Chapter 2: State Differences and Relationships

Chapter 2

State Differences and Relationships

Patterns of Data Analysis

• Are Some Patterns Evidence of Cause and Effect?

  • Exploring the relationship between various state metrics.

• Are There Explanations for Patterns in Texas?

  • Estimating the socio-economic factors contributing to data trends in Texas.

Figures and Data Visualizations

• Figure 2.1: Per Capita Income 2014

  • Income brackets:

  • < $40,000

  • $40,000 - $45,000

  • $45,000 - $50,000

  • $50,000+

• Figure 2.2: Percentage of Population With High School Completion or Higher 2014

  • Completion categories:

  • < 86%

  • 86%

  • 90%

  • 92%

  • ≥ 92%

• Figure 2.3: Percentage of Population With Bachelor's Degree or Higher 2014

  • Degree categories:

  • < 26%

  • 26% - 30%

  • 30% - 33%

  • ≥ 33%

Scatterplot Analysis

• Importance of Scatterplots:

  • Provide more information than simple maps.

  • Enable comparative analysis of Texas to other states.

Correlations in Data

• Correlations Definition:

  • A technique for expressing relationships in quantitative terms.

  • Defined as the degrees of inherent association between any two variables occurring simultaneously in the same universe. (Source: Abraham N, Franzblau)

Empirical Relationships in Scatterplots

• Components of Analysis:

  • Minimum Strength Threshold:

  • Determines the minimum degree required to indicate a meaningful relationship.

  • Direction of Relationship:

  • Positive or negative correlation direction between variables.

  • Possible Interpretations:

  • Interpretation of data results can lead to various conclusions.

• Data Specific to Texas:

  • Correlations observed within Texas' social-economic factors.

Specific Figures on Income and Education

• Figure 2.4: Per Capita Income and Percent High School Completion 2014

  • Correlation Coefficient: $r = 0.43$

  • Visual representation combining income levels and education statistics.

• Figure 2.5: Per Capita Income and Percent Bachelor's Degree or Higher 2014

  • Correlation Coefficient: $r = 0.76$

  • Indicates higher educational attainment relates significantly to higher per capita income.

Table of Correlations Over Time

• Table 2.1: Per Capita Income and Educational Attainment Correlations

  • Yearly Correlation Data:

  • 1950:

    • High School Completion: $r = 0.70$

    • Baccalaureate Degree: $r = 0.52$

  • 1960:

    • High School Completion: $r = 0.66$

    • Baccalaureate Degree: $r = 0.48$

  • 1970:

    • High School Completion: $r = 0.61$

    • Baccalaureate Degree: $r = 0.65$

  • 1980:

    • High School Completion: $r = 0.63$

    • Baccalaureate Degree: $r = 0.64$

  • 1990:

    • High School Completion: $r = 0.44$

    • Baccalaureate Degree: $r = 0.74$

  • 2000:

    • High School Completion: $r = 0.31$

    • Baccalaureate Degree: $r = 0.74$

  • 2010:

    • High School Completion: $r = 0.37$

    • Baccalaureate Degree: $r = 0.79$

  • 2014:

    • High School Completion: $r = 0.43$

    • Baccalaureate Degree: $r = 0.76$

Government Revenue and Expenditure Analysis

• Figure 2.7: Per Capita Total State and Local Government Revenue and Per Capita Income 2014

  • Correlation Coefficient: $r = 0.69$

  • Examines relationship between government revenue and income.

• Figure 2.8: State and Local Government Revenue Per Capita and Percent of Population with Bachelor’s Degree or Higher 2014

  • Highlights how educational attainment can influence revenue generation.

• Figure 2.9: State and Local Government Expenditure Per Capita and Revenue Per Capita 2014

  • Regression line shows equality of expenditure and revenue lines.

Crime and Incarceration Data

• Figure 2.10: Incarceration Rate and Violent Crime Rate 2014

  • Correlation Coefficient: $r = 0.45$

  • Compares the rate of violent crimes to the incarceration rate across states.

• Figure 2.11: Poverty and Per Capita Income 2014

  • Examines the relationship between poverty levels and income.

• Figure 2.12: Life Expectancy and Infant Mortality 2014

  • Correlation Coefficient: $r = -0.78$

  • High correlation indicating that lower infant mortality rates correlate with longer life expectancy.

Issues in Empirical Analyses

• Measurement of Variables:

  • Correlation between various outcomes such as poverty, crime, and educational achievement needs proper linking.

• Causal Relationships:

  • Differentiate between true causal relations versus spurious ones, which may seem correlated purely by coincidence.

Patterns in Poverty and Crimes

• Figure 2.6: Number Living in Poverty Across States

  • Significant correlations between poverty and state populations.

  • Correlation Coefficient: $r = 0.96$ with reference to California.

• Comparative Analyses:

  • Crime Rates vs Personal Income:

  • Number of property crimes: $r = 0.88$ demonstrates the relationship between economic conditions and crime rates.

Importance of Measurement

• Using Rates vs Raw Numbers:

  • Accurately reflecting socio-economic conditions requires rate adjustments for population size and inflation factors.

• Controlling for Influencing Factors:

  • Correct identification of causative versus correlated statistics critical for accurate analysis.

Socioeconomic Trends in Births and Education

• Births to Teens Age 15-19 and Obese Adults:

  • Analysis of correlations in different demographics across states.

• Figure: Births to Teens and Obese Adult Rates

  • Correlation showing significant connections between health and teen birth rates ($r = 0.98$).

• Figure: Christian Population's Influence on Teen Births

  • Underlines demographic factors affecting teenage pregnancies.

Motion Graphs and Animated Scatterplots

• Utility of Animated Graphs:

  • Motion graphs can dynamically illustrate trends over time, further enriching data understanding.

Educational Attainment by State

• Percent Population With Bachelor's Degrees (3 Year Average from 1990-2009)

  • Trends of educational achievement are visually compared, emphasizing disparities and progress across states.