Multi-to-Uni.txt

                       Repeated Measures Designs:
     Converting a Multivariate Data Setup to a Univariate Data Setup
 
     Bob Wendling in Leisure System Studies collected data designed to
determine whether persons prefer interpretative messages (explanatory
text accompanying a display of some interesting piece of natural history)
with many personal words (like 'you'), or no personal words.  For each of
several such displays each subject read a personal interpretative message,
a nonpersonal interpretative message, and a blank message (no text accompanying
the display), and then ordered the three in terms of preference (1 = most
preferred, 2 = intermediate, 3 = least preferred).  Type of message is a
three-level repeated measures variable.  Preference ranks were summed across
several objects for each subject and are in the data file "WENDLING DATA."  In
cols 1-2 are subject id's (0 to 36), in cols 3-4 are preference sums for the
nonpersonal messages, in cols 5-6 for the blank messages, and in cols 7-8 for
the personal messages.  The higher the score the lower the preference.
 
     "WENDLING SAS" (appended)reads this data file, obtains univariate stats on the
preference scores, and does both multivariate and univariate repeated
measures analyses of variance.  Inspection of the output from PROC UNIVARIATE
reveals problems with skewness that cannot be easily resolved with data
transformations (positive skewness in one group, negative in another), so I
decided to use a nonparametric analysis, the FRIEDMAN test.  I like to use
MINITAB for such an analysis, but Minitab wants the data to be in a univariate
setup for a Friedman test.  The setup we have in the wendling data file is
a multivariate setup, all of each subject's scores (for all three conditions)
being on a single line.  In the second part of the program I use a DO OVER
ARRAY to transform the multivariate data setup to a univariate setup.  PROC
PRINT is used just to print the univariate setup data so you can see what
it looks like in that form.  The last part of the program PUTs the univariate
setup data into a file (that goes to the reader) that can be read into
Minitab to do the Friedman test.
 
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     We collected data designed to determine whether persons prefer
interpretative messages (explanatory text accompanying a display of some
interesting piece of natural history) with many personal words (like 'you'), or
no personal words.  For each of several such displays each subject read a
personal interpretative message, a nonpersonal interpretative message, and a
blank message (no text accompanying the display), and then ordered the three in
terms of preference (1 = most preferred, 2 = intermediate, 3 = least preferred).
Type of message is a three-level repeated measures variable.  Preference ranks
were summed across several objects for each subject.  The higher the score the
lower the preference.
 
     Since the data were not normally distributed, we decided to use
a nonparametric analysis of variance, the Friedman test.  The Friedman test
indicated a significant effect of type of interpretative message, H(2, n = 37)
= 14.52, p < .001.  Wilcoxon's signed-ranks test was used to compare each mean
with each other mean (see the means in Table 1).  Nonpersonal messages were
preferred over personal messages, T(n = 34) = 136.5, z = 2.74, p = .006 and
over blank messages, T(n = 36) = 133.5, z = 3.13, p = .002.  Personal messages
were preferred over blank messages, T(n = 34) = 429, z = 2.26, p = .024.
 
                               Table 1
 
       Type of Message     Median    Interquartile Range
      ---------------------------------------------------
       Nonpersonal            9            3.5
       Personal              11            4.0
       Blank                 15            7.0

============================ The SAS Program ==================================
$job sas                                                                        
$mdisk 192 karl pswuensc                                                        
options formdlim='-' ls=78;                                                     
data bob; infile 'wendling data *'; input id 1-2 (y1-y3) (2.0);                 
proc univariate; var y1-y3; proc glm; model y1-y3 =  / nouni;                   
repeated condtn 3 / printe;                                                     
data bob2; set bob;                                                             
array ys (X) y1-y3; do over ys; y=ys; output; end; drop y1-y3; proc print;      
data bob3; set bob2; file 'wendl2 data a'; put id x y;                          

============================= The Data File ====================================

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01091610
02170613
03071811
04130617
05081810
06091512
07081711
08061812
09160614
10091512
11101808
12091216
13111510
14091809
15111807
16110916
17071811
18091512
19130617
20180711
21061515
22061515
23081810
24091809
25081414
26131310
27061812
28081810
29111015
30151011
31101808
32081810
33081612
34121014
35121311
36071811