Module 5 Notes - Generalization, Analogy, and Causation (10/3)

To-Do:

  • Precis 5

  • Module Reply 1 and 2

Inductive Generalization

  • Inductive Generalization - interference from a sample of some population or a set of past events to every member of that population for future events

    • E.g. - Drinking Coke again because you know it wasn’t poisonous last time

  1. Most of a sample of X is Y

  2. Probably, All X’s are Y’s

  • Inductive Generalization is also known as Enumerative Induction

    • More specifically, reasons from a past sample to the next instance of an event (e.g. swans being white)

  • Conditions for a good inductive generalization:

    1. Sample must be random

    2. Sample must be proportionate

    3. Sample must be obtained using a valid instrument

    4. Sample must be obtained using a reliable instrument

(1) Sample Must Be Random (i.e. Unbiased)

  • A random sampling takes information from all relevant portions of the population

    • If the sample isn’t random, it’s biased

  • Self-Selection Bias - Interfaces made from us self-selecting the samples

(2) Sample Must Be Proportionate

  • Too small samples are not a good indication of the whole population

    • e.g. 200 of 100,000,000

  • Hasty Generalization - generalization that draws a conclusion about a population too small/ disproportionate

  • Use your best judgement to determine if the sample is good enough for generalizing

(3) Sample Must Be Obtained Using A Valid Instrument

  • Valid Scientific Instrument - is an instrument that yields the relevant information we are looking for

  • Cultural Bias - Tracking using cultural factors, not indicative of intelligence (invalid)

  • Framing Bias - Asking questions too narrowly or in a closed-ended or question-begging way

    • e.g. “Have you stopping beating your wife?”

  • Gender and Race Bias - Asking questions/ phrasing that lead to different answers from different races or gender

(4) Sample Must Be Obtained Using A Reliable Instrument

  • A scientific instrument must be structured so that it measures the relevant information accurately

  • Ordering Bias - The order you ask certain questions affects responses

    1. Is abortion always wrong?

    2. Is it permissible to abort if not doing so will result in the deaths of both the mother and fetus?

  • Confirmation Bias - Unintentionally choosing data that favors the result you prefer

Errors in Statistics and Probability

  • +-% is called M.O.E

  • Margin of Error/ Random Sampling Error - Measure the error in the statistical calculation

  • Smaller the sample = higher the error

Statistical Fallacies

  • Three common mistakes made when reasoning about stats

    • Regression Fallacy

    • Base Rate Neglect

    • Gambler’s Fallacy

  • Regression Fallacy - Occurs when we attribute especially good or bad effects to an intervention when the more likely explanation is just that effects are simply regressing to their average

    • e.g. your siblings get praises but you get spanked

    • To avoid this, make sure there are enough trials to get a statistically significant result

  • Base Rate Neglect - The rate at which events occur (their base rate) relative to the rate at which we perceive them

    • e.g. running regularly hurts joints, but drinking water immediately after helps, so always drink water after running

  • Gambler’s Fallacy - Occurs when we use evidence of past, independent events to draw probabilistic conclusions for future

    • e.g. coins/ gambling head tails “i’m bound to win tails now”