Question

7.  Is it Type I and II error? Explain why??

a.  Many medical studies have a high error rate because they are not able to use large sample for Medical diagnostic procedure such as Mammogram.

b. When a radiologist interprets a mammogram, is a “false positive” predicting that a woman has a breast cancer when actually she does not!

c.

c. Remdesivir Drug &  Clincial trials - Dr. Fauci Infectious specialist claims at p =0.31 could shorten the time to recover from the Coronavirus infection.

d.  Observations studies have shown, two - meter Social distancing is the best Non Pharmaceutical Medicine to prevent the spread the Corona.

Answer 1

7.

Type I error - This type of error occurs when we reject a true null hypothesis.

Type II error - This type of error occurs when we accept a false null hypothesis.

a.

As the sample size used in medical studies for medical diagnostic procedure such as a Mammogram is small, the study has Type - II error. Due to a small sample size, the test is less sensitive to rejecting a null hypothesis that is ,in fact, false. So, the results that are significant might be considered as insignificant.

b.

It is a Type - I error as the prediction that the women has breast cancer (Alternative Hypothesis) is false and the radiologist interprets it as true. As the radiologist rejected a 'true negative' (Null hypothesis that she doesn't have breast cancer) and accepted a 'false positive' (Alternative hypothesis that she has breast cancer), we can say that it is a type I error.

c.

p = 0.31, this means that Dr. Fauci is 31% not confident that the drug shortens the time to recover i.e. only 69% confident that the Remdesivir drug shortens the time to recover from the Corona virus infection. As the result has a very high p-value (0.31), accepting his claim would require us to have a very high significance level (of 31% or more, ) to consider a 'negative'(The drug does not shorten the time to recover) as 'false'. Since, the 'positive' (The drug shortens the time to recover) can be considered 'true' with only 69% confidence, whereas for the 'negative' (the drug does not shorten time the time to recover) to be 'false' a comparable minimum significant level of 31% is required (that is very high compared to standard significance level of 5%). A result that is 'true' to be 'negative', unless we consider a very high significance level of 31% or more, is to be considered 'false'. This study has Type - I error.

Do comment for any doubts.