Many research questions focus on whether there is a significant difference between two or more groups or conditions. When a group comparison or difference question is asked, the independent variable and design can be classified as between groups or within subjects. Understanding this distinction is one essential aspect of determining the proper statistical analysis for this type of question.
Labeling difference question designs. It is helpful to have a brief descriptive label that identifies the design for other researchers and also guides us toward the proper statistics to use. We do not have comparable design classifications for the descriptive or associational research questions, so this section only applies to difference questions. Designs are usually labeled in terms of (a) the overall type of design (between groups or within subjects), (b) the number of independent variables, and (c) the number of levels within each independent variable.
Between-groups designs. These are designs where each participant in the study is in one and only one condition or group. For example, in a study investigating the “effects” of fathers’ education on math achievement, there may be three groups (or levels or values) of the independent variable, father’s education. These levels are: (a) high school or less, (b) some college, and (c) BS or more. In a between-groups design, each participant is in only one of the three conditions or levels. If the investigator wished to have 20 participants in each group, then 60 participants would be needed to carry out the research.
Within-subjects or repeated-measures designs. These designs are conceptually the opposite of between-groups designs. In within-subjects (sometimes called dependent) designs, each of the conditions or levels of the independent variable is somehow connected to each of the other conditions or levels of the independent variable. Usually, this is because each participant in the study receives or experiences all of the conditions or is assessed on the dependent variable at each of the times at which these assessments occur; however, these designs also include examples where the participants are matched by the experimenter or in some natural way (e.g., twins, husband and wife, or mother and child). In that case, each type of person (e.g., husband vs. wife or child with developmental disability vs. mental-age matched comparison child) is one level of the independent variable. When each participant is assessed on the same measure more than once, these designs are also referred to as repeated-measures designs. Repeated measures designs are common in longitudinal research and intervention research. Comparing performance on the same dependent variable assessed before and after intervention (pretest and posttest) is a common example of a repeated-measures design. We might call the independent variable in such a study “time of measurement” or “change over time.” In the HSB dataset, one of the variables is repeated (visualization score with two levels, visualization and visualization retest) and one is within subjects (education, each student has both a mother’s education and father’s education). We will use a paired or matched statistic to see if mother’s education is on the average higher or lower than father’s education.
Single-factor designs. If the design has only one independent variable (either a between-groups design or a within-subjects design), then it should be described as a basic or single-factor or oneway design. Factor and way are other names for group difference independent variables. Note that the number of factors or “ways” refers to the number of independent variables not the number of levels of an independent variable. For example, a between-groups design with one independent variable that has four levels is a single-factor or “one-way” between-groups design with four levels. If the design was a within-subjects design with four levels, then it would be described as a single-factor repeated-measures design with four levels (e.g., the same test being given four times).
Between-groups factorial designs. When there is more than one group difference independent variable, and each level of each factor (independent variable) is possible in combination with each level, the design is called factorial. For example, a factorial design could have two independent variables (i.e., factors) gender and ethnicity, allowing for male and female members of each ethnic group. In these cases, the number of levels of each factor (independent variable) becomes important in the description of the design. For example, if gender had two levels (male and female) and ethnicity had three levels (Euro-American, African American, and Latino- American), then this design is a 2 x 3 between-groups factorial design. So the number of numbers is the number of factors or ways, and the numbers themselves refer to the number of levels of each of those factors. This design could also be called a two-way or two-factor design because there are two independent variables.
Mixed factorial designs. If the design has a between-groups variable and a within-subjects independent variable, it is called a mixed design. For example, let’s say that the two independent variables are gender (a between-groups variable) and time of measurement (with pretest and posttest as the two within-subjects levels); this is a 2 x 2 mixed factorial design with repeated measures on the second factor. The mixed design is common in experimental studies with a pretest and posttest, but the analysis can be complex.
Remember that when describing a design, each independent variable is described using one number, which is the number of levels for that variable. Thus, a design description with two numbers (e.g., 3 x 4) has two independent variables or factors, which have three and four levels. The dependent variable is not part of the design description, so it was not considered in this section.
Source: Morgan George A, Leech Nancy L., Gloeckner Gene W., Barrett Karen C.
(2012), IBM SPSS for Introductory Statistics: Use and Interpretation, Routledge; 5th edition; download Datasets and Materials.
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