**Li, J. C.-H. **(in press). Effect size measures in a two independent-samples case with non-normal and non-homogeneous data. *Behavior Research Methods. *(Supplementary materials: https://osf.io/msy3h/)

**Supplementary Materials **

The following sections include the supplemental materials for the study entitled as “Effect Size Measures in a Two Independent-Samples Case with Non-Normal and Non-Homogeneous Data”. The first section presents a Mathematica code that can be used to estimate the six effect sizes given a real-world database (named “data.csv”). The second section includes the Monte Carlo simulation code used in the study. The third section presents a URL that links to the full report of the percentage biases that were used to create Figures 1 and 2 in the study.

**1. A Mathematica Code Used to Obtain the Six ES Estimates Based on the Hypothetical Example in the Conclusion and Discussion Section**

- First, save the data as “data.csv”, where the first column contains the vale labels for the two groups (i.e., 0 and 1), and the second includes the observations for each participant.
- For example, enter the hypothetical data shown in the conclusion and discussion section of the study and save it as “data.csv”. Alternatively, download the data file in excel format (data) and save it as “data.csv”. Note that the data file should be placed to the location that can be retrieved in the Mathematica code below (i.e., line 1: data = Import[“C:/data.csv”], where C:/ means that the data is saved to the C:/ drive of your computer).

- Second, run the following Mathematica code.

code1

- Third, obtain the 6 ES estimates below.

—————————————-Output——————————————-

d = -0.135157, dr* = 0.611744, dr = 0.39274, rpb = -0.0674249, CL = 0.446244, Aw = 0.6416

——————————————————————————————

**2. The Monte Carlo Simulation Code Used in the Study**

code2

**3. The Full Values for the Percentage Biases in Figures 1 and 2.**

Table

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