Type I errors galore…

Legatti-Maddox (2019) explored the moderating effect of two leadership styles, transformational and transactional, on the relationship between four types of humor and Organizational Citizenship Behavior. The sample for this study were 42 MBA students.

First, the sample size (N = 42) concerned me since it seemed to be a bit small to find a practical (moderate) effect (f2 = 0.15). Using the pwr.f2.test() function from R’s pwr package (Champerly, 2020), it appears a sample of at least 73 would be required with three independent variables and a minimum power of .80 (see below).

          u = 3
          v = 72.70583
         f2 = 0.15
  sig.level = 0.05
      power = 0.8

So, it appears the study was underpowered by design. With underpowered studies there is a low probability of finding true effects and any effects could be false. Let’s move forward…

Second, when performing a moderation analysis, one has to enter both independent variables along with the interaction (see below)

y = X1 + X2 + X1*X2

If the moderating variable (X1*X2) is significant, then the interaction is explored and the independent variables generally lose their value from a research perspective. However, since no independent or interactive variable’s p-values were reported, no moderation evidence was provided by the emerging scholar. Instead. p-values of unmoderated and moderated models were compared, and an increase in the F-statistic reported as evidence of a moderating effect. That’s a flawed approach and, when the null hypothesis is rejected based on that approach, a Type I error ensues.

In a prior post, I discuss the uses of P-P Plots vs. Q-Q Plots and how it’s a default option in regression under SPSS. This emerging scholar used this plot (from SPSS) and stated that the homoscedasticity assumption was met.

Figure 1. Normal P-P Plot of Regression Standardized Residual (p. 70)

However, there is no reference to the independent variables or which model. I wonder what would have happened if her faculty advisor challenged her and said the residuals are hetroskedastic?

Finally, a quick look at a summary table in the study (Table 19 below)

A learned faculty should have counseled this student that the p-values would need to be adjusted for potential family-wise errors as the student’s premise is that all nine models are true. The widely-cited Bonferroni correction would result in a new p-value of 0.0055 (.05/9). If applied, only Model 9 may have met the criteria. However the focus of the study was not on whether a model could be constructed, but whether the interaction of humor and leadership explained the relationship better than the direct effects. Thus, more Type I errors.

The interaction of humor and leadership may influence OCB, but this study provides no evidence. The results of this study should be ignored.

Student Note: The way to approach this would be through some Structured Equation Model (SEM) that controls for Type I errors.

Reference:

Champely, S. (2020, March 16). pwr: Basic functions of power analysis. https://cran.r-project.org/web/packages/pwr/pwr.pdf

Legatti-Maddox, A. C. (2019). Humor style in the workplace as it relates to leadership style and organizational citizenship behavior (Doctoral dissertation). ProQuest Dissertations & Theses Global: The Humanities and Social Sciences Collection. (22622521)

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