Statistical Methods for Psychology

Section 14.4 Analysis of Variance Applied to Relaxation Therapy 467

Table 14.3 Analysis of data on migraine headaches

(a) Data

Baseline Training
Subject
Subject Week 1 Week 2 Week 3 Week 4 Week 5 Means

12122866 12.6

2 20 19 10 4 4 11.4

317155459.2

4 25 30 13 12 17 19.4

5 30 27 13 8 6 16.8

61927874 13.0

72616525 10.8

817188159.8

9 26 24 14 8 9 16.2

Week 22.333 22.000 9.333 5.778 6.778 13.244

Means

(b) Calculations

(c) Summary table

Source df SS MS F

Between subjects 8 486.71
Within subjects 36 2679.60 85
Weeks 4 2449.20 612.30
Error 32 230.40 7.20

Total 44 3166.31

*p,.05

SSerror=SStotal 2 SSsubjects 2 SSweeks=3166.31 2 486.71 2 2449.20=230.40

SSweeks=na(XW 2 X..)^2 = 93 (22.333 2 13.244)^2 1 Á 1 (6.778 2 13.244)^24 =2449.20

SSsubjects=wa(XS 2 X..)^2 = 53 (12.6 2 13.244)^2 1 Á 1 (16.2 2 13.244)^24 =486.71

SStotal=a(X 2 X..)^2 =(21 2 13.244)^2 1 Á 1 (9 2 13.244)^2 =3166.31

(^2) Because I have rounded the means to three decimal places, there is rounding error in the answers. The answers
given here have been based on more decimal places.
each of those 5 weeks. The data and the calculations are shown in Table 14.3.^2 It is impor-
tant to note that I have identified the means with a subscript naming the variable. Thus in-
stead of using the standard “dot notation” (e.g., for the Week means), I have used the
letter indicating the variable name as the subscript (e.g., the means for Weeks are denoted
and the means for Subjects are denoted ). As usual, the grand mean is denoted ,
and Xrepresents the individual observations.
Look first at the data in Table 14.3a. Notice that there is a great deal of variability, but much
of that variability comes from the fact that some people have more and/or longer-duration
headaches than do others, which really has very little to do with the intervention program. As I
have said, what we are able to do with a repeated-measures design but were not able to do with
between-subjects designs is to remove this variability from , producing a smaller
than we would otherwise have.
SSerror MSerror

XW XS X..

Xi.