Question

What is type 1 error vs type 2 error? What are the differences? How does this apply? Can you give examples? How do I apply this and what is worse? Sorry, just trying to understand the concept. Thank you!

Answer 1

All hypothesis testing is liable to errors. Basically, there are two kinds of errors.

1. Type 1 error
2. Type 2 error

Type 1 error

If we reject the null hypothesis when it is true. Then the error occured is type 1 error. Type 1 error is also called producer's risk.

The probability of type 1 error is called significance level and is denoted by . Then,

= P(type 1 error)

= P(rejecting H0 when it is true)

We can reduce the type 1 error by reducing the significance level. Because, say   =0.05, it indicates that when you are rejecting H0 there is a 5% chance that you are wrong.

Example: H0: Paracetamol is good for fever.

H1: Paracetamol is not good for fever.

We will make type 1 error when we conclude that paracetamol is not good for fever, but in fact, it is good for fever.

Type 2 error

If we accept the null hypothesis when it is false. Then the error occured is type 2 error. Or in other words, type 2 error is occured when we are accepting the null hypothesis given the alternative hypothesis is true. This is also called consumers risk.

= P(type 2 error)

= P(accepting H0 when H1 is true)

Power of the test= 1 -

We can reduce the type 2 error by ensuring the test has sufficient power. We can achieve this by ensuring that sample size is large enough to detect a practical difference when one actually exists.

We reduce type 2 error by increasing the sample size.

Example: H0: Mean gas pressure is 100.

H1: Mean gas pressure is greater than 100.

We will make type 2 error when we conclude that the mean gas pressure is 100, but in fact, greater than 100.

Type 2 error is more worse(severe) than type 1 error.