Errors in Hypothesis Tests

[abhishreshthaa]

Errors in Hypothesis Tests

• We define a type I error as the event of rejecting the null hypothesis when the null hypothesis was true. *The probability of a type I error *(a) is called the significance level.
  
  
• We define a type II error (with probability b) as the event of failing to reject the null hypothesis when the null hypothesis was false.

Type of Errors

When a statistical hypothesis is tested there are four possibilities.

• The hypothesis is true but our test rejects it. ( Type 1 error )
  
  
• The hypothesis is false but our test accepts it. ( Type 2 error )
  
  
• The hypothesis is true and our test accepts it . ( correct decision )
  
  
• The hypothesis is false and our test rejects it (correct Decision )

The first two possibilities lead to errors



Type I Error

• In a hypothesis test, a type I error occurs when the null hypothesis is rejected when it is in fact true; that is, H0 is wrongly rejected.
  
• For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average, than the current drug; that is H0: there is no difference between the two drugs on average.
  
  
• A type I error would occur if we concluded that the two drugs produced different effects when in fact there was no difference between them.

Type II Error

• In a hypothesis test, a type II error occurs when the null hypothesis H0, is not rejected when it is in fact false. For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average, than the current drug; that is H0: there is no difference between the two drugs on average.
  
  
• A type II error would occur if it was concluded that the two drugs produced the same effect, that is, there is no difference between the two drugs on average, when in fact they produced different ones.
  
  
• A type II error is frequently due to sample sizes being too small.

 

[jamescord]

Errors in Hypothesis Tests

• We define a type I error as the event of rejecting the null hypothesis when the null hypothesis was true. *The probability of a type I error *(a) is called the significance level.
  
  
• We define a type II error (with probability b) as the event of failing to reject the null hypothesis when the null hypothesis was false.

Type of Errors

When a statistical hypothesis is tested there are four possibilities.

• The hypothesis is true but our test rejects it. ( Type 1 error )
  
  
• The hypothesis is false but our test accepts it. ( Type 2 error )
  
  
• The hypothesis is true and our test accepts it . ( correct decision )
  
  
• The hypothesis is false and our test rejects it (correct Decision )

The first two possibilities lead to errors



Type I Error

• In a hypothesis test, a type I error occurs when the null hypothesis is rejected when it is in fact true; that is, H0 is wrongly rejected.
  
• For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average, than the current drug; that is H0: there is no difference between the two drugs on average.
  
  
• A type I error would occur if we concluded that the two drugs produced different effects when in fact there was no difference between them.

Type II Error

• In a hypothesis test, a type II error occurs when the null hypothesis H0, is not rejected when it is in fact false. For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average, than the current drug; that is H0: there is no difference between the two drugs on average.
  
  
• A type II error would occur if it was concluded that the two drugs produced the same effect, that is, there is no difference between the two drugs on average, when in fact they produced different ones.
  
  
• A type II error is frequently due to sample sizes being too small.

Hi there,

here i am sharing Introduction to Hypothesis Testing, please check attachment below.