The most important assumption in statistics- IID [Math Mondays]

Everything from basic 8th grade probability to complex Probabilistic Graphs rely on this assumption

Aug 01, 2022

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Happy Monday my amazing readers,

Today we will be covering one of the most important assumptions in all of Math. Statistical Analysis would not be possible without it. Even if you aren’t directly a mathematician/work in Data Analysis, it is crucial that you know this. There are a lot of misunderstandings about this concept. This can lead to terrible consequences since people can make faulty decisions based on flawed reasoning. For example, the notorious gambler’s fallacy can be avoided by understanding this concept. Most human biases in fact, can be improved/fixed by integrating this concept into your thoughts. So you don’t want to miss this. Don’t worry, we’ll keep things simple.

The IID assumption states that all the data samples taken from sampling/observations are IID. IID stands for Independently and Identically Distributed. What do these mean? And how can you spot these? Let’s cover that-

Key Highlights-

What is IID- A distribution is IID if the samples in it are Independently and Identically Distributed.
Independent Distribution- The result of one sample doesn’t influence another. Think of rolling the dice. One die roll doesn’t impact the other.
Identical Distribution- Two samples are from an identical distribution when their behavior across a large number of samples will be identical. Take 2 fair dice. If we rolled them both a 1000000 times and tracked the numbers they throw up, we would imagine that their results would be (close to) identical. Thus they come from identical distributions.
Why this matters- Many statistical sampling and inference techniques need to assume this to make deductions. The video below covers the IID assumption in Machine Learning
What people get wrong- People often make decisions because they incorrectly attribute IID traits to non-IID distributions. Or as is the case with Gambler’s Fallacy, vice versa. Both mistakes you want to avoid.
How to avoid this- Good news, this doesn’t require any fancy math. Any time you find yourself making an assumption about any probability distribution, take a step back and do a double take. You’ll be surprised, how many times our intuitive brains misattribute traits. A great book to learn more about this is the exceptional book, Thinking Fast and Slow.

To those of interested in more Mathy understanding of the subject, take a look at the following definitions

I got it from this excellent presentation. Check it out if you have aspirations of getting into Data Analysis/AI. It will help you a bunch.

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