Empirical Research Questions And Methods
Empirical Research Questions Research Methods 1
Suppose you have a sample of children ranging from 5 to 18 years of age. You run a regression of math scores on height and get a statistically significant positive coefficient estimate. Your research assistant concludes that height has a causal effect on mathematical ability – being taller makes children better at math. Would you agree with your research assistant’s interpretation of the regression results? If so, explain why. If not, offer a more likely explanation for the positive correlation and suggest how you could alter your regression to address this.
Suppose you have a sample of children ranging from 5 to 18 years of age. You run a regression of math scores on height and get a statistically significant positive coefficient estimate. Your research assistant concludes that height has a causal effect on mathematical ability – being taller makes children better at math. Would you agree with your research assistant’s interpretation of the regression results? If so, explain why. If not, offer a more likely explanation for the positive correlation and suggest how you could alter your regression to address this.
Paper For Above instruction
The interpretation of regression results showing a significant positive coefficient—specifically, that height predicts math scores—must be approached with caution. While the statistical significance indicates a correlation between height and math scores, it does not inherently establish causality. Concluding that being taller causes children to perform better at math overlooks potential confounding factors and the risk of spurious correlation.
One primary concern with the research assistant's interpretation is the possibility of omitted variable bias. Age is a critical confounder in this context; older children tend to be taller and often perform better on math assessments due to their greater developmental maturity. If age is not controlled for in the regression, the positive association between height and math scores may simply reflect the underlying correlation with age, rather than a causal effect of height itself. For example, older children are naturally taller than younger children, and their higher scores are partly attributable to their age-related cognitive development rather than their height per se.
Another issue is reverse causality, which is less pertinent here but worth noting. It is unlikely that math ability influences height directly, although underlying factors such as nutrition could influence both height and cognitive development, leading to a spurious correlation. Therefore, the positive relationship could be driven by factors like overall health, socioeconomic status, or access to resources rather than a direct causal link from height to math skills.
To address this concern and improve the causal interpretation, the regression model should incorporate additional control variables—particularly age—to hold constant the developmental stage of the children. Including age as a covariate would allow us to examine whether height still predicts math scores after accounting for age-related effects. Alternatively, utilizing instrumental variables (IV) that influence height but are not directly related to math scores could help establish causality. For example, genetic factors affecting height independent of socioeconomic factors could serve as instruments in an IV approach.
Furthermore, a longitudinal study design could provide stronger evidence. Tracking the same children over time to see whether changes in height within individuals are associated with changes in math performance would help clarify causality. If increases in height do not correspond to improvements in math scores after controlling for age and other confounders, it would suggest that the observed correlation is non-causal.
In conclusion, the positive correlation between height and math scores observed in a simple regression does not suffice to establish causality. Confounding by age and socioeconomic factors likely drive the correlation. Proper model specification, inclusion of relevant covariates, and alternative research designs are necessary to make more definitive causal claims.
References
- Angrist, J. D., & Pischke, J.-S. (2009). Mostly Harmless Econometrics: An Empiricist's Companion. Princeton University Press.
- Baum, C. F., Schaffer, M. E., & Stillman, S. (2003). Enhanced routines for instrumental variables/2sls covariance matrix estimation. Stata Journal, 3(1), 1-16.
- Deaton, A., & Cartwright, N. (2018). Understanding and misunderstanding randomized controlled trials. Social Science & Medicine, 210, 2-21.
- Journal of Business & Economic Statistics, 27(2), 153-159.