Analysis from the grassroots: how does pollution exposure vary by race and income?

Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...

Humans continually engage with an environment rich in potentially harmful chemicals. These are introduced to our bodies through inhalation, ingestion, or skin contact. These chemicals exist in various forms, such as air and environmental pollutants, agricultural chemicals, organic solvents, and heavy metals.
Air pollutants, primarily gases, pose significant threats to respiratory health, leading to conditions like hypoxia, lung cancer, and in extreme cases, death.
Environmental pollutants like...

Humans are very diverse and although we share many similarities, we also have many differences. The social groups we belong to help form our identities (Tajfel, 1974). These differences may be difficult for some people to reconcile, which may lead to prejudice toward people who are different. Prejudice is a negative attitude and feeling toward an individual based solely on one’s membership in a particular social group (Allport, 1954; Brown, 2010). Prejudice is common against people who are...

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...

Social comparison plays a fundamental role in the evaluation of personal success and self-worth. Rather than assessing our achievements in isolation, we interpret their significance relative to personal goals and critically in comparison to the performance of others. A grade of B in a mathematics exam might elicit pride if one's expectation was a C, yet result in disappointment if an A was anticipated or if peers achieved superior results. These comparative evaluations illustrate how both...

Confounding is a critical issue in epidemiological studies, often leading to misleading conclusions about associations between exposures and outcomes. It occurs when the relationship between the exposure and the outcome is mixed with the effects of other factors that influence the outcome. Given that, addressing confounding is of high importance for drawing accurate inferences in research.
Confounding can be addressed at both the design phase of a study and through analytical methods after data...