510 The Professional Counselor | Volume 10, Issue 4 The results of the negative binomial regression indicated faculty at R1 programs published at a rate of 1.32 times that of faculty at R2 programs. Faculty at R1 programs published 3.65 times more than faculty at D/PU programs and 4.85 times more than faculty at M1 programs. Figure 1 provides a visual density plot of the posterior summaries of the group deviations from the intercept. An interpretation of the visual analysis indicated publication rates among faculty arranged into three groupings based on the observed data in the estimated model: R1 and R2 programs, D/PU and M1 programs, and the remainder of the program types. Figure 1 Posterior Density Plot Note. Posterior density plot for differences from the grand mean. To answer the second research question, a series of Bayesian hypothesis testing was conducted. Hypotheses tests were only conducted for doctoral- and master’s-level programs because Newhart et al. (2020) only provided information regarding doctoral- and master’s-level programs. The observed data collected yielded higher mean and standard deviations for each Carnegie classification compared to Newhart et al. Therefore, instead of comparing the differences among means, it appeared more appropriate to assess the differences between self-reported and observed data ratios regarding program Carnegie classification publication productivity. Newhart et al.’s self-reported data indicated that in relation to R1 programs, faculty at R2 programs published .77 times fewer articles, faculty at D/PU programs published .52 times fewer articles, and faculty at master’s-level programs published .31 times fewer articles (see Table 2). These ratios were converted using the logarithmic form to be used as the prior means. After determining the differences of the observed data from the previous question, the prior means were used to compare the plausibility of Newhart et al.’s data with the observed data.
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