Identify the independent variable, two intervening variables, and a moderating variable related to the effect of a new online learning platform on student learning outcomes.

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Topic: The effect of a new online learning platform on student learning outcomes in a university course.

a) Identify the Independent Variable
The Independent Variable (IV) is the factor that is manipulated or changed by the researcher to observe its effect.
In this topic, the independent variable is the:

• Type of learning platform (e.g., traditional Learning Management System vs. a new, innovative online learning platform).

b) Identify TWO Intervening Variables, a Moderating Variable, and Integrate them

• Intervening Variables (Mediating Variables): These variables explain the mechanism or process through which the independent variable influences the dependent variable.

  1. Student engagement with the platform: The new platform might lead to higher student engagement (e.g., more active participation, time spent on tasks), which in turn improves learning outcomes.
  2. Student self-regulation skills: The new platform might foster or require better self-regulation (e.g., planning, monitoring, evaluating one's own learning), which then mediates the effect on learning outcomes.

• Moderating Variable: This variable influences the strength or direction of the relationship between the independent variable and the dependent variable.

  1. Prior experience with online learning: The effect of the new learning platform on student learning outcomes might differ based on whether students have high or low prior experience with online learning environments. For instance, the new platform might be more beneficial for students with less prior experience, or conversely, more experienced students might adapt and benefit more quickly.

• Integration: The new online learning platform (IV) is hypothesized to improve student learning outcomes (DV). This effect is mediated by increased student engagement and enhanced self-regulation skills. Furthermore, the strength of this relationship (IV $\to$ DV) is moderated by prior experience with online learning. This means the platform's effectiveness might be stronger or weaker depending on a student's previous exposure to online learning.

c) Prepare the Factorial Matrix and Indicate the Minimum Sample Size for the Topic

• Factorial Matrix: A factorial matrix illustrates all possible combinations of the independent variable and the moderating variable (when the moderator is treated as a factor in the design). For this example, we will consider two levels for the Independent Variable (Traditional Platform vs. New Platform) and two levels for the Moderating Variable (Low Prior Experience vs. High Prior Experience). This results in a 2x2 factorial design.

  $$\begin{array}{|c|c|c|} \hline \textbf{Independent Variable} & \textbf{Moderating Variable: Low Prior Experience} & \textbf{Moderating Variable: High Prior Experience} \\ \hline \textbf{Traditional Platform} & \text{Group 1: Traditional, Low Experience} & \text{Group 2: Traditional, High Experience} \\ \hline \textbf{New Platform} & \text{Group 3: New Platform, Low Experience} & \text{Group 4: New Platform, High Experience} \\ \hline \end{array}$$

  Each cell in this matrix represents a unique experimental condition, and participants would be assigned to one of these four groups.

• Minimum Sample Size: Determining the minimum sample size requires a power analysis, which considers the desired statistical power (typically 0.80), the significance level ($\alpha = 0.05$), and the expected effect size (small, medium, or large). For a 2x2 factorial design, a common guideline in social sciences to detect moderate effects and interactions is to have at least 15-20 participants per cell. Given 4 cells in our factorial matrix:

  • Minimum sample size = (Number of cells) $\times$ (Participants per cell)
  • Minimum sample size = $4 \times 15 = 60$ participants
  • Recommended sample size for better power = $4 \times 20 = 80$ participants

  Therefore, a minimum sample size of 60 to 80 participants would be a reasonable starting point for this experimental design, ensuring at least 15-20 participants in each of the four experimental conditions. However, a precise sample size would be determined through a formal power analysis based on specific effect size expectations.