Gabriel Weinberg - Super Thinking - Part IV

Bayesian vs Frequentist Approach

• Bayesian approach uses prior beliefs to inform probability estimates.
• Frequentist approach starts from scratch and relies on data alone.
• Both approaches have validity, and the choice depends on the specific situation.
• Prior beliefs can mislead the Bayesian approach if they are based on biases or errors.
• This can lead to longer convergence times as the frequentist approach might be closer to the truth initially.

Sample Size and Statistical Significance

• Larger sample sizes provide more reliable estimates and a higher chance of detecting real effects.
• However, larger sample sizes require more resources and potentially pose ethical risks.
• Increasing sample size reduces both type I (false positive) and type II (false negative) errors.
• The "power" of a study refers to its ability to detect a real effect.
• A typical power level of 80% means that there's a 20% chance of a false negative.
• Lowering type I error increases the likelihood of type II error, and vice versa, assuming a fixed sample size.
• Narrowing confidence intervals (bell curves) through larger sample sizes reduces the overlap between the null and alternative distributions, minimizing error chances.

Meta-Analyses

• Combining data from multiple studies can improve the precision and accuracy of estimates.
• Combining data from studies with significantly different designs or populations is problematic.
• Meta-analyses cannot eliminate biases present in the original studies.
• Publication bias can limit meta-analyses to readily available results.

Pitfalls of Pro-Con Lists

• Often present all pros and cons as equally important, ignoring the impact of interrelations.
• Pros can appear more obvious than cons, leading to a 'grass-is-greener' mentality where positives are emphasized over negatives.
• Limited experience can hinder the identification of all relevant pros and cons.
• It's crucial to consider other mental models when making decisions to gain a holistic understanding.

Maslow's Hammer

• The phrase represents the tendency to over-rely on a specific tool or approach, even if it's not the best fit for the situation.
• We should avoid this by considering multiple tools and perspectives for a more nuanced approach.

Sensitivity Analysis

• Identifies key drivers within inputs and highlights areas needing more precise assumptions.
• Useful for determining the impact of changes in inputs on the overall outcome.
• A specific example relates to sample size and its sensitivity to alpha and beta in statistical experiments.

Discount Rate in Cost-Benefit Analysis

• The discount rate considers the time value of money, accounting for inflation, uncertainty, and alternative investment opportunities.
• There's no standard discount rate, as it varies depending on the specific situation, risk, and time horizon.
• Governments often use rates close to their interest rates, while corporations use more complex methods.
• New businesses typically use higher discount rates due to their higher risk and funding needs.
• A reasonable approach is to use the rate at which you can borrow money, ensuring investment returns exceed this rate.
• Public debates exist regarding appropriate discount rates for specific situations, particularly in government programs.