Type I and Type II Error
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Type I and Type II Error

Type I and II errors

     There are two kinds of errors that can be made in significance testing: (1) a true null hypothesis can be incorrectly rejected and (2) a false null hypothesis can fail to be rejected. The former error is called a Type I error and the latter error is called a Type II error. These two types of errors are defined in the table.
Statistical Decision True State of the Null Hypothesis H True H False Reject H Type I error Correct Do not Reject H Correct Type II error
 
     The probability of a Type I error is designated by the Greek letter alpha (α) and is called the Type I error rate; the probability of a Type II error (the Type II error rate) is designated by the Greek letter beta (ß) . A Type II error is only an error in the sense that an opportunity to reject the null hypothesis correctly was lost. It is not an error in the sense that an incorrect conclusion was drawn since no conclusion is drawn when the null hypothesis is not rejected. 

     A Type I error, on the other hand, is an error in every sense of the word. A conclusion is drawn that the null hypothesis is false when, in fact, it is true. Therefore, Type I errors are generally considered more serious than Type II errors. The probability of a Type I error (α) is called the significance level and is set by the experimenter. There is a tradeoff between Type I and Type II errors. The more an experimenter protects himself or herself against Type I errors by choosing a low level, the greater the chance of a Type II error. Requiring very strong evidence to reject the null hypothesis makes it very unlikely that a true null hypothesis will be rejected. However, it increases the chance that a false null hypothesis will not be rejected, thus lowering power. The Type I error rate is almost always set at .05 or at .01, the latter being more conservative since it requires stronger evidence to reject the null hypothesis at the .01 level then at the .05 level.
 
     A type I error occurs when one rejects the null hypothesis when it is true. The probability of a type I error is the level of significance of the test of hypothesis, and is denoted by *alpha*. Usually a one-tailed test hypothesis is is used when one talks about type I error. 

Examples:

     If the cholesterol level of healthy men is normally distributed with a mean of 180 and a standard deviation of 20, and men with cholesterol levels over 225 are diagnosed as not healthy, what is the probability of a type one error?  z=(225-180)/20=2.25; the corresponding tail area is .0122, which is the probability of a type I error.

     If the cholesterol level of healthy men is normally distributed with a mean of 180 and a standard deviation of 20, at what level (in excess of 180) should men be diagnosed as not healthy if you want the probability of a type one error to be 2%?  2% in the tail corresponds to a z-score of 2.05; 2.05 × 20 = 41; 180 + 41 = 221.
 
     A type II error occurs when one rejects the alternative hypothesis (fails to reject the null hypothesis) when the alternative hypothesis is true.

      The probability of a type II error is denoted by *beta*. One cannot evaluate the probability of a type II error when the alternative hypothesis is of the form µ > 180, but often the alternative hypothesis is a competing hypothesis of the form: the mean of the alternative population is 300 with a standard deviation of 30, in which case one can calculate the probability of a type II error. 

Examples:

      If men predisposed to heart disease have a mean cholesterol level of 300 with a standard deviation of 30, but only men with a cholesterol level over 225 are diagnosed as predisposed to heart disease, what is the probability of a type II error (the null hypothesis is that a person is not predisposed to heart disease).  z=(225-300)/30=-2.5 which corresponds to a tail area of .0062, which is the probability of a type II error (*beta*). 

      If men predisposed to heart disease have a mean cholesterol level of 300 with a standard deviation of 30, above what cholesterol level should you diagnose men as predisposed to heart disease if you want the probability of a type II error to be 1%? (The null hypothesis is that a person is not predisposed to heart disease.)  1% in the tail corresponds to a z-score of 2.33 (or -2.33); -2.33 × 30 = -70; 300 - 70 = 230.

6 Comments to Type I and Type II Error:

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kmn on Tuesday, November 14, 2017 10:52 PM
kmn
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кush my essay on Tuesday, November 21, 2017 12:53 AM
Type I and type II error, kinds of errors that can be made in significance testing null hypothesis is not rejected. More with this bhstats blog for experimenter protects himself or herself against thus lowering power.
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Your content is really good but you can add more flavor in it through good.Anyways good post.Keep it up and keep sharing more posts.
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top 9 assignment writing tools on Thursday, April 26, 2018 6:01 AM
Statistics is a good subject and helpful in different math problems. This blog is also helpful for me. Type I and II error are made significance testing null hypothesis is not rejected.
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Homekitchenary on Friday, May 04, 2018 9:36 AM
Well this error information is really interesting.It is quite relevant with my job.I am also a tester and I picked quite important points from this topic.Thanks for sharing.
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