Background/Context: Single-case experimental designs (SCEDs) play an important role in evaluating interventions in psychological, educational, and behavioral research. Unlike between-subjects designs, SCEDs involve a small number of cases whose responses to controlled experimental conditions are measured repeatedly over time. The evaluation of treatment effects in SCEDs predominantly relies on comparisons of outcomes between different phases, such as a baseline phase and an intervention phase. To effectively synthesize the growing body of high-quality SCEDs, there is a need for effect size measures that can not only be compared with the commonly used effect size metrics in between-subjects designs but are also suitable for the unique characteristics of SCEDs. At present, the only design comparable effect size for SCEDs is the between-case standardized mean difference for multiple baseline design and reversal design (BC-SMD; Hedges et al., 2012, 2013; Pustejovsky et al., 2014; Swaminathan et al., 2014). However, this measure is not suitable for count outcomes (e.g., number of words correct per minute), which are common in SCEDs. Purpose/Objective/Research Questions: The purpose of this study is to develop a design-comparable incidence rate ratio effect size (i.e., BC-IRR) for count data in SCEDs. We aim to define BC-IRR as a causal estimand within the counter-factual framework and show its equivalence to the IRR based on a randomized control trial (RCT) when certain assumptions are met. Defining and Estimating BC-IRR: Assume that the following parametric model adequately captures the data generation mechanism of SCED count data in an AB or multiple baseline design, log([lambda][subscript ij]) = [beta][subscript 0i] + [beta][subscript 1i]Phase[subscript ij] + [beta][subscript 2i]Time[subscript ij] + [beta][subscript 3i]Time'[subscript ij]Phase[subscript ij] where [lambda][subscript ij] represents the conditional expected incidence rate for case i at session j; Phase[subscript ij] is an binary variable that equals to 0 for control phase and 1 for treatment phase; Time[subscript ij] is a time variable representing the time elapsed from a reference time point. Time'[subscript ij] is another centered time variable which equals zero for the first session in the treatment phase (see Table 1 for the coding matrix). Assuming [beta][subscript 0i], [beta][subscript 1i], [beta][subscript 2i], and [beta][subscript 3i] follow a joint normal distribution with a certain mean vector and covariance matrix as follows [covariance matrix omitted], then BC-IRR [equation omitted] where B-C represents the time elapsed between the reference time point C and the outcome measurement occasion B; and B-A represents the time elapsed between the introduction of treatment and the outcome measurement occasion. The parametric outcome model used to develop BC-IRR (Equation 1) can be specified as a generalized linear mixed effect model (GLMM) using either a Poisson distribution or a negative binomial (NB) distribution for the outcome. To compute BC-IRR, the estimates of the fixed effects and variance/covariance components from the GLMM are substituted into Equation 3. The delta method can be used to approximate the standard error of BC-IRR based on the estimated standard errors of the fixed effects and variance/covariance components. Simulation Study: BC-IRR is equivalent to IRR obtained from a hypothetical randomized controlled trial (i.e., IRR[superscript RCT]) if for each case in a SCED there exists a never-treated unit who starts at the same level and evolves in parallel in the hypothetical RCT. While this assumption reflects the nature of SCED in which individuals serve as their own controls, it is a very unrealistic assumption for an RCT. Instead of assuming the existence of a never-treated replicant for each treated unit, it is more realistic to assume that there exists a group of never-treated units which has the same average starting value and the same average trend as those of the treated units in an SCED. We call this relaxed assumption "group equivalence" assumption. To demonstrate the comparability of BC-IRR and IRR[superscript RCT] under the more relaxed group equivalence assumption, a simulation study was conducted. The data were generated mimicking the data structure in Figure 1. For the treatment group, we used the NB model as in Equation 1 for data generation. We also simulated the potential outcomes for the treatment group if a control strategy was adopted based on a reduced model without intervention effects. For the control group, outcome measurements were generated using a model without intervention effects. A pseudopopulation of 8000 cases was generated, among which half was in the treatment condition and half in the control condition. Among those in the treatment group, the series length was set to be 20, with a starting point of the intervention at the session 6, 8, 12, or 14 to mimic a multiple baseline design. The population value of IRR[superscript TRUE] was calculated as the ratio of the average outcome level at a given session in the post-treatment to the average potential outcome level at the same session for the treatment group. The population value of BC-IRR was calculated based on the analytical solution as shown in Equation 3, while the population value of IRR[superscript RCT] was calculated as the ratio of the average outcome level at a given session in the treatment phase of the treatment group to that of the control group. We considered values for B-A = 0, 1 or 5. Results indicated little differences between BC-IRR and IRR[superscript TRUE], with average differences less than 0.01 for each B-A condition. Similarly, we found negligible differences between IRR[superscript RCT] and IRR[superscript TRUE], with average differences also below 0.01 for each B-A condition. Figure 2 shows the distributions of the biases of BC-IRR and IRR[superscript RCT] for each B-A condition. Conclusion: To allow effect sizes obtained from an AB or a multiple baseline across participants design to be synthesized with effect sizes obtained from between-group designs, we proposed BC-IRR, a design comparable incidence rate ratio effect size for count data in single-case experimental designs. The model used to estimate BC-IRR is GLMM, a flexible model that accommodates trend effect, dependency of observations, and overdispersed count data. BC-IRR is comparable to the marginal IRR in a potential RCT where the treated units are compared with a hypothetical control group when certain assumptions are met. First, the hypothetical control group are assumed to have the same mean starting values on the outcome and evolve in parallel as the treated units had the treated units adopted a control strategy. Second, it is assumed that the potential outcome model correctly captures the data-generating process.