Measuring Hypothesis Test

[abhishreshthaa]

Measuring the power of a Hypothesis Test

• The measure of how well the test is working is called the power of the test.
  
  
• Type I error occurs when we reject Ho which is true and a (the significance level of the test) is the probability of making type - I error.
  
  
• Once the significance level is fixed, nothing can be done about a.
  
  
• Type II error occurs when we accept Ho which is false.
  
  
• The probability of type II error is b. The smaller the value of b, the better is the test. Alternately ( 1 - b ) i.e. the probability of rejecting Ho when it is false should be as large as possible.
  
  
• Thus (1 - b ) is the measure of the power of the test. If we plot the values of ( 1 - b ) for each value of m f2 for which Ha is true, the resulting curve is known as a power curve.
  
  
• You can see from the figure given below that the power is simply ( 1 - b ). In testing of a hypothesis high power is desirable.

 

[jamescord]

Measuring the power of a Hypothesis Test

• The measure of how well the test is working is called the power of the test.
  
  
• Type I error occurs when we reject Ho which is true and a (the significance level of the test) is the probability of making type - I error.
  
  
• Once the significance level is fixed, nothing can be done about a.
  
  
• Type II error occurs when we accept Ho which is false.
  
  
• The probability of type II error is b. The smaller the value of b, the better is the test. Alternately ( 1 - b ) i.e. the probability of rejecting Ho when it is false should be as large as possible.
  
  
• Thus (1 - b ) is the measure of the power of the test. If we plot the values of ( 1 - b ) for each value of m f2 for which Ha is true, the resulting curve is known as a power curve.
  
  
• You can see from the figure given below that the power is simply ( 1 - b ). In testing of a hypothesis high power is desirable.

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