1.5 Cause and Effect

Consider the following

• Drivers of red cars are twice as likely to be involved in an accident as drivers of blue cars.

• Does this imply that driving a red car “causes” drivers to have an accident?

• What is going on?

“Averages and relationships and trends and graphs – there may be more in them than meets the eye, and there may be a good deal less.”

Darryl Huff, How to Lie With Statistics

Causation

• Correlation does not imply causation

• Aggressive drivers tend to choose red cars, and also tend to get into more accidents

• There are different kinds of relationships between variables– Causal– Common-cause– Accidental

Causal or cause-and-effect relationship

• a change in A is necessary and sufficient for a change in B.

– necessary: if A doesn't happen, B doesn't happen (that is, if B has happened, A must have happened)

• e.g. being able to breathe is necessary to being able to survive

– sufficient: if A happens, then B follows• e.g. jumping is a sufficient condition for leaving the ground (if

you jump, you leave the ground)• e.g. being a mammal is necessary but not sufficient to being

human (cats are also mammals)

Causal or cause-and-effect relationship

• a change in A is necessary and sufficient for a change in B.

• Examples:– Number of tree rings and diameter of tree– hours of sleep and amount of energy the next

day– Amount of understanding of subject and final

mark

Common-cause Relationship

• both A and B change in common to some third, unseen variable

• Sometimes referred to as a "lurking" variable– Drivers of red cars and accidents

• Common variable is– Positive correlation between ice cream sales and

number of hurricanes as year goes on– Should we stop buying ice cream to reduce the

number of hurricanes?• Common variable is

aggression

temperature

Accidental Relationship

• the effects of X and Y are unrelated to each other

• their correlation is accidental– Positive correlation between consumer price

index and number of known planets in the universe

– Salaries of Presbyterian ministers in Massachusetts and the price of rum in Havana

Warning #1

• If there is a causal relationship, which is cause and which is effect?

• Do you look good because you feel better about yourself, or do you feel better about yourself because you look good?

• Sometimes, it can be both!

Warning #2

• It is often very difficult to determine whether a relationship is causal, common-cause, or accidental

• There is a positive correlation between going to university and salary

• Does it necessarily follow that to get a good salary, you need to go to university?

• Observational studies can give hints, but can never establish cause and effect

• Best way to tell causal relationship is randomized experiment

• Unethical in some cases

• Limitation of experiments:– good for testing presence of causal effect– bad for estimating size of that effect in

population of interest

• For observational studies, inclusion of time can help indicate causal relationship

• Usually, cause comes before the effect

• Are we more confident in results of longitudinal or cross-sectional medical studies?

1. A higher number of ice cream sales corresponds to a higher number of shark attacks on swimmers

Common-causeTemperature (the hotter it is, the more ice cream we eat and the more likely we are to go swimming & be attacked by sharks!)

2. The number of cavities in elementary school children and vocabulary size have a strong positive correlation

Common-causeAge (the older you get, the more cavities you’re likely to have and the more words you know)

3. In a growing municipality, the traffic planner (who never completed Data Management class) observed that over a period of ten years the number of traffic accidents showed a high positive correlation with the number of traffic lights installed.

Common-cause (# of vehicles on the road)

4. There is a strong positive correlation between the number of fire engines responding to a fire and the damage caused by the fire.

Common-cause

On to the handout!