Icon Marijuana Icon

M = Mean

Pretest

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

Kid # Days
Used (x)		 (x-M) (x-M)2
1 0 -1.48 2.19
2 0 -1.48 2.19
3 6 4.52 20.43
4 4 2.52 6.35
5 0 -1.48 2.19
6 0 -1.48 2.19
7 0 -1.48 2.19
8 6 4.52 20.43
9 0 -1.48 2.19
10 3 1.52 2.31
11 5 3.52 12.39
12 0 -1.48 2.19
13 0 -1.48 2.19
14 3 1.52 2.31
15 0 -1.48 2.19
16 0 -1.48 2.19
17 5 3.52 12.39
18 0 -1.48 2.19
19 0 -1.48 2.19
20 0 -1.48 2.19
21 0 -1.48 2.19
22 0 -1.48 2.19
23 4 2.52 6.35
24 0 -1.48 2.19
25 0 -1.48 2.19
26 0 -1.48 2.19
27 0 -1.48 2.19
28 0 -1.48 2.19
29 7 5.52 30.47
 
 

Standard deviation = formula for standard deviation

The square root of: The sum of (each score - mean)2 divided by (number of scores - 1)

Remember that the number of scores is 29, because we're missing one score.

square root of

157.23/(29-1) = square root of5.62 = 2.37

Posttest

M = Mean

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

Kid # Days
Used (X)		 (x-M) (x-M)2
1
2 0 -3.55 12.6
3 10 6.45 41.6
4 4 0.45 0.203
5 0 -3.55 12.6
6 8 4.45 19.8
7 0 -3.55 12.6
8 14 10.45 109.2
9 7 3.45 11.9
10 12 8.45 71.4
11 20 16.45 270.6
12 0 -3.55 12.6
13 0 -3.55 12.6
14 5 1.45 2.1
15 0 -3.55 12.6
16 0 -3.55 12.6
17 7 3.45 11.9
18 0 -3.55 12.6
19 0 -3.55 12.6
20 0 -3.55 12.6
21 0 -3.55 12.6
22 0 -3.55 12.6
23 3 -0.55 0.303
24 0 -3.55 12.6
25 0 -3.55 12.6
26 0 -3.55 12.6
27 4 0.45 0.203
28 0 -3.55 12.6
29 5 1.45 2.1
 
 

Standard deviation = formula for standard deviation

The square root of: The sum of (each score - mean)2 divided by (number of scores - 1)

Remember that the number of scores is 29, because we're missing one score.

square root of

743.112/(29-1) = square root of26.54 = 5.15

Remember the formula for standard deviation?

formula for standard deviation

The English version is as follows:

The square root of: The sum of (each score - the mean)2 divided by (number of scores - 1)

After doing the calculations, here's what Jack came up with.

Standard Deviations for Marijuana Use

  Pretest Posttest
Girls 2.37 5.15
Boys 3.14 2.55

Means for Marijuana Use

  Pretest Posttest
Girls 1.48 3.55
Boys 2.21 1.42
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