Question

When you go in for a cancer screening, they are not always correct. Sometimes you get screened for cancer and the initial results come back that you do not have cancer when actually you do have cancer (false negative), or maybe on your initial cancer screening you get tested positive for cancer but then actually you don’t have cancer (false positive).

You could display this as a hypothesis test and the false positive and false negative are a Type I error and a Type II error.

Null hypothesis (H0): The patient is cancer free.

The alternative hypothesis (H1): The patient has cancer.

Patient has Cancer

Patient does not have Cancer

Reject Null Hypothesis

Correct Conclusion

Type I Error: You conclude with sufficient evidence that the patient does have cancer, but in actuality the patient does not have cancer. (false positive)

Fail to Reject Null Hypothesis

Type II Error: You fail to conclude that the patient has cancer, but in actuality the patient does have cancer. (false negative)

Correct Conclusion

Both these errors could have impacts on the patient. If the patient is told they are cancer free, but they have cancer, then the cancer will have a chance to grow without being treated. If the patient is told they have cancer, but they are in fact cancer free, that is a lot of stress, and worry, and potential treatment like chemotherapy or radiation for nothing.

As you try to reduce one type of error, the other type of error becomes more likely. The costs and the risks have to be assessed, and this assessment of risk is analogous to the significance level.

For your discussion post, include the following:

Think of another example of a false positive and false negative scenario. A false negative is where something didn’t happen that should have happened, and a false positive describes something that happened that shouldn’t have happened. Choose a unique example that nobody else has posted yet. Write the null and alternative hypotheses for your scenario. Remember that H0 should be a statement of equality, status quo, nothing new or concerning happening.

Write the appropriate conclusion for your scenario assuming you get a p-value of 0.035 and use αα= 0.05. Include the decision about the null hypothesis and a conclusion about the claims, written in context.

Write the appropriate conclusion for your scenario assuming you get a p-value of 0.035 and use αα= 0.01. Include the decision about the null hypothesis and a conclusion about the claims, written in context.

Write the Type I and Type II errors for your scenario.

Answer 1

Scenario : A random sample of resisdents of an Indian city are interviewed and classified as male or female and also as drinkers or non-drinkers of tea. We want to know if these data reveals any association between sex and drinking of tea.

The null hypothesis : H₀ : Sex and drinking of tea are independent .

The alternative hypothesis : H₁ : Sex and drinking of tea are associated .

• [ Using α= 0.05 ]

Decision : For this scenario assuming we get a p-value of 0.035 , we should reject the null hypothesis at 5% level of significance since p-value is less than α=0.05 .

Conclusion : These data reveals a significant association between sex and drinking of tea.

• [ Using α= 0.01 ]

Decision : For this scenario assuming we get a p-value of 0.035 , we fail to reject the null hypothesis at 1% level of significance since p-value is greater than α=0.01 .

Conclusion : These data does not reveal any significant association between sex and drinking of tea.

Type I error : Concluding there is association between sex and drinking tea, when actually they are independent.

Type II error : Failing to conclude any association between them when they are actually related to each other.