Mind the Gap: Exploring Social Inequalities in Alcohol Consumption using Nationally Representative Data from the 2019...

The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are:
H0: The two variables (factors)...

In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
The test statistic for a test of independence is similar to that of a goodness-of-fit test:

Stress often leads to unhealthy habits like smoking, excessive drinking, and overeating, which offer short-term relief but ultimately increase long-term health risks. These behaviors create a cycle that temporarily lowers stress levels but can result in severe long-term health consequences. Breaking these habits is essential to reduce the risk of chronic diseases and improve overall well-being. Three primary changes that support better health include quitting smoking, reducing alcohol intake,...

This lesson delves into the concept of protection and deprotection of a functional group fundamental to synthetic organic chemistry. These phenomena are explained in the context of aliphatic and aromatic alcohols.
Protection
It defines a protecting group as the masking agent to make the more reactive species inert to a given set of conditions. This concept is depicted via the illustration of liquid flow through different outlets in an assembly of pipes. The analogy helps to understand the role...

Alcohols (R-OH) ionize to lose one non-bonded electron from the oxygen atom, forming molecular ions. Due to their tendency to fragment rapidly, the intensity of the molecular ion peak in the mass spectrum is weak or sometimes absent. The fragmentation patterns for alcohols occur in two ways, i.e. ⍺-cleavage and dehydration. During ⍺-cleavage, the bond at the ⍺-position adjacent to the hydroxyl group cleaves to give a resonance-stabilized cation and a radical. However, intramolecular...

Reduction is a simple strategy to convert a carbonyl group to a hydroxyl group. The three major pathways to reduce carbonyls to alcohols are catalytic hydrogenation, hydride reduction, and borane reduction.
Catalytic hydrogenation is similar to the reduction of an alkene or alkyne by adding H2 across the pi bond in the presence of transition metal catalysts like Raney Ni, Pd–C, Pt, or Ru. Aldehydes and ketones can be reduced by this method, often under mild to moderate heat (25–100°C) and...