Thursday, May 2, 2024

14 2: Design of experiments via factorial designs Engineering LibreTexts

example of a factorial design

This could be because being in a happy or sad mood has no effect on memories for childhood events. But it could also be that the music was ineffective at putting participants in happy or sad moods. A manipulation check, in this case, a measure of participants’ moods, would help resolve this uncertainty.

1 - The Simplest Case

We've used Minitab to create the factorial design and added the data from the experiment into the Minitab worksheet. First, we will produce a normal probability plot of the effects for this data with all terms included in a full model. We have first discussed factorial designs with replications, then factorial designs with one replication, now factorial designs with one observation per cell and no replications, which will lead us eventually to fractional factorial designs. This is where we are headed, a steady progression to designs with more and more factors, but fewer observations and less direct replication.

Implementing Clinical Research Using Factorial Designs: A Primer

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But he or she might choose to treat time of day as a between-subjects factor by testing each participant either during the day or during the night (perhaps because this only requires them to come in for testing once). Just as including multiple levels of a single independent variable allows one to answer more sophisticated research questions, so too does including multiple independent variables in the same experiment. For example, instead of conducting one study on the effect of disgust on moral judgment and another on the effect of private body consciousness on moral judgment, Schnall and colleagues were able to conduct one study that addressed both questions. But including multiple independent variables also allows the researcher to answer questions about whether the effect of one independent variable depends on the level of another.

1: Introduction to Factorial Designs

We use "(1)" to denote that both factors are at the low level, "a" for when A is at its high level and B is at its low level, "b" for when B is at its high level and A is at its low level, and "ab" when both A and B factors are at their high level. Importantly, the effect of the gas variable on driving depends on the levels of having a key. Or, to state it in reverse, the effect of the key variable on driving depends on the levesl of the gas variable.

If it showed that you had successfully manipulated participants’ moods, then it would appear that there is indeed no effect of mood on memory for childhood events. But if it showed that you did not successfully manipulate participants’ moods, then it would appear that you need a more effective manipulation to answer your research question. For instance, RCTs need not have a true placebo or control condition. Thus, two different active treatments might be contrasted with one another in a two-group design, such as a comparison of two different counseling approaches (e.g., skill training vs. supportive counseling), each paired with the same medication. Neither one of these conditions would be a control condition in a strict sense, since each delivers a different form of active treatment. In addition, an RCT might have a control condition, but this might be used in comparisons with many active treatment conditions.

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Thus, it is important to recognize that such effects do not really constitute experimental artifacts, but rather presage the costs of complex treatments as used in real world application, presumably something worth knowing. In an RCT an “active” treatment arm or condition is statistically contrasted with a “control” treatment arm or condition (Friedman, Furberg, & Demets, 2010). The two conditions should be identical except that the control condition lacks one or more ICs or features that are provided to the active condition. The random assignment of participants to the treatment arms means that the two groups of assigned participants should differ systematically only with regard to exposure to those features that are intentionally withheld from the controls.

Understanding Variable Effects in Factorial Designs

These independent variables are good examples of variables that are truly independent from one another. For example, shoes with a 1 inch sole will always add 1 inch to a person’s height. This will be true no matter whether they wear a hat or not, and no matter how tall the hat is. In other words, the effect of wearing a shoe does not depend on wearing a hat.

3.10. Interpreting main effects and interactions¶

They measured their participants’ SES and had them play the “dictator game.” They told participants that each would be paired with another participant in a different room. (In reality, there was no other participant.) Then they gave each participant 10 points (which could later be converted to money) to split with the “partner” in whatever way he or she decided. Because the participants were the “dictators,” they could even keep all 10 points for themselves if they wanted to.

Contrasts, main effects and interactions

example of a factorial design

Next, look at the effect of being tired only for the “5 hour” condition. We see the red bar (tired) is 3 units lower than the green bar (not tired). So, there is an effect of 3 units for being tired in the 5 hour condition. Clearly, the size of the effect for being tired depends on the levels of the time since last meal variable. Main effects occur when the levels of an independent variable cause change in the measurement or dependent variable. There is one possible main effect for each independent variable in the design.

The following table is obtained for a 2-level, 4 factor, full factorial design. None of the levels were specified as they appear as -1 and 1 for low and high levels, respectively. The following Yates algorithm table using the data from second two graphs of the main effects section was constructed. Besides the first row in the table, the main total effect value was 10 for factor A and 20 for factor B.

Manipulation checks are usually done at the end of the procedure to be sure that the effect of the manipulation lasted throughout the entire procedure and to avoid calling unnecessary attention to the manipulation. Manipulation checks become especially important when the manipulation of the independent variable turns out to have no effect on the dependent variable. Imagine, for example, that you exposed participants to happy or sad movie music—intending to put them in happy or sad moods—but you found that this had no effect on the number of happy or sad childhood events they recalled.

If they were high in private body consciousness, then those in the messy room made harsher judgments. If they were low in private body consciousness, then whether the room was clean or messy did not matter. Often a researcher wants to know how an independent variable affects several distinct dependent variables.

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