Omitted variable bias occurs in most statistical models. Whenever a confounding variable that is correlated with both dependent and independent variables is omitted from a statistical model, estimated effects of included variables are likely to be biased due to omitted variables. This issue is particularly problematic in physics education research where many research studies are quasiexperimental or observational in nature due to ethical and logistical limitations. In this paper, we illustrate the mechanisms behind omitted variable bias in explanatory modeling using authentic data and analytical solutions. We demonstrate that omitting confounding variables that are strongly correlated with included variables and have large effects on the dependent variable can significantly bias estimated effects for included variables. We also find that controlling for variables that are uncorrelated with other variables or have no effect on the dependent variable does not appreciably bias estimated effects and may or may not affect the precision of those estimates. These results suggest that removing from explanatory models variables that are not “statistically significant” can have unintended consequences on model and variable interpretations. Our results underscore the importance of carefully considering why or why not to include a variable in a model, informed by both data and theory.

中文翻译：

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探索遗漏变量偏差在物理教育研究中的作用

在大多数统计模型中都会发生遗漏的变量偏差。每当从统计模型中忽略与自变量和自变量都相关的混淆变量时，由于遗漏变量，所包含变量的估计效果很可能会产生偏差。这个问题在物理教育研究中尤其成问题，在物理教育研究中，由于伦理和后勤方面的限制，许多研究在本质上都是准实验性或观察性的。在本文中，我们将说明在使用真实数据和分析解决方案的解释性建模中，省略变量偏差背后的机理。我们证明，忽略与包含变量高度相关且对因变量具有较大影响的混杂变量，可能会明显偏向包含变量的估计效果。我们还发现，控制与其他变量不相关或对因变量没有影响的变量不会明显偏倚估计的影响，并且可能会或可能不会影响这些估计的精度。这些结果表明，从解释性模型中删除不具有“统计意义”的变量可能会对模型和变量解释产生意想不到的后果。我们的结果强调了认真考虑为什么或为什么不在数据和理论的指导下将变量包括在模型中的重要性。这些结果表明，从解释性模型中删除不具有“统计意义”的变量可能会对模型和变量解释产生意想不到的后果。我们的结果强调了认真考虑为什么或为什么不在数据和理论的指导下将变量包括在模型中的重要性。这些结果表明，从解释性模型中删除不具有“统计意义”的变量可能会对模型和变量解释产生意想不到的后果。我们的结果强调了认真考虑为什么或为什么不在数据和理论的指导下将变量包括在模型中的重要性。