“ Y Y ” ”
VARIABLE “X”
VARIABLE “X”
X
X11 XX22
Y
Y11 OO11 OO2 2
Y
Y22 OO33 OO44
Using our feedback example to illustrate this arrangement, we would Using our feedback example to illustrate this arrangement, we would expect a sample of students to be randomly assigned to two groups, one expect a sample of students to be randomly assigned to two groups, one receiving feedback and the second receiving no feedback (or conventional receiving feedback and the second receiving no feedback (or conventional feedback.)
feedback.) Perhaps the researcher feels that Perhaps the researcher feels that boys and girls may boys and girls may respondrespond differently to feedback, so gender
differently to feedback, so gender is used as is used as a control variable. a control variable. TheThe Y Y variablevariable then represents student’s gender, and the
then represents student’s gender, and the X X variable represents the feedbackvariable represents the feedback group, as shown in Table 5-2.
group, as shown in Table 5-2.
TABLE 5-2
TABLE 5-2 Factorial Arrangement of Feedback Group and Gender Factorial Arrangement of Feedback Group and Gender
FEEDBACK GROUP FEEDBACK GROUP
F
Feeeeddbbaacckk NNo o FFeeeeddbbaacckk
G G E E N N D D E E R R
Male
Male OO11 OO2 2
Female
Female OO33 OO44
This arrangement allows the comparison of those in the experimental This arrangement allows the comparison of those in the experimental group (feedback) with those in the control group (no feedback) and the
group (feedback) with those in the control group (no feedback) and the comparison of males with females.
comparison of males with females. In addition, it also In addition, it also permits analysis of anypermits analysis of any possible interaction between the two variable (group and gender), that is, whether possible interaction between the two variable (group and gender), that is, whether or not feedback is more
or not feedback is more or less effective for boys than for girls. or less effective for boys than for girls. A variation on thisA variation on this factorial arrangement is shown in the following:
factorial arrangement is shown in the following:
O
O11Y Y 11 àà X X 11 àà OO2 2
O
O33Y Y 11 ààX X 2 2 àà OO44
R R
O
O5 5 Y Y 2 2 ààX X 11 àà OO6 6
O
O7 7 Y Y 2 2 ààX X 2 2 àà OO8 8
This arrangement is basically a pretest-posttest control group design (discussed This arrangement is basically a pretest-posttest control group design (discussed in the preceding section) with the addition of a second independent (or control) in the preceding section) with the addition of a second independent (or control) variable in the same way as the factorial arrangement described earlier.
variable in the same way as the factorial arrangement described earlier.
Using the feedback example, this arrangement shows how the Using the feedback example, this arrangement shows how the pretest-posttest control group design, described earlier, can be expanded to include the posttest control group design, described earlier, can be expanded to include the additional variable, gender, as shown in Table 5-3.
additional variable, gender, as shown in Table 5-3.
TABLE 5-3
TABLE 5-3 Factorial Arrangement of Feedback Group and Gender Factorial Arrangement of Feedback Group and Gender with Pretest and Posttest Observations
The factorial arrangement described in this section has two independent The factorial arrangement described in this section has two independent or control variables.
or control variables. This arrangement, when depicted in This arrangement, when depicted in a table, results in a table, results in a 2 a 2 xx 2 matrix.
2 matrix. The number of The number of integers indicates the number of integers indicates the number of independent or controlindependent or control variables, and the value of each integer indicates the number of groups there are variables, and the value of each integer indicates the number of groups there are for that variable.
for that variable. For example, if there For example, if there had been had been three feedback groups (i.e., nothree feedback groups (i.e., no feedback, moderate feedback, extensive feedback), with gender as a control feedback, moderate feedback, extensive feedback), with gender as a control variable, the arrangement would result in a 3 x
variable, the arrangement would result in a 3 x 2 matrix. 2 matrix. There are two integersThere are two integers (3 and
(3 and 2), so there 2), so there are two independent are two independent or control variables. or control variables. The “3” indicatesThe “3” indicates that there are three groups of one variable (no feedback, moderate feedback, that there are three groups of one variable (no feedback, moderate feedback, extensive feedback), and the “2” indicates that there are two groups of the other extensive feedback), and the “2” indicates that there are two groups of the other variable (male and female).
variable (male and female).
Factorial arrangements can be expanded to include additional Factorial arrangements can be expanded to include additional independent and control variables.
independent and control variables. If, for example, we If, for example, we designed this study so designed this study so thatthat data were collected at grades 2, 5, 8, and 11, grade level would be a new
data were collected at grades 2, 5, 8, and 11, grade level would be a new variable and the arrangement would result in a
variable and the arrangement would result in a 3 x 2 3 x 2 x 4 matrix. x 4 matrix. There are nowThere are now three integers (3, 2, and 4), indicating three independent or control variables three integers (3, 2, and 4), indicating three independent or control variables (feedback group, gender,
(feedback group, gender, grade level). grade level). The “3” The “3” again indicates the again indicates the threethree
feedback groups, the “2” again indicates the two genders, and the “4” indicates feedback groups, the “2” again indicates the two genders, and the “4” indicates the four different grades.
the four different grades.