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Type 1 and Type 2 Errors

Type Ⅰ Error :-
- When the null hypothesis is true and you reject it, you make a type I error. The probability of making a type I error is α, which is the level of significance you set for your hypothesis test. 
- An α of 0.05 indicates that you are willing to accept a 5% chance that you are wrong when you reject the null hypothesis. 
- To lower this risk, you must use a lower value for α.
- However, using a lower value for alpha means that you will be less likely to detect a true difference if one really exists. 
Type Ⅱ Error :-
- When the null hypothesis is false and you fail to reject it, you make a type II error. 
- The probability of making a type II error is β, which depends on the power of the test. 
- You can decrease your risk of committing a type II error by ensuring your test has enough power. 
- You can do this by ensuring your sample size is large enough to detect a practical difference when one truly exists.

Rejecting and failing to reject the null hypothesis :-

Acceptance Matrix

Type Ⅰ and Type Ⅱ Errors

Prior to any data collection your type 1 error could be as high as alpha, and after analysis it is exactly equal to your p-value.

Type Ⅱ error is more complicated. Why?
  • It is a function of Delta
  • It is a function of Sample Size
  • It is a function of the Type Ⅰ error
  • A graph of beta versus delta for a given sample size (n) is known as an OC curve (Operational Characteristic)
  • The power of a test = 1 - beta

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