Chapter 7 - Reasoning About Causes

Clustering illusion

When we see patterns or groups in random data, even though they aren't really there. It's like when you look at a bunch of randomly placed dots and think they are forming a shape or pattern, but they’re just scattered without any real connection.

• Our brains naturally seek patterns.

Post Hoc Ergo Propter Hoc

“After this therefore because of this.”

Ever since I started wearing my lucky socks, my favorite team has been winning every game. The socks must be the reason they are winning.

• Assuming that because event B happens after event A, it must have been caused by A.

• Things can follow one and other without being related.

Immediate Causes

A cause that is immediately (and at least partially) responsible for an event.

• A certain drought might have a clear immediate cause, such as a long-term lack of rain.

• A dam broke releasing a large amount of water into a specific area.

Distal Causes

An underlying or distant cause that happens far from the immediate event, but still influences it. It’s a long-term or indirect cause that might not be obvious at first but plays a role in creating the situation over time.

• A company faces financial collapse.

  • Distal Cause: Poor management decisions made over a long period (such as overexpansion or mismanagement of funds).

Inferring Causation (3 Steps)

1. Correlation observed between A and B (induction)

2. General correlation between A and B (inferred/induction from 1); and

3. A causes B (coming up with an explanation of how 2 causes 3)

Because we could go wrong at any step, we should become less confident with each interim conclusion.

3 Steps of a Good Casual Argument of Correlation

(1) Correlation exists in the cases we've observed;

(2) There is a general correlation that holds beyond the cases we've observed;

(3) The general correlation is not misleading: it really results from A causing B. 

Correlations & 2 Types

When two things are related in some way, meaning that when one thing happens, the other tends to happen too.

• However, just because two things are correlated doesn't mean that one causes the other. It just means there’s a pattern or relationship between them.

• Types are Binary Correlations (positive / negative)

  • Scalar Correlations (positive / negative)

Causal Argument

The attempt to establish a causal connection between two factors (i.e., anything that can stand in a causal relation such as events, situations, or features of objects).

Causal Mechanism

Seeks to establish a cause-and-effect relationship between two or more variables. It goes beyond showing that two things are correlated (i.e., they happen together) and tries to demonstrate that one thing directly causes the other.

The goal is to provide evidence or reasoning that shows how and why a particular event or phenomenon leads to another.

• For example, the causal mechanism by which smoking causes cancer involves the formation of DNA adducts by the carcinogens from cigarette smoke that are taken into the body.

Common Cause (Misleading Correlation)

Refers to a situation where two things appear to be related, but they are actually both being caused by a third factor.

Two events, A and B, are correlated due to common cause when some third event C is responsible for both of them, and that's why they occur together at a higher rate than alone.

• Imagine that people in a certain town often get sick (A) and it seems like they also have high levels of air pollution (B). On the surface, it might appear that the sickness is caused by the air pollution. However, if we discover that cold weather (C) is the common cause, the cold weather could be the reason both the sickness (A) and the high pollution levels (B) are happening more frequently at the same time.

Double-blind Trial

An experiment is double-blind when neither the subject nor the experimenter is aware of which subjects belong to the control arm and which belong to the experimental arm of the trial.

Ensures that only the treatments effects are considered between the two groups (gets rid of misleading correlations).

• This experimental design helps defy the misleading correlations.

Immediate vs. distal causes

• Immediate cause: A proximate cause of x is one that is immediately responsible for the event. 

• Distal cause: A distal cause of x is one that is effective through intermediate causes.

Mere Chance

Refers to the idea that certain events or outcomes happen randomly, without any underlying cause or intention.

• We often identify correlations due to mere chance by assessing the plausibility of the causal mechanism required for a causal connection between the relevant factors.

  • Two people meet at a party and discover they have the same birthday.

  • Someone wins the lottery.

P-Value

A number that helps you determine whether the results of your experiment are statistically significant or if they could have happened by mere chance.

It is usually 0.5 in social sciences. A small p-value means it's very unlikely that the results happened by chance.

• If the p-value is less than 0.05 (commonly used threshold), there's strong evidence that the result is real and not due to chance.

• If a medical study shows a p-value of 0.02 for the effect of a drug, you might conclude that the drug has a statistically significant effect on the outcome being measured.

Pattern-seeking

The tendency to be over-sensitive to patterns even in scarce data that could be entirely random.

Placebo-controlled

When an experiment is placebo-controlled, the control group (the participants in the experiment who are not given the intervention being tested) receives a placebo treatment.

• This experimental design helps to rule out the placebo effect as a possible explanation for observed differences in outcomes between the group receiving the intervention and the control group.

Placebo effect (Misleading Correlation)

A positive effect arising from the expectation that an intervention (usually medical or dietary) will be effective. This effect works entirely through a subject's psychology.

• For example, when subjects take pills that they believe are effective for pain or depression, some report that the pills are effective even when they are not in fact biologically active.

Randomized controlled trial

In this kind of experiment, subjects are randomly divided into two groups, and some intervention (e.g., a drug) is applied to members of one group only.

• This procedure helps to rule out other factors (aside from the intervention being tested) that might explain differences in the observed outcomes between the two groups.

Regression to the Mean (Misleading Correlation)

Means that extreme results (very high or very low) are often followed by more average or typical results. Can work together with the placebo effect.

• For example, if someone scores unusually high on a test, their next score is likely to be closer to their usual average. This can make it seem like there's a bigger change or correlation than there actually is, which can be misleading if you don't account for this tendency.

Reverse Causation (Misleading Correlation)

Means that the relationship between two things might be the opposite of what we think.

• When we assume that A causes B, but actually, B might be causing A.

• Challenges our assumptions about cause and effect, reminding us to be cautious in interpreting relationships between things.

Robust (Strong) Evidence

Evidence that stems from a wide range of experiments (i.e., from different sources and from different kinds of experiments).

• This helps to ensure that we are drawing on lots of data, and that the result does not stem from some flaw in the study's design, or error on the part of the experimenters.

Side effect (Misleading Correlation)

Unintended or unexpected consequences that happen as a result of an action or decision. These side effects can be both positive or negative, and they may not be immediately obvious.

A genuine causal relationship between A and B, but it's not the relationship we expected. In particular, B may be caused by a side effect of A.

• For example, a drug may be correlated with a reported reduction in pain, even if a fake pill with no active ingredients would be just as effective (placebo effect).

Statistical significance

A way of determining whether the results of an experiment or study are likely to be real or if they could have happened by chance. High probability that the result you found is not just a random coincidence.

The threshold is set by convention in each field with respect to a p-value.

• For example, the social sciences tend to use a threshold of a p-value of .05. If the value is under 5 is has a stat significance. If it is over 5 it does not.

Positive Scalar Correlation (Variables)

As one thing increases, the other thing also increases. Both things are moving in the same direction.

The variables are typically on a scale (such as height, weight, age, income, etc.), and they can take a wide range of values.

Moves in both positive and negative directions, however if one variable is going down, so is the other. If one variable is going up so it the other. Up and down, in the same direction.

• More study hours → higher exam scores

• Fewer study hours → lower exam scores

Neglecting the Base Rate

Ignoring the background information or the general likelihood of something happening. The statistical rate of occurrence of a feature or event in general.

• Imagine you hear that a friend wins a small lottery prize every time they buy a ticket. You might think they are very lucky. But if you ignore the fact that they buy hundreds of tickets, you’re neglecting the base rate of winning, which is actually quite low.

Positive Binary Correlation (Yes/Yes) (No/No)

Looks at whether two things are likely to happen together in a No/No or Yes/Yes way. For example, if you say "Yes" to one thing, you are more likely to say "Yes" to the other thing too.

• Event 1: If you have an umbrella with you (Yes), you're more likely to stay dry (Yes).

• Event 2: If you don't have an umbrella (No), you're more likely to get wet (No).

Negative (Inverse) Binary Correlation (Yes / No)

When one thing happens (Yes), the other thing is more likely not to happen (No), and vice versa.

In a negative binary correlation, both events are likely to occur together in either a Yes/No or No/Yes way.

In other words, the two factors are inversely related, meaning when one happens, the other tends to not happen.

• If you smoke a cigarette (Yes), you're less likely to be healthy (No). If you don't smoke (No), you're more likely to be healthy (Yes).

Scalar Correlation (Variables)

Refers to a relationship between two variables that is measured on a continuous scale, like numbers or amounts. It describes how one variable changes in relation to another.

In simpler terms:

• A scalar refers to a quantity that has a size or value, but no direction (like a temperature of 30°C or a weight of 50 kg).

• Correlation describes how two things are related to each other.

A Negative Scalar Correlation (Variables)

Means that as one variable increases, the other variable tends to decrease. They move in opposite directions.

• The more time you spend exercising (increasing Variable 1), the lower your body fat percentage (decreasing Variable 2).

• As exercise increases, body fat decreases.

Causation

Making it the case that something happens. Something follows or results in another.

• Trying to figure out if one thing really causes another, or if they just happen to occur together. This is important because just because two things happen at the same time doesn’t mean one caused the other.

Sources of Misleading Correlations

• Reverse causation

• Common cause

• A side effect (e.g., placebo)

• Regression to the mean

• Mere chance