# Statistical Analysis of School Types and Intervention Effects on Academic Performance

Discover a comprehensive statistical analysis that delves into the influence of different school types and intervention strategies on academic performance. This in-depth examination provides valuable insights into the relationships between school choices and students' end reading scores and engagement levels. Through rigorous statistical methods, we unveil the significance of these factors, helping educators, researchers, and policymakers make informed decisions to improve educational outcomes. Dive into the data-driven world of academic performance, where we explore the nuances of null and alternative hypotheses, F-statistics, and their implications for the education landscape.

## Problem Description

This statistical analysis assignment involves the analysis of the impact of different school types and intervention groups on end reading scores and engagement scores. The goal is to determine whether there are significant differences among these groups. Explore the impact of school types and intervention strategies on academic performance in this comprehensive statistical analysis. Our investigation assesses whether different school environments and intervention programs yield distinct end reading scores and engagement levels among students. By conducting rigorous statistical analyses, we aim to uncover significant variations, providing valuable insights for educators and researchers to make data-driven decisions that enhance educational outcomes.

• Null Hypothesis: All school types have the same end reading scores.
• Alternative Hypothesis: At least one of the school types has different end reading scores.
• Alpha (Significance Level): 0.05
• F-Critical Value: 3.042
• F-Statistics: 12.17

Result: Since the F-Statistics (12.17) is greater than the F-Critical (3.042), we reject the null hypothesis. One-way ANOVA indicates a significant effect of school types on end reading scores at the 0.05 significance level, with F(2,197) = 12.17 and p = 0.000. Therefore, we conclude that at least one of the school types has different end reading scores.

Engagement Scores Analysis

School Types:

• Null Hypothesis: All school types result in the same engagement scores.Alternative Hypothesis: At least one school type has different engagement scores.
• Alpha (Significance Level): 0.05
• F-Critical Value: F(0.05, 2, 196) = 3.042
• F-Statistics for School Types: 0.914

Result: Since the F-Statistics for school types (0.914) is less than its F-Critical (3.042), we fail to reject the null hypothesis. The ANOVA was not significant at the 0.05 significance level, with F(2,194) = 0.914 and p = 0.403. Therefore, we conclude that all the school types have the same engagement scores.

Intervention Groups:

• Null Hypothesis: All intervention groups result in the same engagement scores.
• Alternative Hypothesis: At least one intervention group has different engagement scores.
• Alpha (Significance Level): 0.05
• F-Critical Value: F(0.05, 1, 196) = 3.889
• F-Statistics for Intervention Groups: 0.433

Result: Since the F-Statistics for intervention groups (0.433) is less than its F-Critical (3.889), we fail to reject the null hypothesis. The ANOVA was not significant at the 0.05 significance level, with F(1,194) = 0.432 and p = 0.312. Therefore, we conclude that all the intervention groups have the same engagement scores.

``` # Load the dataset df <- read.csv("Martinez_reading.csv") ``` ``` # End Reading Scores Analysis annova_res <- aov(ReadEnd ~ factor(SchoolSES), data = df) summary(annova_res) ``` ``` # Engagement Scores Analysis for School Types and Intervention Groups res2 <- aov(Engagement ~ SchoolSES + Intervention, data = df) summary(res2) ```

Please note that the results are based on the provided data and analysis. The conclusion may vary if different data or statistical methods are used.