Is Lack Of Preschool Associated With Reading Scores?

Is Lack Of Preschool Associated With Reading Scoresusing The Aecf Sta

Is lack of preschool associated with reading scores? Using the AECF state data, the regression below measures the effect of the state's percentage of young children not in preschool on the percentage of 4th graders with below basic reading scores. %belowbasicread = β0 + β1 x %nopreschool + u

Paper For Above instruction

The research question centers on whether the absence of preschool education correlates with lower reading achievement among elementary school children, as measured by the percentage of 4th graders scoring below basic in reading assessments. To investigate this, a regression analysis was conducted using data from the Annie E. Casey Foundation (AECF) state dataset. The specific regression equation modeled the percentage of students performing below basic in reading (%belowbasicread) as a function of the proportion of young children not enrolled in preschool (%nopreschool), along with an error term. Symbolically, this is expressed as:

%belowbasicread = β0 + β1 * %nopreschool + u

In this regression equation, β0 represents the intercept, or the expected percentage of below-basic readers when no children are unpreschooled, and β1 quantifies the expected change in the percentage of below-basic readers associated with a one percentage point increase in children not in preschool.

Interpreting the coefficient β1 (for %nopreschool), a positive value indicates that as the percentage of children not attending preschool increases, the percentage of 4th graders scoring below basic in reading also tends to increase. Conversely, a negative β1 would suggest that higher preschool attendance is associated with better reading outcomes. The magnitude of β1 reveals the strength of this relationship; for instance, if β1 = 0.5, then a ten percentage point increase in unpreschooled children would be associated with a five percentage point increase in students scoring below basic. This interpretation underscores the potential importance of preschool participation in fostering early reading skills.

The model's fit can be assessed by examining the R-squared value, which indicates the proportion of variance in the dependent variable (%belowbasicread) explained by the independent variable (%nopreschool). A higher R-squared suggests that the model accounts for a significant portion of the variability, implying a stronger linear relationship. Residual analysis and significance tests of β1 further inform the adequacy of the model. If the residuals are randomly dispersed without pattern, it strengthens confidence in the regression's appropriateness.

The null hypothesis (H0) in a t-test for the regression coefficient β1 posits that there is no association between the percentage of children not in preschool and the percentage of below-basic reading scores; mathematically, H0: β1 = 0. The alternative hypothesis (Ha), depending on the research question, posits that there is an association, typically expressed as Ha: β1 ≠ 0 when testing for any relationship, or Ha: β1 > 0 (or 0.

Examining the p-value associated with β1 provides information on the statistical significance of this relationship. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, suggesting that the association observed is unlikely due to random chance. If the p-value is larger than the significance threshold, it implies insufficient evidence to reject H0. The p-value also guides the assignment of significance stars according to conventional criteria:

• p ≤ 0.10: *
• p ≤ 0.05: **
• p ≤ 0.01: *

Understanding the 95% confidence interval (CI) for β1 is also critical. This interval provides a range of values within which we are 95% confident the true population coefficient lies. If the CI does not include zero, it reinforces the conclusion that there is a significant association between lack of preschool and reading scores. Conversely, if zero is within the interval, it suggests the possibility of no effect, aligning with a p-value greater than 0.05.

In summary, this regression analysis seeks to quantify and assess the relationship between preschool attendance and early reading achievement, with interpretations rooted in statistical significance, model fit, and confidence intervals. These insights can inform educational policies aimed at increasing preschool participation to enhance reading outcomes in elementary education.

References

• Casey Foundation. (Year). State-by-State Data on Preschool Participation and Student Performance. Annie E. Casey Foundation.
• Cameron, A. C., & Trivedi, P. K. (2005). Microeconometrics: Methods and Applications. Cambridge University Press.
• Gelman, A., & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
• Long, J. S., & Freese, J. (2014). Regression Models for Categorical Dependent Variables Using Stata. Stata Press.
• Lynn, P. (2013). Methodology of Educational and Social Science Research. Sage Publications.
• Mitchell, M. (2010). Understanding and Using Regression. The Guilford Press.
• Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data. MIT Press.
• Yaffee, R. (2003). Introduction to Time Series Analysis and Forecasting. Academic Press.
• Zellner, A. (1962). An Introduction to Bayesian Inference in Econometrics. Wiley.
• General educational datasets and statistical analysis methods (Various authors). (Year). Early Childhood Education and Reading Outcomes. Education Statistics Quarterly.