Module 2.3 Lecture Notes - Simpson's Paradox, Percent Change

Example of Simpson's Paradox

when you calculate the probabilities of the information provided on the picture, you'll essentially find that the probability of death via helicopter is higher than that of ambulance. However, if you separate by a third variable which is severe/not severe injury, you'll find that it flips and the probability is significantly lower via helicopter than in ambulance. This is referred to as Simpson's Paradox. an argument can be made that, dependent upon the situation, incorporating the third variable might not be logical and/or fair, and therefore might not want to do it. In this scenario, it's important that you introduce the concept of severe/not sever into the equation to account for the probabilities/outcome

Recognizing Percent Change

examples of percent change in the world: - bike accidents have decreased by 10% on campus - sales have increased by 5% this year note that when we say thing 1 is 30% higher than thing 2, we consider thing 1 to be the new and thing 2 to be the old within the formula

Percent Change v. Change in Percentage Points

- if you are measuring something that is already in percentages it is usually easier to just talk about percentage points, where a percentage point is 1% - for example, if your grade in this class increases from an 80% to a 85% you should say it increased by 5 percentage points. The percent change is 6.25% but this would be confusing to tell people and you might mislead them - watch out for language about percent change and percentage point change when talking about things that are already measured in percentages

What to do regarding Simpson's Paradox

always be aware of possible confounding variables - sometimes the confounding variables will be in your data and you'll be able to take a deeper look right away - sometimes the confounding variable is impossible to measure - no matter what, remind yourself that it exists then think critically - is it better to split up the data into smaller groups based on this other variable or do I want a generalization? - this will depend on your situation

Percent Change

one way of comparing two values (an old and a new) or compare two groups formula for percent change: percent change = new - old / old x 100 unlike probability, percent change can be negative indicating a value decrease, and can be greater than 100%

Simpson's Paradox

sometimes when we break data apart by a confounding variable, we might see that a particular relationship might change - which is called (sometimes) Simpson's Paradox a paradox is a seemingly absurd or self-contradictory statement or proposition that when investigated or explained might prove to be well founded or true