Solomon Experimental Design Analysis

This repository contains the implementation and analysis of a study based on the Solomon experimental design. The study investigates the effect of a treatment on post-test scores while accounting for potential pre-test effects.

Overview

The Solomon experimental design is a robust method for testing the effects of a treatment while controlling for the influence of a pre-test. This analysis uses simulated data to compare four groups:

• Group 1: Pre-test + Treatment
• Group 2: Treatment Only
• Group 3: Pre-test + Control
• Group 4: Control Only

The main goals of this study are:

1. To determine whether the treatment has a significant effect on post-test scores.
2. To examine the influence of the pre-test on the observed outcomes.
3. To verify group differences using ANOVA and post-hoc analysis.

Project Structure

• solomon_experiment.py: Main Python script containing all the steps for data simulation, analysis, and visualization.
• results/: Directory containing plots generated during the analysis, including boxplots, mean comparisons, and Tukey HSD results.
• README.md: Project documentation (this file).

Analysis Steps

1. Data Simulation:

   • Simulated data for the four experimental groups is generated with specific parameters (e.g., group size, treatment effect, and variability).
   • Each group reflects different combinations of pre-test and treatment conditions.

2. Statistical Analysis:

   • A one-way ANOVA is performed to detect significant differences between groups.
   • Post-hoc Tukey's HSD tests are used to identify specific group differences.

3. Visualization:

   • Boxplots show the distribution of post-test scores across groups.
   • Mean comparisons with confidence intervals highlight the treatment's impact.
   • Tukey's plot visually represents significant pairwise differences.

Key Findings

• ANOVA Results: Significant differences were found between groups, indicating a strong treatment effect.
• Mean Comparisons: Groups receiving the treatment consistently scored higher than control groups.
• Tukey HSD: Post-hoc comparisons confirmed that the treatment effects were statistically significant.