Statistics vs Words vs Pictures vs Power: which method is more effective?

Depends on the situation

I consider there to be 5 main methods of knowing. Verbal inference (anecdotes/stories), Verbal deduction, statistical inference, authority, and visual/artistic impression.

Authority is the best at convincing others — I am not sure why this is, but I think it is because all humans can innately understand it, other methods rely more heavily on either intelligence or background knowledge. There are massive individual differences in the extent to which authority works: when talking to normals, it is best to appeal to some “authorities” who advocate for your position, for abnormals it just comes off as underhanded. It is possible to debate the competence of the cited authorities, but power itself cannot be dismantled by calling it incompetent — at least not in the moment.

Ignoring that, there is not really a proper answer to the question in the title. For what, when, and for who? Most fields of philosophy are innately anumeric and cannot be studied using mathematics. People also differ in their innate capacities for understanding certain arguments: some people prefer quantitative methods, others prefer verbal methods.

My experience dictates that most people can understand visual media, about half can read well, and maybe a fifth can do math well. The fact that mathematical ability is rarer than verbal ability can be inferred by several observations: numeracy is more valued than literacy on the labour market (both the PIAAC and SAT data vindicate this) and more people report having trouble with math than science or reading classes.

Part of this is because math has an inherent proof system where the truth of a statement can be formally verified, but evaluations of writing quality will vary more by person. However, this theory cannot explain why people find reading easier than mathematics, leading me to suspect there is another mechanism at play: evolutionary novelty. Math is newer to humans than language, and language is newer to humans than sight. If a particular belief or practice is novel to humans, there will not be genes specifically associated with it (unlike say, language), so novel tasks will have to be learned by the general intelligence module (aka g).

For the purposes of maximizing audience size, visual media surpasses verbal media, which surpasses quantitative media. I am unsure whether this translates to greater efficacy in terms of persuasion — consider that the type of person who is persuaded by television and art. Is this somebody who can be swayed by truth, or do they just want to believe what they want to believe? But it remains to be known what causes people to want to believe things. Is it something innate, or something that is determined by media? A messy question.

II.

Inferential statistics lead to less biased thinking than verbal arguments or anecdotal evidence, though the advantage is overstated. I doubt the recent study of MZ twins reared apart is going to convince Sasha Gusev and his crew that intelligence isn’t highly heritable. Motivated reasoning is real — see my old review of the literature.

There is truth in the quote above, though this depends on the statistical method used — complex statistical methods are generally less trsutworthy than simple ones. Means and proportions are trustworthy; I don’t doubt that the United States is 60% non-Hispanic White, or that China is about 90% Han Chinese. Linear regression can generally be trusted if the p-value is low enough (I am satisfied with anything under .001, and, if priors dictate, under .01), though even something this simple can filter the dumbest idiot. Spline models, factor analysis, and multiple linear regression can be handled by statistician, though this is the point at which statistics become too inaccessible. When it comes to forecasting and modeling, I do not take the numbers at face value, instead I see them as an approximation.

I once heard a man say something along the lines of “statistics are what you use when you do not know the underlying mechanisms of what is occuring — it’s just inference”. There is also truth to this statement, but an advantage that statistics have over other learning methods is that the former are much more precise — it is easy to notice that high earners tend to be more intelligent than the poor, but statistics show that this relationship is not that strong (r = .38), even when income is aggregated from measurements based on multiple years.

I suspect that younger thinkers tend to prefer statistics while older ones prefer verbal argument and historical analysis. Statistics are quick and easy, but can be easily misused without careful thinking that will be more difficult in the elderly. On the other hand, historical analysis is cognitively easier, but it requires a longer attention span and a lot of background knowledge.