As an example of Type 1 and Type 2 errors, let\'s say a person is on trial and o

Question

As an example of Type 1 and Type 2 errors, let's say a person is on trial and only they know they are guilty or not guilty (see the table below).

We'll let Ho=person guilty. Ha must be opposite of Ho, so Ha=person not guilty. Let's say the person is really guilty. Both sides present evidence and then the jury decides based on the evidence presented. If the jury fails to reject Ho, they come to the correct conclusion that the person is guilty. If the jury, on the other hand, rejects Ho and concludes the person is not guilty, the jury frees a guilty person and a Type 1 error results. Type 1 errors occur when we reject Ho when we should not. Now let's assume the person is really not guilty (Ha is true), and the jury rejects Ho and comes to the correct conclusion that the person is innocent. But what if the jury does not reject Ho and finds the person guilty, where an innocent person is convicted. This is an example of Type 2 error, where Ho is not rejected when it should be.

Statistically speaking, we are generally agnostic to which is a bigger problem, type I ( (false positive) errors or type II (false negative) errors. However, in certain circumstances it may be important to try and put more emphasis on avoiding one or the other. Can you think of an example of where you may want to try harder to avoid one type or another? Can you think of a political, social, economic, etc. policy that pushes people toward avoiding one type or another? What are the repercussions of such policies?

Ho True Ha True Do Not Reject Ho Correct Conclusion Incorrect Conclusion Type 2 Error Reject Ho Incorrect Conclusion Type 1 Error Correct Conclusion

Explanation / Answer

Consider a classical example of maggie being banned in a country ( It happened in India in 2015).

H0 = The present maggie has no higher content of lead than prescribed amount

Ha = The present maggie has higher content of lead than prescribed amount

Now the decision with maggie whether to ban or not lies with FDA

Here in most of the tests conducted by FDA for different samples proves that Ha is true

But the company tried to influence the FDA and succumb to make a type I error. i.e Accept H0 even though Ha is true, i.e maggie can be produced even though it has higher lead material.

Now, FDA finally decided to implement Ha and ban the maggie in whole country.

But the problem is samples are colloected from only few areas of the country. Later it was recognised that most of the other places, H0 is true.

But the FDA rule made type II error in most of the places.

Now, FDA has to decide which type of error it has to make inorder to avoid one other. Only thing that can FDA to say is the accpetance or rejectance of FDA affects the whole country.

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If you are interested to know about why maggie is banned in the nation, please refer internet sources. (2015)

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