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1. Background and purpose of the study

Academic performance is affected by multiple factors, including individual characteristics, family background and educational resources. The purpose of this study was to systematically analyze the effects of gender, test preparation curriculum, ethnicity, parental education level, and lunch type on students' math, reading, and writing scores, and to provide data support for educational equity policies.

2. Methodological selection and basis

1. Data distribution characteristics

Although the histograms of math, reading, and writing scores appear to be approximately normally distributed to the naked eye, the Shapiro-Wilk test shows that all the score data do not conform to the normal distribution (p < 0.05), and there are a small number of extreme values at both ends of the data, resulting in a "truncated" tail and a slight rightward bias , the two endpoints of the Q-Q diagram deviate from the red line.

Therefore, this study is not considered to be suitable for parametric test methods such as t-test or ANOVA.

2. The necessity of non-parametric testing

Based on the results, the following non-parametric methods are used for analysis:

Mann-Whitney U test: Used to compare two independent samples, this study was used to compare the effects of gender differences, test preparation on performance.

Kruskal-Wallis H test: Used for comparisons between multiple groups, this study was used to compare racial differences

Spearman rank correlation: used to analyze the relationship between ordinal and continuous variables, this study was used to compare the relationship between parental education level and achievement

3. Visualization methods

The visualization of this study was implemented by Python pandas, seaborn, scipy, matplotlib, and all graphs included statistical annotations to enhance the readability of the results.

3. Task analysis and results

Task 1: Boxplot of gender distribution

subjects

U-value

p-value

conclusion

mathematics

101768

<0.001

Males are significantly better than females

Read

160508

<0.001

Women are significantly better than men

writing

169956

<0.001

Women are significantly better than men

Task 2: The impact of exam preparation courses on grades

Removing some extreme values, U=150320, p<0.001 was obtained, and the average score of students who completed the test preparation course was significantly higher than that of those who did not complete the three subjects (about 8 points higher on average ). And the dispersion is relatively less (SD=13<14.2), and the play is more stable.

Task 3: Differences in performance by race/ethnicity

Constituencies

Grade point average

standard deviation

Kruskal-Wallis 检验

Group A

65.5

14.7

H = 9.10, p < 0.001

Group B

67.1

13.9

Group C

63.0

14.4

Group D

69.2

13.3

Group E

72.8

14.6

Group E is significantly better than Group A

H=9.1, Group E students had the highest average grade, Group A had the lowest and was significant.

Task 4: The relationship between parental education and grades

Educational attainment

Grade point average

Spearman correlation coefficient (r).

p-value

some high school

65.1

r = 0.19

<0.001

high school

63.1

some college

68.5

associate's degree

69.6

bachelor's degree

71.9

master's degree

73.6

Conclusion: There is a weak positive correlation between parental education level and student achievement (r = 0.19), and there is a significant difference.

Task 5: Analysis of other factors

Effect of Lunch Type on Grades:

Lunch type:

Grade point average

standard deviation

Mann-Whitney U 检验

standard

70.8

13.2

U = 152822, p < 0.001

free/reduced

62.2

14.5

The difference was significant (mean difference = 10.6).

Standard lunch students scored an average of 12.3 points higher than free lunch students.

Grade Correlation Heatmap:

Conclusion: The results of the three subjects are highly correlated, indicating that the learning ability is consistent as a whole. And the correlation between writing and reading is greater than that between writing and math and reading and math.

4. Summary of key findings

Analyze dimensions

Key conclusions:

Statistical basis

gender

Girls are significantly better than boys in reading and writing

Mann-Whitney U 检验

Exam Preparation Courses

The average grade point of students who completed the course increased significantly

Mann-Whitney U 检验

Race/Ethnicity

Group E had the highest score and Group A had the lowest score, with a significant difference

Kruskal-Wallis H 检验

Parental education

There was a weak positive correlation between educational attainment and achievement (r = 0.19).

Spearman grade

Lunch type:

Standard lunch students were 10.6 points higher than free lunch students

Mann-Whitney U 检验

5. Suggestions and strategies

Gender-specific interventions

Strengthen language subject tutoring (reading, writing) for male students

Designing mathematical thinking training courses for female students to close the gender gap

Promote exam preparation courses

Provide free/low-cost resources, especially for underachievers

Racial Equity Policy

Additional academic support for Group A students (e.g. cram classes, tutor programs)

Analyze Group E's successes and replicate them to other groups

Parent Educational Involvement

Develop workshops for parents to increase educational engagement (especially for parents with high school education)

Provide family education guidance manuals to promote the optimization of the home learning environment

Optimization of lunch subsidy

Evaluate the practical effect of the free lunch policy, combined with comprehensive measures such as after-school tutoring

Provide nutritional supplementation programs for students from low-income families to improve their learning status