Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

Overview: Three Basic Data Structures 703
■ Category 2: A Single Group of Participants with Two Variables
Measured for Each Participant
These research studies are specifically intended to examine relationships between variables.
Note that different variables are being measured, so each participant has two or more
scores, each representing a different variable. Typically, there is no attempt to manipulate
or control the variables; they are simply observed and recorded as they exist naturally.
Although several variables may be measured, researchers usually select pairs of variables
to evaluate specific relationships. Therefore, we present examples showing pairs of
variables and focus on statistics that evaluate relationships between two variables. Table 2
presents four examples of data in this category. Once again, the four data sets differ in
terms of the scales of measurement that are used. The first set of data (a) shows numerical
scores for each set of measurements. For the second set (b) we have ranked the scores from
the first set and show the resulting ranks. The third data set (c) shows numerical scores for
one variable and nominal scores for the second variable. In the fourth set (d), both scores
are measured on a nominal scale of measurement. The appropriate statistical analyses for
these data are discussed in Section II.
TABLE 2
Examples of data with
two scores for each
participant for one group
of participants.
(a) SAT Score (X) and College
Freshman GPA (Y)
(b) Ranks for the Scores
in Set (a)
X Y X Y
620 3.90 7 8
540 3.12 3 2
590 3.45 6 5
480 2.75 1 1
510 3.20 2 3
660 3.85 8 7
570 3.50 5 6
560 3.24 4 4
(c) Age (X ) and Wrist Watch
Preference (Y )
(d) Gender (X ) and Academic
Major (Y )
X Y X Y
27 digital M Sciences
43 analogue M Humanities
19 digital F Arts
34 digital M Professions
37 digital F Professions
49 analogue F Humanities
22 digital F Arts
65 analogue M Sciences
46 digital F Humanities
■ Category 3: Two or More Groups of Scores with Each
Score a Measurement of the Same Variable
A second method for examining relationships between variables is to use the categories of
one variable to define different groups and then measure a second variable to obtain a set