Question

A researcher claims to have evidence of a strong positive correlation \((r=0.88)\) between a person's blood alcohol content \((\mathrm{BAC})\) and the type of \(\mathrm{alco}-\) holic drink consumed (beer, wine, or hard liquor). Explain, statistically, why this claim makes no sense.

Short answer

The researcher's claim of having evidence of a strong positive correlation between a person's BAC and the type of alcoholic drink consumed doesn't make sense, because correlation necessitates that both variables are continuous and from either interval or ratio scale. There's no ordering to the categories (beer, wine, hard liquor) therefore, does not make sense to compute a correlation between a nominal and a ratio variable.

Step-by-step solution

Understand the Variable Types

The type of alcoholic drink (beer, wine, or hard liquor) is a nominal variable, because there's no intrinsic ordering to the categories. The BAC is ratio level data since it has a clear definition of zero.

Understand the Correlation Coefficient

Correlation is a measure of linear association between two continuous variables, and makes no sense when applied to nominal variables, because it requires the variability in the data to be from an interval or ratio scale. The correlation coefficient (\(r\)) quantifies the strength and direction of the linear relationship between the two variables.

Explain Why the Claim Makes No Sense

The claim that there's a strong correlation between a nominal variable and a ratio variable doesn't make sense, because the correlation coefficient requires both variables to be continuous and from either interval or ratio scale. In other words, one cannot sensibly compute a correlation coefficient between BAC (continuous ratio variable) and type of drink (nominal variable).