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# When Neutral is Harmful

Emotion researchers often examine the divergent effects of two or more emotions on behavior. Such research designs involve inducing emotion states in groups of participants and comparing the average response on a behavioral measure across groups. For example, one might predict that experiencing a pleasant mood increases the positivity of participants’ judgments of a hypothetical individual. A researcher here could induce positive mood in 30 participants and negative mood in 30 participants before comparing the positivity of each group’s mean judgment.

An experimental design such as this one would become far more theoretically rich, however, with the addition of a neutral emotion condition in which participants were not induced to feel any particular mood. This would allow a researcher to ask whether or not any observed difference between the positive mood condition and the negative mood condition is driven by a) the positive mood, b) the negative mood, or c) both. In the first case, we would expect the positive mood group’s ratings to be very positive, whereas the negative and neutral mood group’s ratings would be more negative and roughly equal. In the second case, we would expect the negative mood group’s ratings to be very negative, whereas the positive and neutral mood group’s ratings would be more positive and roughly equal. In the final case, we would expect the positive mood group’s ratings to be more positive than the neutral group’s ratings, which in turn would be more positive than the negative group’s ratings.

The addition of a neutral emotion condition, while adding an important theoretical layer to the study, would introduce an unwanted statistical impediment in the context of an analysis of variance. Let’s assume case “c” would be the result, indicating that both positive and negative mood are theoretically important, and let’s further assume that the mean positivity of each group’s judgments for this sample was 8, 5, and 2 (on a 10-point scale) for positive, neutral, and negative, respectively. An ANOVA tests the ratio of between-groups variance (i.e., meaningful group differences; denoted B for this example) to within-groups variance (i.e., error; denoted W), with larger numbers yielding increasingly significant and meaningful results. B is calculated by summing the difference between grand mean (in this case (8 + 5 + 2) / 3 = 5) of all participants and the mean of a given group for all groups. We also know that, under the traditional homogeneity of variance assumption, each experimental group will have equal within-groups variances; for the purposes of this example, let’s assume that each group’s W is equal to 1.

The equations for the ANOVA components show us that, if positive mood and negative mood were the only two conditions employed in the experiment, the ratio of B/W would equal (3^2 + 3^2)/2 = 9. Now consider the three group design “c” in which the mean positivity of judgments in the positive and negative mood groups *are the exact same* as in the two-group condition. Our ANOVA would yield a result of (3^2 + 3^2 + 0^2)/3 = 6. Our test just got weaker—and possibly dipped below significance—even though the effect of positive and negative mood *did not get weaker*! How did this happen? We introduced an additional source of within-groups variance without introducing an additional source of between-groups variance. The neutral mood condition is expected to fall at exactly the grand mean of the entire sample, or half way between the positive and negative mood conditions, because feeling no emotion should not cause systematic shifts in people’s judgments. Thus, for the neutral group, B = 0 and W = 1. The researcher, simply by adding a condition of great theoretical import, has statistically shot himself in the ear with a loaded gun by reducing the chances that he will conduct a statistically significant test of his hypothesis.

How should emotion researchers balance theoretical richness with the necessity of arriving at statistically meaningful conclusions? One potentially fruitful solution would be to conduct planned contrasts between only the groups of interest—here the positive and negative mood groups—as such tests can be employed without first producing a significant omnibus ANOVA. If planned contrasts yielded significant results, this would allow the researcher to conclude that positive mood and negative mood indeed have divergent effects on judgments of others. While this analytic strategy still bypasses the question of whether positive or negative emotion, or a combination of the two, are driving the effect, it allows the researcher to reach an important conclusion from a data set that may look spuriously messy due to the inclusion of the neutral condition. Given that emotion researchers include neutral conditions for the purpose of arriving at the most complete and theoretically meaningful conclusions possible, they should not be penalized for the unwanted statistical byproducts.

*Note*: Inspired by a late night chat with one Conor M. Steckler in Gastown, Vancouver, BC.