Now that you have familiarity with the new key terms of this chapter, it is time to begin using the terms in the context of the chapter material. See if you can fill-in-the-blanks in the following discussions. To get the correct answer, click on the blank.
There are times when we want to evaluate two or more independent variables in the same experiment. These design, called __________- __________ , allow us not only to study the effects of each independent variable, but also to study the interactive effect of the independent variables on the dependent measure. An __________ effect between two variables is an effect that is greater than summing the effects of the two variables. That is, a true interaction is not simply additive but, rather, represents an enhancement.
In a factorial design the independent variables are called __________. In a particular study, there might be two, three, four, or more factors being evaluated simultaneously. If we have two factors in a study and the first factor (Factor A) has four levels and the second factor (Factor B) has two levels, we would write that in notational form as a __________ factorial design. Such a design would produce 8 (4 times 2) different combinations of conditions. Similarly, a 3 X 2 X 2 design would have __________ independent variables or factors with __________ levels of the first factor, __________ levels of the second factor, and __________ levels of the third factor, and would produce a matrix containing 12 cells (3 times 2 times 2).
In a factorial design there are several different effects to be evaluated. For each effect, we need to test the statistical or __________ hypothesis. In a two-factor study, there will be null hypotheses for the individual effects of Factors A and B. These individual effects are referred to as __________- __________. There will also be a null hypothesis for the combined or __________ effect of the two factors. All of these effects are independent of one another, so that it is possible to get any combination of statistically __________ effects. If there is a statistically significant __________ and one or more statistically significant main effects, one should always begin the interpretation with the __________. Main effect should always be interpreted in light of the interaction.
As we increase the number of independent variables or factors in a study, we also increase the number of __________-__________ to test statistically. With two factors, we have __________ null hypotheses. With three factors, we will have seven null hypotheses: three __________-__________ (A, B, & C); three two-way interactions in which two independent variables interact (AB, AC, BC); and one three-way interaction in which three independent variables interact (ABC). With four independent variables, we will have four main effects (A, B, C, & D), six two-way interactions ( __________, __________, __________, __________, __________, & __________ ), three three-way interactions ( __________, __________, & __________ ), and one __________-__________ interaction (ABCD).
Information from an analysis of variance computation is usually organized in an ANOVA __________- __________. Each __________ in the summary table represents a different effect (main effect or interaction). The __________ list information such as the degrees of freedom for an effect, the __________-__________-__________ for an effect, the mean squares, and the F-ratios. Each effect will have its own F-ratio, which allows us to evaluate the statistical __________ of the effect. This same summary table structure will be used regardless of the complexity of the ANOVA.
Many variations on the basic factorial design are possible. It is possible to have a complete __________-__________ factorial in which all participants appear in one and only one cell. It is also possible to have a complete __________- __________ factorial in which the same participants appear in all cells. Finally, it is possible to have designs in which some of the factors are within-subjects factors, while other factors are between-subjects factors. This arrangement is known as a mixed design. The term __________ design is sometimes confusing because it is also used to describe another type of mixing of independent variables. In this second case, some of the variables are __________ independent variables, with participants randomly assigned to each level of the variable, while other variables are __________ independent variables in which participants are assigned to a particular level of the independent variable based on preexisting characteristics of the participants. The significance of a mixed design in this latter case is realized when we __________ the data. Having a mixed design of between- and within-subjects factors will not affect the __________ of the data but will affect the statistical procedures used to analyze the data.
Analysis of variance is a flexible statistical tool for the evaluation of data. It can handle single __________ variable studies or multiple independent variable ( __________ ) studies. Analysis of variance can take into account whether the independent variable(s) have different people at each level ( __________-__________ factor) or have the same participants at all levels ( __________- __________ factor). Analysis of variance can also be used to simultaneously evaluate more than one dependent measure (known as a(n) __________ analysis of variance or MANOVA). Another variation of the analysis of variance is analysis of __________ (ANCOVA), where the effects of a theoretically unimportant but powerful variable are removed from the dependent measure as part of the analysis.