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Mixed Level Design

A mixed level design is one that uses a combination of fixed and random factors. A fixed factor is one whose levels are chosen based on theoretical or practical interest, and the researcher wishes to draw conclusions about those particular conditions or levels. Examples include whether a message is one- or two-sided and whether arguments are strong or weak. A random factor is one whose levels are selected randomly from a larger population of options. The chosen levels are assumed to be representative of the population of interest, and the researcher is interested in statistical generalizations back to that population. The most common example is the participants factor in an experimental design. Participants are presumed to be randomly selected from a population of interest and results are generalized back to similar participants. In communication research, common random factors include specific messages or arguments that are selected from a larger population of options and represent examples of message or argument types. Another way of thinking about fixed versus random factors is whether the levels or conditions would be identical in a replication. If replicating a persuasion experiment, the researcher likely will retain the levels of message sidedness as one- versus two-sided and argument strength as strong versus weak but would collect data from a different sample of participants using different messages and arguments. Levels of fixed factors remain constant across studies whereas levels of random factors vary across studies. In practice, a mixed level design typically involves at least one fixed factor and one random factor that is not the participants factor. This entry identifies four types of mixed level designs, their advantages and disadvantages, and their implications for validity and analysis.

Types of Mixed Level Designs

To illustrate four types of mixed level designs, consider the following research example. The researcher is interested in whether cultural self-construal (i.e., independent vs. interdependent) influences people’s tendency to present themselves as normatively appropriate and socially sensitive. The researcher manipulates self-construal by having participants read a story that activates thoughts of either being independent from others (i.e., distinct, self-reliant) or being interdependent with others (i.e., maintaining harmony with others, saving face). Assume that this assignment to conditions is done randomly. After reading the story, participants complete a dependent measure of impression management indicating their tendency to self-present in a socially appropriate manner. In this example, self-construal is a fixed factor because the researcher is interested in the theoretical comparison between the constructs of independence and interdependence. If replicating the experiment, the same two levels of self-construal would be repeated. Consider four variations of this experiment that accommodate variability due to the particular story read by participants by (a) randomizing over it, (b) holding it constant, (c) blocking it across levels, or (d) nesting it within levels. Each of these variations is examined in the following discussion.

Design 1: Randomizing Across the Random Factor

The particular story used to manipulate self-construal comes from a population of possible stories that would do so. In this sense, story is a random factor. The researcher may sample many stories that activate either an independent or interdependent self-construal, matching the stories on length, topic, interest, and so on. Imagine that there are 40 such stories (20 independent and 20 interdependent). The researcher samples 40 participants for the experiment and assigns each participant to read one of the stories. That is, each story is read by just one participant in the study. In this example, both participants and stories are random factors, whereas self-construal is a fixed factor. The conventional analysis of variance (ANOVA) procedure assumes that all factors (other than participants) are fixed. Because the story factor is completely overlapping with the participants factor (each story is unique to one participant), the variation due to story overlaps with participant variation. Variation of scores on the dependent measure within self-construal conditions is due to participants (i.e., individual differences), story, and other random and systematic error. In this case, the researcher can average across participants (and stories) within conditions using the single-factor, between-participants ANOVA.

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