The correlation between legalised abortion and crime rate in New York between 1973 - 2000
This document is an IB Mathematics Exploration titled "The Correlation Between Legalised Abortion and Crime Rate in New York Between 1973 - 2000," authored by Amy Su for the May 2022 examination session at Bexley Grammar School. Below is a summary of its main content, structured according to the key sections of the document:
1. Introduction- Context: Inspired by Freakonomics by Levitt and Dubner, the exploration investigates their theory that legalizing abortion in 1973 reduced crime rates in New York by decreasing the number of unwanted children raised in poor conditions, who are more likely to become criminals.
- Objective: To statistically explore the correlation between abortion rates and crime rates in New York from 1973 to 2000, considering Levitt and Dubner’s hypothesis of an inverse relationship.
- Methodology: A statistical investigation using data on abortion and crime rates, with tools like box plots, regression analysis, Pearson’s correlation coefficient, and a Chi-squared test of independence.
2. Data Collection- Sources: Abortion data is sourced from the CDC, AGI (Alan Guttmacher Institute), and merged estimates; crime data comes from the Uniform Crime Reporting (UCR) Program via the Disaster Centre.
- Variables: Uses "abortion rate merged" (abortions per 1,000 women aged 15-44) due to its comprehensive nature, despite provisional estimates. Crime rate is adjusted from per 100,000 to per 1,000 for consistency.
- Limitations: Data reliability is affected by estimates and voluntary reporting, with potential underrepresentation of abortions due to illegal procedures.
3. Plan and Statistical Analysis- Initial Steps: Box plots identify outliers; crime rate data is adjusted for comparison with abortion rate.
- Graphical Analysis:
- Scatter plots of abortion and crime rates over time (1973-2000) to observe trends.
- A scatter plot of abortion rate (x-axis) vs. crime rate (y-axis) to test for correlation.
- Statistical Tests:
- Pearson’s Correlation Coefficient (r): To quantify the strength and direction of the relationship.
- Chi-squared Test: To determine if abortion and crime rates are independent.
- Hypothesis: Expects a negative correlation per Levitt’s theory (higher abortion rate, lower crime rate).
4. Data Analysis- Box Plots:
- Crime rate: No outliers, skewed left, IQR = 22.942, range = 38.12.
- Abortion rate: One outlier (54.27 in 1973), IQR = 4.15, range = 15.18; fairly consistent spread.
- Insight: Abortion rate remains stable (38-47), while crime rate varies more widely.
- Trendline Graphs:
- Over time, crime rate declines (especially 1991-2000), but abortion rate does not rise inversely, suggesting no clear correlation.
- Regression Analysis:
- Scatter plot (abortion rate vs. crime rate) shows a positive correlation initially, then weakens.
- Pearson’s r = 0.773 (strong positive correlation), regression line: y=4.26x−131 y = 4.26x - 131 y=4.26x−131.
- Contradicts Levitt’s theory, as crime rate increases with abortion rate.
- Chi-squared Test:
- Null hypothesis (H0H_0H0): Abortion and crime rates are independent.
- Adjusted data into broader intervals (e.g., 30-45, 45-60) due to small expected frequencies.
- χ2=0.305 \chi^2 = 0.305 χ2=0.305 (with Yates’ correction), below critical values (e.g., 10.828 at 0.001 significance).
- Result: Fail to reject H0H_0H0, indicating independence and no significant relationship.
5. Conclusion- Findings:
- Regression suggests a strong positive correlation (r = 0.773), opposing Levitt’s inverse hypothesis.
- Chi-squared test overrides this, concluding abortion and crime rates are independent, implying no causal link.
- Implications: Levitt and Dubner’s theory is not supported; other factors (e.g., policing, economic policies) likely influenced crime rates.
- Limitations:
- Unreliable data due to estimates and unreported illegal abortions.
- Failure to account for time lags (e.g., abortion effects manifesting years later) or other variables.
- Reflection: Future analysis should consider age-specific crime rates and lagged effects (e.g., crime in 1991-2018 for abortions in 1973-2000).
6. Key Takeaways- The exploration demonstrates statistical techniques (box plots, regression, Pearson’s r, Chi-squared) to test an economic hypothesis.
- Despite initial evidence of correlation, rigorous testing shows no relationship between abortion and crime rates in New York (1973-2000), challenging Freakonomics’ claims.
- Highlights the complexity of social phenomena and the need for comprehensive data and multi-factor analysis.
This document effectively blends mathematical rigor with real-world application, though it acknowledges data and methodological constraints that limit its conclusiveness.
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