What is the cause of the error 1
Type 1 error, Type 2 error | Failure to test hypotheses
Any decision we make based on a hypothesis can be wrong. Most of the time the mistake is that we came to a premature conclusion or that we used incomplete information from our sample to make a general statement about the whole.
When testing hypotheses, there are two different types of mistakes we can make: the Error of the first kind (also α error) and the Error of the second kind (also β error).
|H0 accept||right decision||Type 2 error|
|H0 reject||Type 1 error||right decision|
- Type 1 error
H0 is rejected even if it is actually true
- Type 2 error
H0 is accepted even if in reality it is wrong
Type 1 and type 2 errors are often confused. But one can build a donkey's bridge: if one assumes that the null hypothesis is "person is innocent", a first type error would be "condemn an innocent person" and a second type would be "let a guilty person go". Another example below:
In a factory, one machine packs 250g of cheese at a time.
|H0: µ = 250g||(the machine works correctly)|
|H1: µ ≠ 250g||(the machine does not work correctly)|
where µ is the average weight of the packages.
Errors 1st and 2nd kind
Let us now consider what errors can occur in our hypotheses.
- At a Type 1 error, the null hypothesis (H0) rejected despite the fact that it is true. For our example this would mean that the machine would work correctly (hence µ = 250g), but we would find in our sample that the average weight is µ ≠ 250g.
- At the Type 2 error exactly the opposite happens: the machine does not work correctly, so it does not pack an average weight of 250g cheese, but our sample does not show this. According to her, the machine is working correctly.
Of course, we can also make the right decision based on our sample.
But what happens if our sample says that our null hypothesis is wrong - hence that µ ≠ 250g. How does this affect the error when the average weight is actually 250g and when it is not 250g?
- If µ = 250g, the null hypothesis is true. If we reject them, we commit a mistake of type I.
- If µ ≠ 250g, the null hypothesis is false. If we reject them, we will make the right decision.
Calculate the probability of an error type 1 and 2
If you want to know how good or bad a hypothesis is, you also have to know how high the probability is of making a wrong statement. A type I mistake happens when we reject a true null hypothesis. The probability of making a Type I mistake is called the significance level or Probability of error. It is abbreviated with the small Greek letter α and is usually 5% or 1%. In contrast to the 1st type error, the probability of the 2nd type error can usually not be calculated.
In general, the following applies: the smaller the probabilities for an error of the 1st and 2nd type, the better.
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