Strategies for Efficient Experimental Design in Studies Probing 2-1-1 Mediation

Robustness of Statistical Power in Group-Randomized Studies of Mediation Under an Optimal Sampling Framework

“…Relative power did vary across models and tests when the path coefficients were misspecified with the exception of the MC interval test for which power demonstrated consistent robustness. The MC interval test result can be traced back to stable n opt 1 values when using the test even with different a and b path coefficient values (Cox & Kelcey, 2019, Kelcey & Shen, 2019. Conversely, power under the optimal sampling framework for the joint and Sobel test varied in robustness to misspecified a and b path coefficient values across models reflecting the conditions in which these parameters influenced n opt 1 values for that specific test.…”

“…The general form of the mediation tests and subsequent power formulations presented for the 2-2-1 design are similar for 2-1-1 design. The error variances associated with each path and the error variance of the mediated effects do change substantially but formulations utilizing path coefficients, budget, and sampling cost are available in the literature along with related optimal sample allocation formulations (see ESM 1; Kelcey, Dong, Spybrook, & Cox, 2017;Kelcey & Shen, 2019).…”

“…Similar processes are used to determine n opt 1 under the joint test for 2-1-1 and 2-2-1 designs. Using the cost function formulations for n 1 and the error variance path formulations, we directly maximize the power function (see ESM 1; Kelcey & Shen, 2019). The…”

“…Unlike 2-2-1 designs, there is no simple closed form solution for under the Sobel test. We can, however, determine for the Sobel test numerically (see ; Kelcey & Shen, 2019). Similar processes are used to determine under the joint test for 2-1-1 and 2-2-1 designs.…”

“…Similar processes are used to determine under the joint test for 2-1-1 and 2-2-1 designs. Using the cost function formulations for n 1 and the error variance path formulations, we directly maximize the power function (see ; Kelcey & Shen, 2019). The values from the Sobel and joint test formulations approximate those of the MC interval test for 2-1-1 designs but we again use a linear search algorithm to identify values for the MC interval test to avoid possible confounding effects.…”