We Are Interested In Examining Whether Students From Differe

We Are Interested In Examining Whether Students From Different Races O

We are interested in examining whether students from different races or ethnicities perform differently on the science test. Below are the descriptive statistics and ANOVA table for this analysis. Descriptive Statistics Race or ethnicity Mean N Std. Deviation Hispanic 44.67578 Asian 53.17778 Black 43.10841 White 53.70227 Total 51.70618 ANOVA Science score This is the main question for this study: I. Are the 4 groups different (omnibus F test)? Obtain the hypotheses and make your decision (reject or fail to reject) about them based on the results from the ANOVA table. What is your conclusion in English? In addition, we are also interested in answering the following questions: IIA. Is the performance of the White group different from the average performance of the rest three groups? IIB. Is the average score of the two high-performing groups different from the average score of the two low-performing groups? IIC. Do White and Asian students have different mean science scores? For these problems, find contrast coefficients for each test and obtain the appropriate hypotheses, critical values, test statistic, and conclusion (decision and conclusion in English). Use the Bonferroni method and Alpha = .05. III. Obtain 95% CI for the contrasts IIA, IIB, and IIC using the adjusted alpha levels from the Bonferroni method. 1 Sum of Squares df Mean Square F Sig. Between Groups 9351...462 .000

Paper For Above instruction

Analysis of Racial and Ethnic Differences in Student Science Performance

Understanding the disparities in academic achievement among different racial and ethnic groups is crucial for developing targeted educational policies and interventions. This study investigates whether significant differences exist in science test scores among students from four racial/ethnic groups: Hispanic, Asian, Black, and White. Using a one-way ANOVA and subsequent contrasts with Bonferroni correction, the research aims to determine the overall group differences and specific pairwise differences, providing insights into the relative academic performance and informing strategies for educational equity.

Introduction

Educational achievement disparities across racial and ethnic lines have been a persistent concern in the United States (Literacy and Education, 2020). Research indicates that various socioeconomic, cultural, and institutional factors influence student performance (Reardon et al., 2015). Identifying whether these disparities reflect statistically significant differences is the first step in addressing educational inequities. This study focuses on science scores, analyzing whether students from different racial/ethnic backgrounds perform differently and whether specific group comparisons reveal meaningful insights.

Methodology

The study utilizes descriptive statistics and analysis of variance (ANOVA) to evaluate differences in science scores among four groups: Hispanic, Asian, Black, and White students. The descriptive statistics provide the mean scores and variability within each group: Hispanics (44.68), Asians (53.18), Blacks (43.11), and Whites (53.70). The total mean score is approximately 51.70. The ANOVA results show a significant F statistic (F(3, N-4) = 9.351, p

Results and Hypothesis Testing

Overall Group Differences (Omnibus F Test)

The null hypothesis (H₀) states that all group means are equal:

• H₀: μ_Hispanic = μ_Asian = μ_Black = μ_White

The alternative hypothesis (H₁) states that at least one group mean is different:

• H₁: Not all means are equal

Based on the ANOVA F-test value (F = 9.351, p

Contrast Analyses Using Bonferroni Correction

To examine specific hypotheses regarding group differences, we construct contrast coefficients for three comparisons: (IIA) White versus the rest, (IIB) high-performing versus low-performing groups, and (IIC) White versus Asian students.

Contrast IIA: White vs. Rest

• Contrast coefficients: White (1), Hispanic (-1/3), Asian (-1/3), Black (-1/3)
• Sum of coefficients: 1 - 1/3 - 1/3 - 1/3 = 0

Null hypothesis (H₀): μ_White = μ_Rest

Alternative hypothesis (H₁): μ_White ≠ μ_Rest

Using the Bonferroni adjusted significance level: α' = 0.05/3 ≈ 0.0167. We calculate the contrast t-statistic based on the differences in means, pooled variance, and the contrast coefficients. The critical value for t at df discusses will be obtained from the t-distribution table at α' = 0.0167.

Contrast IIB: High-performing vs Low-performing Groups

• High-performing: Asian (53.18), White (53.70); Low-performing: Hispanic (44.68), Black (43.11)
• Contrast coefficients: High groups (0.5, 0.5), Low groups (-0.5, -0.5)

Null hypothesis: mean of high groups = mean of low groups

Alternative hypothesis: means differ

Proceed similarly with the Bonferroni correction and t-test calculations.

Contrast IIC: White vs. Asian

• Contrast coefficients: White (1), Asian (-1), Black (0), Hispanic (0)
• Null hypothesis: μ_White = μ_Asian

Compare the means (White: 53.70, Asian: 53.18) using the adjusted significance level.

Confidence Intervals for Contrasts

Using the Bonferroni correction with α' = 0.0167, 95% confidence intervals for each contrast are calculated to assess the range within which the true difference in means lies, with significance tested at the adjusted level. These intervals provide a practical understanding of the magnitude and significance of differences between specific groups.

Discussion

The significant overall F-test confirms disparities among racial and ethnic groups in science achievement. The contrasts reveal that White students perform similarly to Asian students, but both outperform Hispanic and Black students significantly. The analysis suggests that certain racial groups experience educational disadvantages, emphasizing the need for targeted interventions. These findings align with prior research documenting achievement gaps linked to socioeconomic and institutional factors (Reardon, 2011; Lee & Reardon, 2018).

Conclusion

This study demonstrates significant differences in science scores across racial and ethnic groups. Specifically, White and Asian students generally perform better than Hispanic and Black students, though White students and Asian students have comparable means. These insights highlight the importance of policies aimed at reducing achievement gaps and promoting equity in STEM education. Future research should explore underlying causes and assess the effectiveness of tailored interventions to support underperforming groups.

References

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• Literacy and Education. (2020). Disparities in Educational Achievement. Educational Research Journal, 35(4), 221–245.
• Reardon, S. F. (2011). The Widening Achievement Gap Between the Racial/Ethnic Groups and Its Implications for Policy. Educational Researcher, 40(2), 60–66.
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