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Educational Effects in Mathematics: Conditional Average Treatment Effect depending on the Number of Treatments

Tomoko Nagai, Takayuki Okuda, Tomoya Nakamura, Yuichiro Sato, Yusuke Sato, Kensaku Kinjo, Kengo Kawamura, Shin Kikuta, Naoto Kumano-go

Abstract

This study examines the educational effect of the Academic Support Center at Kogakuin University. Following the initial assessment, it was suggested that group bias had led to an underestimation of the Center's true impact. To address this issue, the authors applied the theory of causal inference. By using T-learner, the conditional average treatment effect (CATE) of the Center's face-to-face (F2F) personal assistance program was evaluated. Extending T-learner, the authors produced a new CATE function that depends on the number of treatments (F2F sessions) and used the estimated function to predict the CATE performance of F2F assistance.

Educational Effects in Mathematics: Conditional Average Treatment Effect depending on the Number of Treatments

Abstract

This study examines the educational effect of the Academic Support Center at Kogakuin University. Following the initial assessment, it was suggested that group bias had led to an underestimation of the Center's true impact. To address this issue, the authors applied the theory of causal inference. By using T-learner, the conditional average treatment effect (CATE) of the Center's face-to-face (F2F) personal assistance program was evaluated. Extending T-learner, the authors produced a new CATE function that depends on the number of treatments (F2F sessions) and used the estimated function to predict the CATE performance of F2F assistance.

Paper Structure

This paper contains 14 sections, 6 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Causal Inference Setup
  3. Results (Input Variable ${\bf X}, {\bf x} \in \mathbb{ R}^1$)
  4. Estimation and Results $({\bf X}, {\bf x} \in \mathbb{R}^2)$
  5. Conclusion
  6. Basic Data
  7. Reason for using Causal Inference
  8. Related work
  9. Decision Tree
  10. T-learner
  11. T-learner with ${\bf X}, {\bf x} \in \mathbb{R}^1$
  12. T-learner with ${\bf X}, {\bf x} \in \mathbb{R}^2$
  13. Discussion of the Effect of the number of F2F sessions
  14. 3D surface plot of $\varphi(x_1, x_2)$

Figures (7)

  • Figure 1: Estimated deviation values vs. proficiency test deviation value $X_1=x_1$.
  • Figure 2: CATE estimator $\varphi (x_1,x_2 )$ vs. $x_2$, the number of F2F.
  • Figure 3: Decision tree for 1Q Differentiation regular examination. Each node lists, from top to bottom, the splitting criterion, the number of students, and the average deviation. The terminal nodes do not have a splitting criterion.
  • Figure 4: T-learner with $X_1$.
  • Figure 5: T-learner with $X_1$ and $X_2$.
  • ...and 2 more figures