Question

Type I and Type II errors were introduced recently. You will use the following real world situation of those type of errors along with the complements of each one of those, that is, a full 2 x 2 table showing the possible four outcomes.

OraQuick In-Home HIV Test is a product that was approved by the FDA on July 3, 2012. According to the FDA website, its indications are for use as an in-vitro diagnostic home-use test for HIV in oral fluid. The product works by looking for the antibodies for the HIV virus. The FDA Website and the labeling on the product warns that the results of the test are not definitive and that further testing is needed if a positive result is obtained. Thus, there is a risk of obtaining a false positive. You must post a paragraph-length comment on each outcome to receive all 15 points. Ho will be that the patient does not have HIV (test comes back negative). You will determine the appropriate Ha and lay out the 2x2 table accordingly.

Reference: http://www.fda.gov/BiologicsBloodVaccines/BloodBloodProducts/ApprovedProducts/PremarketApprovalsPMAs/ucm310436.htm

Alternatively, you can choose Ho to be Drug X will help with symptoms vs. Ha that Drug X does not help with symptoms.

Answer 1

CONFUSION MATRIX		actual values
		positive	negative
predicted values	positive	true positive (Power)	false positive (type I error)
	negative	false negative (type II error)	true negative

Now proceeding further with the same HIV example: Keep in mind you are somebody who are testing how this "Home HIV test " is , not somebody on which this test is getting performed. Now suppose you have performed the test and it comes out to be positive then as suggested you went for further testing. Suppose there also you got the result positive. That means this home test has given the correct result. That means the purpose for which this test has been made is achieved.  

so that's why probability of getting true positive result is called Power of the test.

Now suppose on further testing you got negative result. That means your product is not good because It is giving wrong result which can result into customer dissatisfaction. So getting false positive is error in every sense.and that's why this is called type l error and seen as a more dangerous error than type ll error.

Now suppose instead of getting positive result you got negative result , in the first stage itself (while testing with "Home HIV test") and suppose you went for further testing and there you got positive result . Here also your home HIV test has given wrong result so this is a error (called type II error) . But this doesn't became a huge issue as the patient for further testing.

Now suppose after getting negative result you went for further testing and there also you got the negative result. So that's a good result. So you are correctly able to find out whether a person is diseased or not.

lternative Hypothesis (Ha) - Hypothesis which states that there is statistical significance between the two variables in the hypothesis. It is a statement of “Difference”. It states that there is real effect and the observations are affected by the effect and some pure chance variations

Type I Error - is rejection of Null Hypothesis when it is true. In simpler words, Type I error occurs when we conclude that there is a statistical difference when there is actually no difference. This is also known as a false positive or producer's risk

Type II Error - is failing to reject a Null Hypothesis when it is false or rejection of Alternate Hypothesis when it is true. In simpler words, Type II error occurs when we conclude that there is no difference when there is actually a statistical difference. This is also known as false negative or consumer's risk